what is statistical analysis in quantitative research

• Skip to secondary menu
• Skip to main content
• Skip to primary sidebar

Statistics By Jim

Making statistics intuitive

Statistical Analysis Overview

By Jim Frost Leave a Comment

What is Statistical Analysis?

Statistical analysis involves assessing quantitative data to identify data characteristics, trends, and relationships. Scrolling through the raw values in a dataset provides virtually no useful information. Statistical analysis takes the raw data and provides insights into what the data mean. This process can improve understanding of the subject area by testing hypotheses, producing actionable results leading to improved outcomes, and making predictions, amongst many others.

The field of statistics is the science of learning from data, and it studies that process from beginning to end to understand how to produce trustworthy results. While statistical analysis provides tremendous benefits, obtaining valid results requires proper methods for collecting your sample , taking measurements, designing experiments, and using appropriate analytical techniques. Consequently, data analysts must carefully plan and understand the entire process, from data collection to statistical analysis. Alternatively, if someone else collected the data, the analyst must understand that context to interpret their results correctly.

If you’re good with numbers and enjoy working with data, statistical analysis could be the perfect career path for you. As big data, machine learning, and technology grow, the demand for skilled statistical analysts is rising. It’s a great time to build these skills and find a job that fits your interests.

Some of the fastest-growing career paths use statistical analysis, such as statisticians , data analysts, and data engineers. In this post, you’ll learn the different types of statistical analysis, their benefits, and the key steps.

Types of Statistical Analysis

Given the broad range of uses for statistical analysis, there are several broad categories. These include descriptive, inferential, experimental, and predictive statistics. While the goals of these approaches differ, they all aim to take the raw data and turn them into meaningful information that helps you understand the subject area and make decisions.

Choosing the correct approach to bring the data to life is an essential part of the craft of statistical analysis. For all the following types of statistical analyses, you’ll use statistical reports, graphs, and tables to explain the results to others.

Descriptive

Descriptive statistical analysis describes a sample of data using various summary statistics such as measures of central tendency , variability , relative standing , and correlation . These results apply only to the items or people that the researchers measure and not to a broader population . Additionally, correlations do not necessarily imply causation.

For example, you can report the mean test score and the correlation between hours of studying and test scores for a specific class. These results apply only to this class and no one else. Do not assume the correlation implies causation.

Inferential

Inferential statistical analysis goes a step further and uses a representative sample to estimate the properties of an entire population. A sample is a subset of the population. Usually, populations are so large that it’s impossible to measure everyone in a population.

For example, if you draw a simple random sample of students and administer a test, statistical analysis of the data allows you to estimate the properties of the population. Statistical analysis in the form of hypothesis testing can determine whether the effects and correlations you observe in the sample also exist in the population.

Suppose the hypothesis test results for the correlation between hours studying and test score is statistically significant . In that case, you can conclude that the correlation you see in the sample also exists in the larger population. Despite being statistically significant, the correlation still does not imply causation because the researchers did not use an experimental design.

The sample correlation estimates the population correlation. However, because you didn’t measure everyone in the population, you must account for sampling error by applying a margin of error around the sample estimate using a confidence interval .

Learn more about the Differences between Descriptive and Inferential Statistical Analysis .

Designed Experiments

Statistical analysis of experimental designs strives to identify causal relationships between variables rather than mere correlation. Observing a correlation in inferential statistics does not suggest a causal relationship exists. You must design an experiment to evaluate causality. Typically, this process involves randomly assigning subjects to treatment and control groups.

Does increasing study hours cause test scores to improve or not? Without a designed experiment, you can’t rule out the possibility that a confounding variable and not studying caused the test scores to improve.

Suppose you randomly assign students to high and low study-time experimental groups. The statistical analysis indicates the longer-duration study group has a higher mean score than the shorter-duration group. The difference is statistically significant. These results provide evidence that study time causes changes in the test scores.

Learn more about Correlation vs. Causation and Experimental Design: Definition and Types .

Predictive statistical analysis doesn’t necessarily strive to understand why and how one variable affects another. Instead, it predicts outcomes as precisely as possible. These analyses can use causal or non-causal correlations to predict outcomes.

For example, assume that the number of ice cream cones consumed predicts the number of shark attacks in a beach town. The correlation is not causal because ice cream cone consumption doesn’t cause shark attacks. However, the number of cones sold reflects favorable weather conditions and the number of beachgoers. Those variables do cause changes in the number of shark attacks. If the number of cones is easier to measure and predicts shark attacks better than other measures, it’s a good predictive model.

Three Key Steps in Statistical Analysis

Producing trustworthy statistical analysis requires following several key steps. Each phase plays a vital role in ensuring that the data collected is accurate, the methods are sound, and the results are reliable. From careful planning to adequate sampling and insightful data analysis, these steps help researchers and businesses make informed, data-driven decisions. Below, I outline the major steps involved in conducting solid statistical analysis.

The planning step is essential for creating well-structured experiments and studies that effectively set up the statistical analysis from the start. Whether working in a lab, conducting fieldwork, or designing surveys, this stage ensures that the research design gathers data that statistical analysis can use to answer the research question effectively. Researchers can make informed decisions about variables, sample sizes, and sampling methods by analyzing data patterns and previous statistical analyses. Using the proper sampling techniques allows researchers to work with a manageable portion of the population while maintaining accuracy.

This careful preparation reduces errors and saves resources, leading to more reliable results. Optimizing research strategies during the planning phase allows scientists and businesses to focus on the most relevant aspects of their investigations, which results in more precise findings. Researchers design the best studies when they keep the statistical analysis in mind.

Learn more about Planning Sample Sizes and Sampling Methods: Different Types in Research .

Data Collection

After all the planning, the next step is to go out and execute the plan. This process involves collecting the sample and taking the measurements. It might also require implementing the treatment under controlled conditions if it’s an experiment.

For studies that use data collected by others, the researchers must acquire, prepare, and clean the data before performing the statistical analysis. In this context, a crucial part of sound statistical analysis is understanding how the data were gathered. Analysts must review the methods used in data collection to identify potential sampling biases or errors that could affect the results. Sampling techniques, data sources, and collection conditions can all introduce variability or skew the data. Without this awareness, an analyst risks drawing flawed conclusions.

Analysts can adjust their approach and account for any limitations by carefully examining how the data was collected, ensuring their statistical analysis remains accurate and trustworthy.

Statistical Analysis

After data collection, the statistical analysis step transforms raw data into meaningful insights that can inform real-world decisions. Ideally, the preceding steps have all set the stage for this analysis.

Successful research plans and their effective execution allow statistical analysis to produce clear, understandable results, making it easy to identify trends, draw conclusions, and forecast outcomes. These insights not only clarify current conditions but also help anticipate future developments. Statistical analysis drives business strategies and scientific advancements by converting data into actionable information.

Learn more about Hypothesis Testing and Regression Analysis .

Share this:

Reader Interactions

Comments and questions cancel reply.

What Is Statistical Analysis?

Statistical analysis helps you pull meaningful insights from data. The process involves working with data and deducing numbers to tell quantitative stories.

Statistical analysis is a technique we use to find patterns in data and make inferences about those patterns to describe variability in the results of a data set or an experiment. 

In its simplest form, statistical analysis answers questions about:

• Quantification — how big/small/tall/wide is it?
• Variability — growth, increase, decline
• The confidence level of these variabilities

What Are the 2 Types of Statistical Analysis?

• Descriptive Statistics:  Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 
• Inferential Statistics:  Inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests.

What’s the Purpose of Statistical Analysis?

Using statistical analysis, you can determine trends in the data by calculating your data set’s mean or median. You can also analyze the variation between different data points from the mean to get the standard deviation . Furthermore, to test the validity of your statistical analysis conclusions, you can use hypothesis testing techniques, like P-value, to determine the likelihood that the observed variability could have occurred by chance.

More From Abdishakur Hassan The 7 Best Thematic Map Types for Geospatial Data

Statistical Analysis Methods

There are two major types of statistical data analysis: descriptive and inferential. 

Descriptive Statistical Analysis

Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 

Within the descriptive analysis branch, there are two main types: measures of central tendency (i.e. mean, median and mode) and measures of dispersion or variation (i.e. variance , standard deviation and range). 

For example, you can calculate the average exam results in a class using central tendency or, in particular, the mean. In that case, you’d sum all student results and divide by the number of tests. You can also calculate the data set’s spread by calculating the variance. To calculate the variance, subtract each exam result in the data set from the mean, square the answer, add everything together and divide by the number of tests.

Inferential Statistics

On the other hand, inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests. 

There are two main types of inferential statistical analysis: hypothesis testing and regression analysis. We use hypothesis testing to test and validate assumptions in order to draw conclusions about a population from the sample data. Popular tests include Z-test, F-Test, ANOVA test and confidence intervals . On the other hand, regression analysis primarily estimates the relationship between a dependent variable and one or more independent variables. There are numerous types of regression analysis but the most popular ones include linear and logistic regression .  

Statistical Analysis Steps  

In the era of big data and data science, there is a rising demand for a more problem-driven approach. As a result, we must approach statistical analysis holistically. We may divide the entire process into five different and significant stages by using the well-known PPDAC model of statistics: Problem, Plan, Data, Analysis and Conclusion.

In the first stage, you define the problem you want to tackle and explore questions about the problem. 

2. Plan

Next is the planning phase. You can check whether data is available or if you need to collect data for your problem. You also determine what to measure and how to measure it. 

The third stage involves data collection, understanding the data and checking its quality. 

4. Analysis

Statistical data analysis is the fourth stage. Here you process and explore the data with the help of tables, graphs and other data visualizations.  You also develop and scrutinize your hypothesis in this stage of analysis. 

5. Conclusion

The final step involves interpretations and conclusions from your analysis. It also covers generating new ideas for the next iteration. Thus, statistical analysis is not a one-time event but an iterative process.

Statistical Analysis Uses

Statistical analysis is useful for research and decision making because it allows us to understand the world around us and draw conclusions by testing our assumptions. Statistical analysis is important for various applications, including:

• Statistical quality control and analysis in product development 
• Clinical trials
• Customer satisfaction surveys and customer experience research 
• Marketing operations management
• Process improvement and optimization
• Training needs 

More on Statistical Analysis From Built In Experts Intro to Descriptive Statistics for Machine Learning

Benefits of Statistical Analysis

Here are some of the reasons why statistical analysis is widespread in many applications and why it’s necessary:

Understand Data

Statistical analysis gives you a better understanding of the data and what they mean. These types of analyses provide information that would otherwise be difficult to obtain by merely looking at the numbers without considering their relationship.

Find Causal Relationships

Statistical analysis can help you investigate causation or establish the precise meaning of an experiment, like when you’re looking for a relationship between two variables.

Make Data-Informed Decisions

Businesses are constantly looking to find ways to improve their services and products . Statistical analysis allows you to make data-informed decisions about your business or future actions by helping you identify trends in your data, whether positive or negative. 

Determine Probability

Statistical analysis is an approach to understanding how the probability of certain events affects the outcome of an experiment. It helps scientists and engineers decide how much confidence they can have in the results of their research, how to interpret their data and what questions they can feasibly answer.

You’ve Got Questions. Our Experts Have Answers. Confidence Intervals, Explained!

What Are the Risks of Statistical Analysis?

Statistical analysis can be valuable and effective, but it’s an imperfect approach. Even if the analyst or researcher performs a thorough statistical analysis, there may still be known or unknown problems that can affect the results. Therefore, statistical analysis is not a one-size-fits-all process. If you want to get good results, you need to know what you’re doing. It can take a lot of time to figure out which type of statistical analysis will work best for your situation .

Thus, you should remember that our conclusions drawn from statistical analysis don’t always guarantee correct results. This can be dangerous when making business decisions. In marketing , for example, we may come to the wrong conclusion about a product . Therefore, the conclusions we draw from statistical data analysis are often approximated; testing for all factors affecting an observation is impossible.

Recent Big Data Articles

Quantitative Data Analysis: A Comprehensive Guide

By: Ofem Eteng | Published: May 18, 2022

Related Articles

A healthcare giant successfully introduces the most effective drug dosage through rigorous statistical modeling, saving countless lives. A marketing team predicts consumer trends with uncanny accuracy, tailoring campaigns for maximum impact.

Table of Contents

These trends and dosages are not just any numbers but are a result of meticulous quantitative data analysis. Quantitative data analysis offers a robust framework for understanding complex phenomena, evaluating hypotheses, and predicting future outcomes.

In this blog, we’ll walk through the concept of quantitative data analysis, the steps required, its advantages, and the methods and techniques that are used in this analysis. Read on!

What is Quantitative Data Analysis?

Quantitative data analysis is a systematic process of examining, interpreting, and drawing meaningful conclusions from numerical data. It involves the application of statistical methods, mathematical models, and computational techniques to understand patterns, relationships, and trends within datasets.

Quantitative data analysis methods typically work with algorithms, mathematical analysis tools, and software to gain insights from the data, answering questions such as how many, how often, and how much. Data for quantitative data analysis is usually collected from close-ended surveys, questionnaires, polls, etc. The data can also be obtained from sales figures, email click-through rates, number of website visitors, and percentage revenue increase. 

Ditch the manual process of writing long commands to migrate your data and choose Hevo’s no-code platform to streamline your migration process to get analysis-ready data .

• Transform your data for analysis with features like drag and drop and custom Python scripts.
• 150+ connectors , including 60+ free sources.
• Eliminate the need for manual schema mapping with the auto-mapping feature.

Try Hevo and discover how companies like EdApp have chosen Hevo over tools like Stitch to “build faster and more granular in-app reporting for their customers.”

Quantitative Data Analysis vs Qualitative Data Analysis

When we talk about data, we directly think about the pattern, the relationship, and the connection between the datasets – analyzing the data in short. Therefore when it comes to data analysis, there are broadly two types – Quantitative Data Analysis and Qualitative Data Analysis.

Quantitative data analysis revolves around numerical data and statistics, which are suitable for functions that can be counted or measured. In contrast, qualitative data analysis includes description and subjective information – for things that can be observed but not measured.

Let us differentiate between Quantitative Data Analysis and Quantitative Data Analysis for a better understanding.

Data Preparation Steps for Quantitative Data Analysis

Quantitative data has to be gathered and cleaned before proceeding to the stage of analyzing it. Below are the steps to prepare a data before quantitative research analysis:

• Step 1: Data Collection

Before beginning the analysis process, you need data. Data can be collected through rigorous quantitative research, which includes methods such as interviews, focus groups, surveys, and questionnaires.

• Step 2: Data Cleaning

Once the data is collected, begin the data cleaning process by scanning through the entire data for duplicates, errors, and omissions. Keep a close eye for outliers (data points that are significantly different from the majority of the dataset) because they can skew your analysis results if they are not removed.

This data-cleaning process ensures data accuracy, consistency and relevancy before analysis.

• Step 3: Data Analysis and Interpretation

Now that you have collected and cleaned your data, it is now time to carry out the quantitative analysis. There are two methods of quantitative data analysis, which we will discuss in the next section.

However, if you have data from multiple sources, collecting and cleaning it can be a cumbersome task. This is where Hevo Data steps in. With Hevo, extracting, transforming, and loading data from source to destination becomes a seamless task, eliminating the need for manual coding. This not only saves valuable time but also enhances the overall efficiency of data analysis and visualization, empowering users to derive insights quickly and with precision

Now that you are familiar with what quantitative data analysis is and how to prepare your data for analysis, the focus will shift to the purpose of this article, which is to describe the methods and techniques of quantitative data analysis.

Methods and Techniques of Quantitative Data Analysis

Quantitative data analysis employs two techniques to extract meaningful insights from datasets, broadly. The first method is descriptive statistics, which summarizes and portrays essential features of a dataset, such as mean, median, and standard deviation.

Inferential statistics, the second method, extrapolates insights and predictions from a sample dataset to make broader inferences about an entire population, such as hypothesis testing and regression analysis.

An in-depth explanation of both the methods is provided below:

• Descriptive Statistics
• Inferential Statistics

1) Descriptive Statistics

Descriptive statistics as the name implies is used to describe a dataset. It helps understand the details of your data by summarizing it and finding patterns from the specific data sample. They provide absolute numbers obtained from a sample but do not necessarily explain the rationale behind the numbers and are mostly used for analyzing single variables. The methods used in descriptive statistics include: 

• Mean:   This calculates the numerical average of a set of values.
• Median: This is used to get the midpoint of a set of values when the numbers are arranged in numerical order.
• Mode: This is used to find the most commonly occurring value in a dataset.
• Percentage: This is used to express how a value or group of respondents within the data relates to a larger group of respondents.
• Frequency: This indicates the number of times a value is found.
• Range: This shows the highest and lowest values in a dataset.
• Standard Deviation: This is used to indicate how dispersed a range of numbers is, meaning, it shows how close all the numbers are to the mean.
• Skewness: It indicates how symmetrical a range of numbers is, showing if they cluster into a smooth bell curve shape in the middle of the graph or if they skew towards the left or right.

2) Inferential Statistics

In quantitative analysis, the expectation is to turn raw numbers into meaningful insight using numerical values, and descriptive statistics is all about explaining details of a specific dataset using numbers, but it does not explain the motives behind the numbers; hence, a need for further analysis using inferential statistics.

Inferential statistics aim to make predictions or highlight possible outcomes from the analyzed data obtained from descriptive statistics. They are used to generalize results and make predictions between groups, show relationships that exist between multiple variables, and are used for hypothesis testing that predicts changes or differences.

There are various statistical analysis methods used within inferential statistics; a few are discussed below.

• Cross Tabulations: Cross tabulation or crosstab is used to show the relationship that exists between two variables and is often used to compare results by demographic groups. It uses a basic tabular form to draw inferences between different data sets and contains data that is mutually exclusive or has some connection with each other. Crosstabs help understand the nuances of a dataset and factors that may influence a data point.
• Regression Analysis: Regression analysis estimates the relationship between a set of variables. It shows the correlation between a dependent variable (the variable or outcome you want to measure or predict) and any number of independent variables (factors that may impact the dependent variable). Therefore, the purpose of the regression analysis is to estimate how one or more variables might affect a dependent variable to identify trends and patterns to make predictions and forecast possible future trends. There are many types of regression analysis, and the model you choose will be determined by the type of data you have for the dependent variable. The types of regression analysis include linear regression, non-linear regression, binary logistic regression, etc.
• Monte Carlo Simulation: Monte Carlo simulation, also known as the Monte Carlo method, is a computerized technique of generating models of possible outcomes and showing their probability distributions. It considers a range of possible outcomes and then tries to calculate how likely each outcome will occur. Data analysts use it to perform advanced risk analyses to help forecast future events and make decisions accordingly.
• Analysis of Variance (ANOVA): This is used to test the extent to which two or more groups differ from each other. It compares the mean of various groups and allows the analysis of multiple groups.
• Factor Analysis:   A large number of variables can be reduced into a smaller number of factors using the factor analysis technique. It works on the principle that multiple separate observable variables correlate with each other because they are all associated with an underlying construct. It helps in reducing large datasets into smaller, more manageable samples.
• Cohort Analysis: Cohort analysis can be defined as a subset of behavioral analytics that operates from data taken from a given dataset. Rather than looking at all users as one unit, cohort analysis breaks down data into related groups for analysis, where these groups or cohorts usually have common characteristics or similarities within a defined period.
• MaxDiff Analysis: This is a quantitative data analysis method that is used to gauge customers’ preferences for purchase and what parameters rank higher than the others in the process. 
• Cluster Analysis: Cluster analysis is a technique used to identify structures within a dataset. Cluster analysis aims to be able to sort different data points into groups that are internally similar and externally different; that is, data points within a cluster will look like each other and different from data points in other clusters.
• Time Series Analysis: This is a statistical analytic technique used to identify trends and cycles over time. It is simply the measurement of the same variables at different times, like weekly and monthly email sign-ups, to uncover trends, seasonality, and cyclic patterns. By doing this, the data analyst can forecast how variables of interest may fluctuate in the future. 
• SWOT analysis: This is a quantitative data analysis method that assigns numerical values to indicate strengths, weaknesses, opportunities, and threats of an organization, product, or service to show a clearer picture of competition to foster better business strategies

How to Choose the Right Method for your Analysis?

Choosing between Descriptive Statistics or Inferential Statistics can be often confusing. You should consider the following factors before choosing the right method for your quantitative data analysis:

1. Type of Data

The first consideration in data analysis is understanding the type of data you have. Different statistical methods have specific requirements based on these data types, and using the wrong method can render results meaningless. The choice of statistical method should align with the nature and distribution of your data to ensure meaningful and accurate analysis.

2. Your Research Questions

When deciding on statistical methods, it’s crucial to align them with your specific research questions and hypotheses. The nature of your questions will influence whether descriptive statistics alone, which reveal sample attributes, are sufficient or if you need both descriptive and inferential statistics to understand group differences or relationships between variables and make population inferences.

Pros and Cons of Quantitative Data Analysis

1. Objectivity and Generalizability:

• Quantitative data analysis offers objective, numerical measurements, minimizing bias and personal interpretation.
• Results can often be generalized to larger populations, making them applicable to broader contexts.

Example: A study using quantitative data analysis to measure student test scores can objectively compare performance across different schools and demographics, leading to generalizable insights about educational strategies.

2. Precision and Efficiency:

• Statistical methods provide precise numerical results, allowing for accurate comparisons and prediction.
• Large datasets can be analyzed efficiently with the help of computer software, saving time and resources.

Example: A marketing team can use quantitative data analysis to precisely track click-through rates and conversion rates on different ad campaigns, quickly identifying the most effective strategies for maximizing customer engagement.

3. Identification of Patterns and Relationships:

• Statistical techniques reveal hidden patterns and relationships between variables that might not be apparent through observation alone.
• This can lead to new insights and understanding of complex phenomena.

Example: A medical researcher can use quantitative analysis to pinpoint correlations between lifestyle factors and disease risk, aiding in the development of prevention strategies.

1. Limited Scope:

• Quantitative analysis focuses on quantifiable aspects of a phenomenon ,  potentially overlooking important qualitative nuances, such as emotions, motivations, or cultural contexts.

Example: A survey measuring customer satisfaction with numerical ratings might miss key insights about the underlying reasons for their satisfaction or dissatisfaction, which could be better captured through open-ended feedback.

2. Oversimplification:

• Reducing complex phenomena to numerical data can lead to oversimplification and a loss of richness in understanding.

Example: Analyzing employee productivity solely through quantitative metrics like hours worked or tasks completed might not account for factors like creativity, collaboration, or problem-solving skills, which are crucial for overall performance.

3. Potential for Misinterpretation:

• Statistical results can be misinterpreted if not analyzed carefully and with appropriate expertise.
• The choice of statistical methods and assumptions can significantly influence results.

This blog discusses the steps, methods, and techniques of quantitative data analysis. It also gives insights into the methods of data collection, the type of data one should work with, and the pros and cons of such analysis.

Gain a better understanding of data analysis with these essential reads:

• Data Analysis and Modeling: 4 Critical Differences
• Exploratory Data Analysis Simplified 101
• 25 Best Data Analysis Tools in 2024

Carrying out successful data analysis requires prepping the data and making it analysis-ready. That is where Hevo steps in.

Want to give Hevo a try? Sign Up for a 14-day free trial and experience the feature-rich Hevo suite first hand. You may also have a look at the amazing Hevo price , which will assist you in selecting the best plan for your requirements.

Share your experience of understanding Quantitative Data Analysis in the comment section below! We would love to hear your thoughts.

Ofem Eteng is a seasoned technical content writer with over 12 years of experience. He has held pivotal roles such as System Analyst (DevOps) at Dagbs Nigeria Limited and Full-Stack Developer at Pedoquasphere International Limited. He specializes in data science, data analytics and cutting-edge technologies, making him an expert in the data industry.

No-code Data Pipeline for your Data Warehouse

• Data Analysis
• Data Warehouse
• Quantitative Data Analysis

Continue Reading

Data Mesh vs Data Warehouse: A Guide to Choosing the Right Data Architecture

Vinita Mittal

Data Lake vs Data Warehouse: How to choose?

Rashmi Joshi

Matillion vs dbt: 5 Key Differences

I want to read this e-book.

• Privacy Policy

Home » Quantitative Research – Methods, Types and Analysis

Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

Quantitative Research Methods

Quantitative Research Methods are as follows:

Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

• Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
• Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
• Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
• Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
• Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

• Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
• Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
• Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
• Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
• Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
• Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
• Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

• Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
• Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
• Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
• Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
• Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
• Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
• Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

• Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
• Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
• Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
• Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
• Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
• Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

• To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
• To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
• To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
• To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
• To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

• Description : To provide a detailed and accurate description of a particular phenomenon or population.
• Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
• Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
• Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

Advantages of Quantitative Research

There are several advantages of quantitative research, including:

• Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
• Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
• Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
• Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
• Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
• Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

Limitations of Quantitative Research

There are several limitations of quantitative research, including:

• Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
• Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
• Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
• Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
• Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
• Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Triangulation in Research – Types, Methods and...

Basic Research – Types, Methods and Examples

Correlational Research – Methods, Types and...

Questionnaire – Definition, Types, and Examples

Research Methods – Types, Examples and Guide

Observational Research – Methods and Guide

Skip to main content

• SAS Viya Platform
• Capabilities
• Why SAS Viya?
• Move to SAS Viya
• Managed Services
• Artificial Intelligence (AI)
• Risk Management
• All Products & Solutions
• Public Sector
• Life Sciences
• Retail & Consumer Goods
• All Industries
• Contracting with SAS
• Customer Stories
• Generative AI Solutions

Why Learn SAS?

Demand for SAS skills is growing. Advance your career and train your team in sought after skills

• Train My Team
• Course Catalog
• Free Training
• My Training
• Academic Programs
• Free Academic Software
• Certification
• Choose a Credential
• Why get certified?
• Exam Preparation
• My Certification
• Communities
• Ask the Expert
• All Webinars
• Video Tutorials
• YouTube Channel
• SAS Programming
• Statistical Procedures
• New SAS Users
• Administrators
• All Communities
• Documentation
• Installation & Configuration
• SAS Viya Administration
• SAS Viya Programming
• System Requirements
• All Documentation
• Support & Services
• Knowledge Base
• Starter Kit
• Support by Product
• Support Services
• All Support & Services
• User Groups
• Partner Program
• Find a Partner
• Sign Into PartnerNet

Learn why SAS is the world's most trusted analytics platform, and why analysts, customers and industry experts love SAS.

Learn more about SAS

• Annual Report
• Vision & Mission
• Office Locations
• Internships
• Search Jobs
• News & Events
• Newsletters
• Trust Center
• support.sas.com
• documentation.sas.com
• blogs.sas.com
• communities.sas.com
• developer.sas.com

Select Your Region

Middle East & Africa

Asia Pacific

• Canada (English)
• Canada (Français)
• United States
• Česká Republika
• Deutschland
• Schweiz (Deutsch)
• Suisse (Français)
• United Kingdom
• Middle East
• Saudi Arabia
• South Africa
• New Zealand
• Philippines
• Thailand (English)
• ประเทศไทย (ภาษาไทย)
• Worldwide Sites

Create Profile

Get access to My SAS, trials, communities and more.

Edit Profile

Analytics Insights

Connect with the latest insights on analytics through related articles and research., more on statistical analysis.

• A guide to machine learning algorithms (and when to use them)
• 5 tips for choosing a statistical computing environment
• Get certified! Statistics for machine learning

Statistics is so unique because it can go from health outcomes research to marketing analysis to the longevity of a light bulb. It’s a fun field because you really can do so many different things with it.

Besa Smith President and Senior Scientist Analydata

Statistical Computing

Traditional methods for statistical analysis – from sampling data to interpreting results – have been used by scientists for thousands of years. But today’s data volumes make statistics ever more valuable and powerful. Affordable storage, powerful computers and advanced algorithms have all led to an increased use of computational statistics.

Whether you are working with large data volumes or running multiple permutations of your calculations, statistical computing has become essential for today’s statistician. Popular statistical computing practices include:

• Statistical programming – From traditional analysis of variance and linear regression to exact methods and statistical visualization techniques, statistical programming is essential for making data-based decisions in every field.
• Econometrics – Modeling, forecasting and simulating business processes for improved strategic and tactical planning. This method applies statistics to economics to forecast future trends.
• Operations research – Identify the actions that will produce the best results – based on many possible options and outcomes. Scheduling, simulation, and related modeling processes are used to optimize business processes and management challenges.
• Matrix programming – Powerful computer techniques for implementing your own statistical methods and exploratory data analysis using row operation algorithms.
• Statistical quality improvement – A mathematical approach to reviewing the quality and safety characteristics for all aspects of production.

Careers in Statistical Analysis

With everyone from The New York Times to Google’s Chief Economist Hal Varien proclaiming statistics to be the latest hot career field, who are we to argue? But why is there so much talk about careers in statistical analysis and data science? It could be the shortage of trained analytical thinkers. Or it could be the demand for managing the latest big data strains. Or, maybe it’s the excitement of applying mathematical concepts to make a difference in the world.

If you talk to statisticians about what first interested them in statistical analysis, you’ll hear a lot of stories about collecting baseball cards as a child. Or applying statistics to win more games of Axis and Allies. It is often these early passions that lead statisticians into the field. As adults, those passions can carry over into the workforce as a love of analysis and reasoning, where their passions are applied to everything from the influence of friends on purchase decisions to the study of endangered species around the world.

Learn more about the field of statistics and real-world statisticians:

• Read the personal stories of data scientists solving real-world problems.
• Learn about statistics and advanced analytics on the SAS Data Science blog .

Statistics Procedures Community

Join our statistics procedures community, where you can ask questions and share your experiences with SAS statistical products. SAS Statistical Procedures

Statistical Analysis Resources

• Statistics training
• Statistical analytics tutorials
• Statistics and operations research news
• SAS ® statistics products

Want more insights?

Risk & Fraud

Discover new insights on risk and fraud through research, related articles and much  more..

Get more insights on big data including articles, research and other hot topics.

Explore insights from marketing movers and shakers on a variety of timely topics.

Get a free trial.

Experience SAS Viya firsthand in our private trial environment.

Request Pricing

Embark on your path to the future in a single, expandable environment.

Request a Demo

See SAS in action with a demo customized for your industry and business needs.

Get Free Training

Get the training you need to make the most of your SAS investment.

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

The PMC website is updating on October 15, 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• Indian J Anaesth
• v.60(9); 2016 Sep

Basic statistical tools in research and data analysis

Zulfiqar ali.

Department of Anaesthesiology, Division of Neuroanaesthesiology, Sheri Kashmir Institute of Medical Sciences, Soura, Srinagar, Jammu and Kashmir, India

S Bala Bhaskar

1 Department of Anaesthesiology and Critical Care, Vijayanagar Institute of Medical Sciences, Bellary, Karnataka, India

Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise only if proper statistical tests are used. This article will try to acquaint the reader with the basic research tools that are utilised while conducting various studies. The article covers a brief outline of the variables, an understanding of quantitative and qualitative variables and the measures of central tendency. An idea of the sample size estimation, power analysis and the statistical errors is given. Finally, there is a summary of parametric and non-parametric tests used for data analysis.

INTRODUCTION

Statistics is a branch of science that deals with the collection, organisation, analysis of data and drawing of inferences from the samples to the whole population.[ 1 ] This requires a proper design of the study, an appropriate selection of the study sample and choice of a suitable statistical test. An adequate knowledge of statistics is necessary for proper designing of an epidemiological study or a clinical trial. Improper statistical methods may result in erroneous conclusions which may lead to unethical practice.[ 2 ]

Variable is a characteristic that varies from one individual member of population to another individual.[ 3 ] Variables such as height and weight are measured by some type of scale, convey quantitative information and are called as quantitative variables. Sex and eye colour give qualitative information and are called as qualitative variables[ 3 ] [ Figure 1 ].

Classification of variables

Quantitative variables

Quantitative or numerical data are subdivided into discrete and continuous measurements. Discrete numerical data are recorded as a whole number such as 0, 1, 2, 3,… (integer), whereas continuous data can assume any value. Observations that can be counted constitute the discrete data and observations that can be measured constitute the continuous data. Examples of discrete data are number of episodes of respiratory arrests or the number of re-intubations in an intensive care unit. Similarly, examples of continuous data are the serial serum glucose levels, partial pressure of oxygen in arterial blood and the oesophageal temperature.

A hierarchical scale of increasing precision can be used for observing and recording the data which is based on categorical, ordinal, interval and ratio scales [ Figure 1 ].

Categorical or nominal variables are unordered. The data are merely classified into categories and cannot be arranged in any particular order. If only two categories exist (as in gender male and female), it is called as a dichotomous (or binary) data. The various causes of re-intubation in an intensive care unit due to upper airway obstruction, impaired clearance of secretions, hypoxemia, hypercapnia, pulmonary oedema and neurological impairment are examples of categorical variables.

Ordinal variables have a clear ordering between the variables. However, the ordered data may not have equal intervals. Examples are the American Society of Anesthesiologists status or Richmond agitation-sedation scale.

Interval variables are similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced. A good example of an interval scale is the Fahrenheit degree scale used to measure temperature. With the Fahrenheit scale, the difference between 70° and 75° is equal to the difference between 80° and 85°: The units of measurement are equal throughout the full range of the scale.

Ratio scales are similar to interval scales, in that equal differences between scale values have equal quantitative meaning. However, ratio scales also have a true zero point, which gives them an additional property. For example, the system of centimetres is an example of a ratio scale. There is a true zero point and the value of 0 cm means a complete absence of length. The thyromental distance of 6 cm in an adult may be twice that of a child in whom it may be 3 cm.

STATISTICS: DESCRIPTIVE AND INFERENTIAL STATISTICS

Descriptive statistics[ 4 ] try to describe the relationship between variables in a sample or population. Descriptive statistics provide a summary of data in the form of mean, median and mode. Inferential statistics[ 4 ] use a random sample of data taken from a population to describe and make inferences about the whole population. It is valuable when it is not possible to examine each member of an entire population. The examples if descriptive and inferential statistics are illustrated in Table 1 .

Example of descriptive and inferential statistics

Descriptive statistics

The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion.

Measures of central tendency

The measures of central tendency are mean, median and mode.[ 6 ] Mean (or the arithmetic average) is the sum of all the scores divided by the number of scores. Mean may be influenced profoundly by the extreme variables. For example, the average stay of organophosphorus poisoning patients in ICU may be influenced by a single patient who stays in ICU for around 5 months because of septicaemia. The extreme values are called outliers. The formula for the mean is

where x = each observation and n = number of observations. Median[ 6 ] is defined as the middle of a distribution in a ranked data (with half of the variables in the sample above and half below the median value) while mode is the most frequently occurring variable in a distribution. Range defines the spread, or variability, of a sample.[ 7 ] It is described by the minimum and maximum values of the variables. If we rank the data and after ranking, group the observations into percentiles, we can get better information of the pattern of spread of the variables. In percentiles, we rank the observations into 100 equal parts. We can then describe 25%, 50%, 75% or any other percentile amount. The median is the 50 th percentile. The interquartile range will be the observations in the middle 50% of the observations about the median (25 th -75 th percentile). Variance[ 7 ] is a measure of how spread out is the distribution. It gives an indication of how close an individual observation clusters about the mean value. The variance of a population is defined by the following formula:

where σ 2 is the population variance, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The variance of a sample is defined by slightly different formula:

where s 2 is the sample variance, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. The formula for the variance of a population has the value ‘ n ’ as the denominator. The expression ‘ n −1’ is known as the degrees of freedom and is one less than the number of parameters. Each observation is free to vary, except the last one which must be a defined value. The variance is measured in squared units. To make the interpretation of the data simple and to retain the basic unit of observation, the square root of variance is used. The square root of the variance is the standard deviation (SD).[ 8 ] The SD of a population is defined by the following formula:

where σ is the population SD, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The SD of a sample is defined by slightly different formula:

where s is the sample SD, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. An example for calculation of variation and SD is illustrated in Table 2 .

Example of mean, variance, standard deviation

Normal distribution or Gaussian distribution

Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point.[ 1 ] The standard normal distribution curve is a symmetrical bell-shaped. In a normal distribution curve, about 68% of the scores are within 1 SD of the mean. Around 95% of the scores are within 2 SDs of the mean and 99% within 3 SDs of the mean [ Figure 2 ].

Normal distribution curve

Skewed distribution

It is a distribution with an asymmetry of the variables about its mean. In a negatively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the right of Figure 1 . In a positively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the left of the figure leading to a longer right tail.

Curves showing negatively skewed and positively skewed distribution

Inferential statistics

In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population. The purpose is to answer or test the hypotheses. A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. Hypothesis tests are thus procedures for making rational decisions about the reality of observed effects.

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty).

In inferential statistics, the term ‘null hypothesis’ ( H 0 ‘ H-naught ,’ ‘ H-null ’) denotes that there is no relationship (difference) between the population variables in question.[ 9 ]

Alternative hypothesis ( H 1 and H a ) denotes that a statement between the variables is expected to be true.[ 9 ]

The P value (or the calculated probability) is the probability of the event occurring by chance if the null hypothesis is true. The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ].

P values with interpretation

If P value is less than the arbitrarily chosen value (known as α or the significance level), the null hypothesis (H0) is rejected [ Table 4 ]. However, if null hypotheses (H0) is incorrectly rejected, this is known as a Type I error.[ 11 ] Further details regarding alpha error, beta error and sample size calculation and factors influencing them are dealt with in another section of this issue by Das S et al .[ 12 ]

Illustration for null hypothesis

PARAMETRIC AND NON-PARAMETRIC TESTS

Numerical data (quantitative variables) that are normally distributed are analysed with parametric tests.[ 13 ]

Two most basic prerequisites for parametric statistical analysis are:

• The assumption of normality which specifies that the means of the sample group are normally distributed
• The assumption of equal variance which specifies that the variances of the samples and of their corresponding population are equal.

However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used. Non-parametric tests are used to analyse ordinal and categorical data.

Parametric tests

The parametric tests assume that the data are on a quantitative (numerical) scale, with a normal distribution of the underlying population. The samples have the same variance (homogeneity of variances). The samples are randomly drawn from the population, and the observations within a group are independent of each other. The commonly used parametric tests are the Student's t -test, analysis of variance (ANOVA) and repeated measures ANOVA.

Student's t -test

Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:

where X = sample mean, u = population mean and SE = standard error of mean

where X 1 − X 2 is the difference between the means of the two groups and SE denotes the standard error of the difference.

• To test if the population means estimated by two dependent samples differ significantly (the paired t -test). A usual setting for paired t -test is when measurements are made on the same subjects before and after a treatment.

The formula for paired t -test is:

where d is the mean difference and SE denotes the standard error of this difference.

The group variances can be compared using the F -test. The F -test is the ratio of variances (var l/var 2). If F differs significantly from 1.0, then it is concluded that the group variances differ significantly.

Analysis of variance

The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups.

In ANOVA, we study two variances – (a) between-group variability and (b) within-group variability. The within-group variability (error variance) is the variation that cannot be accounted for in the study design. It is based on random differences present in our samples.

However, the between-group (or effect variance) is the result of our treatment. These two estimates of variances are compared using the F-test.

A simplified formula for the F statistic is:

where MS b is the mean squares between the groups and MS w is the mean squares within groups.

Repeated measures analysis of variance

As with ANOVA, repeated measures ANOVA analyses the equality of means of three or more groups. However, a repeated measure ANOVA is used when all variables of a sample are measured under different conditions or at different points in time.

As the variables are measured from a sample at different points of time, the measurement of the dependent variable is repeated. Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: The data violate the ANOVA assumption of independence. Hence, in the measurement of repeated dependent variables, repeated measures ANOVA should be used.

Non-parametric tests

When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results. Non-parametric tests (distribution-free test) are used in such situation as they do not require the normality assumption.[ 15 ] Non-parametric tests may fail to detect a significant difference when compared with a parametric test. That is, they usually have less power.

As is done for the parametric tests, the test statistic is compared with known values for the sampling distribution of that statistic and the null hypothesis is accepted or rejected. The types of non-parametric analysis techniques and the corresponding parametric analysis techniques are delineated in Table 5 .

Analogue of parametric and non-parametric tests

Median test for one sample: The sign test and Wilcoxon's signed rank test

The sign test and Wilcoxon's signed rank test are used for median tests of one sample. These tests examine whether one instance of sample data is greater or smaller than the median reference value.

This test examines the hypothesis about the median θ0 of a population. It tests the null hypothesis H0 = θ0. When the observed value (Xi) is greater than the reference value (θ0), it is marked as+. If the observed value is smaller than the reference value, it is marked as − sign. If the observed value is equal to the reference value (θ0), it is eliminated from the sample.

If the null hypothesis is true, there will be an equal number of + signs and − signs.

The sign test ignores the actual values of the data and only uses + or − signs. Therefore, it is useful when it is difficult to measure the values.

Wilcoxon's signed rank test

There is a major limitation of sign test as we lose the quantitative information of the given data and merely use the + or – signs. Wilcoxon's signed rank test not only examines the observed values in comparison with θ0 but also takes into consideration the relative sizes, adding more statistical power to the test. As in the sign test, if there is an observed value that is equal to the reference value θ0, this observed value is eliminated from the sample.

Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums.

Mann-Whitney test

It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other.

Mann–Whitney test compares all data (xi) belonging to the X group and all data (yi) belonging to the Y group and calculates the probability of xi being greater than yi: P (xi > yi). The null hypothesis states that P (xi > yi) = P (xi < yi) =1/2 while the alternative hypothesis states that P (xi > yi) ≠1/2.

Kolmogorov-Smirnov test

The two-sample Kolmogorov-Smirnov (KS) test was designed as a generic method to test whether two random samples are drawn from the same distribution. The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves.

Kruskal-Wallis test

The Kruskal–Wallis test is a non-parametric test to analyse the variance.[ 14 ] It analyses if there is any difference in the median values of three or more independent samples. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic.

Jonckheere test

In contrast to Kruskal–Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal–Wallis test.[ 14 ]

Friedman test

The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.[ 13 ]

Tests to analyse the categorical data

Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups (i.e., the null hypothesis). It is calculated by the sum of the squared difference between observed ( O ) and the expected ( E ) data (or the deviation, d ) divided by the expected data by the following formula:

A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables. It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability. McNemar's test is used for paired nominal data. It is applied to 2 × 2 table with paired-dependent samples. It is used to determine whether the row and column frequencies are equal (that is, whether there is ‘marginal homogeneity’). The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable. If the outcome variable is dichotomous, then logistic regression is used.

SOFTWARES AVAILABLE FOR STATISTICS, SAMPLE SIZE CALCULATION AND POWER ANALYSIS

Numerous statistical software systems are available currently. The commonly used software systems are Statistical Package for the Social Sciences (SPSS – manufactured by IBM corporation), Statistical Analysis System ((SAS – developed by SAS Institute North Carolina, United States of America), R (designed by Ross Ihaka and Robert Gentleman from R core team), Minitab (developed by Minitab Inc), Stata (developed by StataCorp) and the MS Excel (developed by Microsoft).

There are a number of web resources which are related to statistical power analyses. A few are:

• StatPages.net – provides links to a number of online power calculators
• G-Power – provides a downloadable power analysis program that runs under DOS
• Power analysis for ANOVA designs an interactive site that calculates power or sample size needed to attain a given power for one effect in a factorial ANOVA design
• SPSS makes a program called SamplePower. It gives an output of a complete report on the computer screen which can be cut and paste into another document.

It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results. Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article. Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.

Financial support and sponsorship

Conflicts of interest.

There are no conflicts of interest.

• Data Center
• Applications
• Open Source

Datamation content and product recommendations are editorially independent. We may make money when you click on links to our partners. Learn More .

Statistical analysis is a systematic method of gathering, analyzing, interpreting, presenting, and deriving conclusions from data. It employs statistical tools to find patterns, trends, and links within datasets to facilitate informed decision-making. Data collection, description, exploratory data analysis (EDA), inferential statistics, statistical modeling, data visualization, and interpretation are all important aspects of statistical analysis.

Used in quantitative research to gather and analyze data, statistical data analysis provides a more comprehensive view of operational landscapes and gives organizations the insights they need to make strategic, evidence-based decisions. Here’s what you need to know.

Table of Contents

How Does Statistical Analysis Work?

The strategic use of statistical analysis procedures helps organizations get insights from data to make educated decisions. Statistical analytic approaches, which include everything from data extraction to the creation of actionable recommendations, provide a systematic approach to comprehending, interpreting, and using large datasets. By navigating these complex processes, businesses uncover hidden patterns in their data and extract important insights that can be used as a compass for strategic decision-making.

Extracting and Organizing Raw Data

Extracting and organizing raw data entails gathering information from a variety of sources, combining datasets, and assuring data quality through rigorous cleaning. In healthcare, for example, this method may comprise combining patient information from several systems to assess patterns in illness prevalence and treatment outcomes.

Identifying Essential Data

Identifying key data—and excluding irrelevant data—necessitates a thorough analysis of the dataset. Analysts use variable selection strategies to filter datasets to emphasize characteristics most relevant to the objectives, resulting in more focused and meaningful analysis.

Developing Innovative Collection Strategies 

Innovative data collection procedures include everything from creating successful surveys and organizing experiments to data mining to extract data from a wide range of sources. Researchers in environmental studies might use remote sensing technology to obtain data on how plants and land cover change over time. Modern approaches such as satellite photography and machine learning algorithms help scientists improve the depth and precision of data collecting, opening the way for more nuanced analyses and informed decision-making.

Collaborating With Experts

Collaborating with clients and specialists to review data analysis tactics can align analytical approaches with organizational objectives. In finance, for example, engaging with investment professionals ensures that data analysis tactics analyze market trends and make educated investment decisions. Analysts may modify their tactics by incorporating comments from domain experts, making the ensuing study more relevant and applicable to the given sector or subject.

Creating Reports and Visualizations 

Creating data reports and visualizations entails generating extensive summaries and graphical representations for clarity. In e-commerce, reports might indicate user purchase trends using visualizations like heatmaps to highlight popular goods. Businesses that display data in a visually accessible format can rapidly analyze patterns and make data-driven choices that optimize product offers and improve the entire consumer experience.

Analyzing Data Findings 

This step entails using statistical tools to discover patterns, correlations, and insights in the dataset. In manufacturing, data analysis can identify connections between production factors and product faults, leading process improvement efforts. Engineers may discover and resolve fundamental causes using statistical tools and methodologies, resulting in higher product quality and operational efficiency.

Acting on the Data

Synthesizing findings from data analysis leads to the development of organizational recommendations. In the hospitality business, for example, data analysis might indicate trends in client preferences, resulting in strategic suggestions for tailored services and marketing efforts. Continuous improvement ideas based on analytical results help the firm adapt to a changing market scenario and compete more effectively.

The Importance of Statistical Analysis

The importance of statistical analysis goes far beyond data processing; it is the cornerstone in giving vital insights required for strategic decision-making, especially in the dynamic area of presenting new items to the market. Statistical analysis, which meticulously examines data, not only reveals trends and patterns but also provides a full insight into customer behavior, preferences, and market dynamics.

This abundance of information is a guiding force for enterprises, allowing them to make data-driven decisions that optimize product launches, improve market positioning, and ultimately drive success in an ever-changing business landscape.

2 Types of Statistical Analysis

There are two forms of statistical analysis, descriptive statistics, and statistical inference, both of which play an important role in guaranteeing data correctness and communicability using various analytical approaches.

By combining the capabilities of descriptive statistics with statistical inference, analysts can completely characterize the data and draw relevant insights that extend beyond the observed sample, guaranteeing conclusions that are resilient, trustworthy, and applicable to a larger context. This dual method improves the overall dependability of statistical analysis, making it an effective tool for obtaining important information from a variety of datasets.

Descriptive Statistics

This type of statistical analysis is all about visuals. Raw data doesn’t mean much on its own, and the sheer quantity can be overwhelming to digest. Descriptive statistical analysis focuses on creating a basic visual description of the data or turning information into graphs, charts, and other visuals that help people understand the meaning of the values in the data set. Descriptive analysis isn’t about explaining or drawing conclusions, though. It is only the practice of digesting and summarizing raw data to better understand it.

Statistical Inference

Inferential statistics practices involve more upfront hypotheses and follow-up explanations than descriptive statistics. In this type of statistical analysis, you are less focused on the entire collection of raw data and instead, take a sample and test your hypothesis or first estimation. From this sample and the results of your experiment, you can use inferential statistics to infer conclusions about the rest of the data set.

6 Benefits of Statistical Analysis

Statistical analysis enables a methodical and data-driven approach to decision-making and helps organizations maximize the value of their data, resulting in increased efficiency, informed decision-making, and innovation. Here are six of the most important benefits:

• Competitive Analysis: Statistical analysis illuminates your company’s objective value—knowing common metrics like sales revenue and net profit margin allows you to compare your performance to competitors.
• True Sales Visibility: The sales team says it is having a good week, and the numbers look good, but how can you accurately measure the impact on sales numbers? Statistical data analysis measures sales data and associates it with specific timeframes, products, and individual salespeople, which gives better visibility of marketing and sales successes.
• Predictive Analytics: Predictive analytics allows you to use past numerical data to predict future outcomes and areas where your team should make adjustments to improve performance.
• Risk Assessment and Management: Statistical tools help organizations analyze and manage risks more efficiently. Organizations may use historical data to identify possible hazards, anticipate future outcomes, and apply risk mitigation methods, lowering uncertainty and improving overall risk management.
• Resource Optimization: Statistical analysis identifies areas of inefficiency or underutilization, improving personnel management, budget allocation, and resource deployment and leading to increased operational efficiency and cost savings.
• Informed Decision Making: Statistical analysis allows businesses to base judgments on factual data rather than intuition. Data analysis allows firms to uncover patterns, trends, and correlations, resulting in better informed and strategic decision-making processes.

5-Step Statistical Analysis Process

Here are five essential steps for executing a thorough statistical analysis. By carefully following these stages, analysts may undertake a complete and rigorous statistical analysis, creating the framework for informed decision-making and providing actionable insights for both individuals and businesses.

Step 1: Data Identification and Description

Identify and clarify the features of the data to be analyzed. Understanding the nature of the dataset is critical in building the framework for a thorough statistical analysis.

Step 2: Establishing the Population Connection

Make progress toward creating a meaningful relationship between the studied data and the larger sample population from which it is drawn. This stage entails contextualizing the data within the greater framework of the population it represents, increasing the analysis’s relevance and application.

Step 3: Model Construction and Synthesis

Create a model that accurately captures and synthesizes the complex relationship between the population under study and the unique dataset. Creating a well-defined model is essential for analyzing data and generating useful insights.

Step 4: Model Validity Verification

Apply the model to thorough testing and inspection to ensure its validity. This stage guarantees that the model properly represents the population’s underlying dynamics, which improves the trustworthiness of future analysis and results.

Step 5: Predictive Analysis of Future Trends

Using predictive analytics tools , you may take your analysis to the next level. This final stage forecasts future trends and occurrences based on the developed model, providing significant insights into probable developments and assisting with proactive decision-making.

5 Statistical Analysis Methods

There are five common statistical analysis methods, each adapted to distinct data goals and guiding rapid decision-making. The approach you choose is determined by the nature of your dataset and the goals you want to achieve.

Finding the mean—the average, or center point, of the dataset—is computed by adding all the values and dividing by the number of observations. In real-world situations, the mean is used to calculate a representative value that captures the usual magnitude of a group of observations. For example, in educational evaluations, the mean score of a class provides educators with a concise measure of overall performance, allowing them to determine the general level of comprehension.

Standard Deviation

The standard deviation measures the degree of variance or dispersion within a dataset. By demonstrating how far individual values differ from the mean, it provides information about the dataset’s general dispersion. In practice, the standard deviation is used in financial analysis to analyze the volatility of stock prices. A higher standard deviation indicates greater price volatility, which helps investors evaluate and manage risks associated with various investment opportunities.

Regression analysis seeks to understand and predict connections between variables. This statistical approach is used in a variety of disciplines, including marketing, where it helps anticipate sales based on advertising spend. For example, a corporation may use regression analysis to assess how changes in advertising spending affect product sales, allowing for more efficient resource allocation for future marketing efforts.

Hypothesis Testing

Hypothesis testing is used to determine the validity of a claim or hypothesis regarding a population parameter. In medical research, hypothesis testing may be used to compare the efficacy of a novel medicine against a traditional treatment. Researchers develop a null hypothesis, implying that there is no difference between treatments, and then use statistical tests to assess if there is sufficient evidence to reject the null hypothesis in favor of the alternative.

Sample Size Determination

Choosing an adequate sample size is critical for producing trustworthy and relevant results in a study. In clinical studies, for example, researchers determine the sample size to ensure that the study has the statistical power to detect differences in treatment results. A well-determined sample size strikes a compromise between the requirement for precision and practical factors, thereby strengthening the study’s results and helping evidence-based decision-making.

Bottom Line: Identify Patterns and Trends With Statistical Analysis

Statistical analysis can provide organizations with insights into customer behavior, market dynamics, and operational efficiency. This information simplifies decision-making and prepares organizations to adapt and prosper in changing situations. Organizations that use top-tier statistical analysis tools can leverage the power of data, uncover trends, and stay at the forefront of innovation, assuring a competitive advantage in today’s ever-changing technological world.

Interested in statistical analysis? Learn how to run Monte Carlo simulations and master logistic regression in Excel.

Subscribe to Data Insider

Learn the latest news and best practices about data science, big data analytics, artificial intelligence, data security, and more.

Similar articles

8 best data analytics tools: gain data-driven advantage in 2024, common data visualization examples: transform numbers into narratives, what is data management a guide to systems, processes, and tools, get the free newsletter.

Subscribe to Data Insider for top news, trends & analysis

Latest Articles

Exploring multi-tenant architecture: a..., 8 best data analytics..., common data visualization examples:..., what is data management....

LEARN STATISTICS EASILY

Learn Data Analysis Now!

What is: Quantitative Research

What is quantitative research.

Quantitative research is a systematic investigation that primarily focuses on quantifying relationships, behaviors, phenomena, and patterns through statistical, mathematical, or computational techniques. This type of research is characterized by the collection and analysis of numerical data, which can be transformed into usable statistics. It is widely used across various fields, including social sciences, marketing, health sciences, and education, to draw conclusions based on measurable evidence.

Ad description. Lorem ipsum dolor sit amet, consectetur adipiscing elit.

Characteristics of Quantitative Research

The main characteristics of quantitative research include its structured approach, reliance on measurable data, and the use of statistical analysis. Researchers often employ surveys, experiments, and observational studies to gather data that can be quantified. This structured methodology allows for the replication of studies, ensuring reliability and validity in the findings. Furthermore, quantitative research often seeks to establish patterns and predict outcomes, making it a powerful tool for decision-making.

Types of Quantitative Research Methods

There are several methods used in quantitative research, including descriptive research, correlational research, causal-comparative research, and experimental research. Descriptive research aims to provide an overview of a phenomenon by summarizing data points. Correlational research examines the relationship between two or more variables, while causal-comparative research seeks to identify cause-and-effect relationships. Experimental research, on the other hand, involves manipulating one variable to determine its effect on another, providing strong evidence for causal relationships.

Data Collection Techniques in Quantitative Research

Data collection in quantitative research can be achieved through various techniques, such as surveys, questionnaires, and structured interviews. Surveys are often designed with closed-ended questions that yield quantifiable responses, making it easier to analyze data statistically. Questionnaires can be distributed online or in person, allowing researchers to reach a broader audience. Structured interviews follow a predetermined set of questions, ensuring consistency in data collection across different respondents.

Importance of Sampling in Quantitative Research

Sampling plays a crucial role in quantitative research, as it determines the representativeness of the data collected. Researchers must carefully select a sample that accurately reflects the population being studied to ensure the validity of their findings. Various sampling techniques, such as random sampling, stratified sampling, and cluster sampling, can be employed to achieve this goal. A well-designed sample enhances the generalizability of the research results, allowing for broader conclusions to be drawn.

Statistical Analysis in Quantitative Research

Statistical analysis is a fundamental component of quantitative research, as it allows researchers to interpret numerical data and draw meaningful conclusions. Various statistical methods, including descriptive statistics, inferential statistics, and multivariate analysis, are utilized to analyze data. Descriptive statistics summarize data through measures such as mean, median, and mode, while inferential statistics enable researchers to make predictions and generalizations about a population based on sample data. Multivariate analysis examines the relationships between multiple variables simultaneously, providing deeper insights into complex phenomena.

Limitations of Quantitative Research

Despite its strengths, quantitative research has limitations that researchers must consider. One significant limitation is its inability to capture the complexity of human behavior and social phenomena, as it often relies on numerical data that may oversimplify intricate issues. Additionally, quantitative research may overlook the context in which data is collected, leading to potential biases. Researchers must be aware of these limitations and complement quantitative methods with qualitative approaches when necessary to gain a more comprehensive understanding of the research topic.

Applications of Quantitative Research

Quantitative research has a wide range of applications across various fields. In marketing, businesses utilize quantitative research to analyze consumer behavior, preferences, and trends, enabling them to make data-driven decisions. In health sciences, researchers employ quantitative methods to assess the effectiveness of treatments and interventions. Education professionals use quantitative research to evaluate teaching methods and student performance. The versatility of quantitative research makes it an invaluable tool for professionals seeking to understand and improve their respective fields.

Conclusion on the Role of Quantitative Research

In summary, quantitative research is a vital methodology that provides valuable insights through the systematic collection and analysis of numerical data. Its structured approach, reliance on statistical analysis, and wide-ranging applications make it an essential tool for researchers and professionals across various disciplines. By understanding the principles and techniques of quantitative research, individuals can effectively leverage data to inform decision-making and drive progress in their fields.

• Databank Solution
• Credit Risk Solution
• Valuation Analytics Solution
• ESG Sustainability Solution
• Quantitative Finance Solution
• Regulatory Technology Solution
• Product Introduction
• Service Provide Method
• Learning Video

Quantitative Data Analysis Guide: Methods, Examples & Uses

This guide will introduce the types of data analysis used in quantitative research, then discuss relevant examples and applications in the finance industry.

Table of Contents

An Overview of Quantitative Data Analysis

What is quantitative data analysis and what is it for .

Quantitative data analysis is the process of interpreting meaning and extracting insights from numerical data , which involves mathematical calculations and statistical reviews to uncover patterns, trends, and relationships between variables.

Beyond academic and statistical research, this approach is particularly useful in the finance industry. Financial data, such as stock prices, interest rates, and economic indicators, can all be quantified with statistics and metrics to offer crucial insights for informed investment decisions. To illustrate this, here are some examples of what quantitative data is usually used for:

• Measuring Differences between Groups: For instance, analyzing historical stock prices of different companies or asset classes can reveal which companies consistently outperform the market average.
• Assessing Relationships between Variables: An investor could analyze the relationship between a company’s price-to-earnings ratio (P/E ratio) and relevant factors, like industry performance, inflation rates, interests, etc, allowing them to predict future stock price growth.
• Testing Hypotheses: For example, an investor might hypothesize that companies with strong ESG (Environment, Social, and Governance) practices outperform those without. By categorizing these companies into two groups (strong ESG vs. weak ESG practices), they can compare the average return on investment (ROI) between the groups while assessing relevant factors to find evidence for the hypothesis. 

Ultimately, quantitative data analysis helps investors navigate the complex financial landscape and pursue profitable opportunities.

Quantitative Data Analysis VS. Qualitative Data Analysis

Although quantitative data analysis is a powerful tool, it cannot be used to provide context for your research, so this is where qualitative analysis comes in. Qualitative analysis is another common research method that focuses on collecting and analyzing non-numerical data , like text, images, or audio recordings to gain a deeper understanding of experiences, opinions, and motivations. Here’s a table summarizing its key differences between quantitative data analysis:

Due to their characteristics, quantitative analysis allows you to measure and compare large datasets; while qualitative analysis helps you understand the context behind the data. In some cases, researchers might even use both methods together for a more comprehensive understanding, but we’ll mainly focus on quantitative analysis for this article.

The 2 Main Quantitative Data Analysis Methods

Once you have your data collected, you have to use descriptive statistics or inferential statistics analysis to draw summaries and conclusions from your raw numbers. 

As its name suggests, the purpose of descriptive statistics is to describe your sample . It provides the groundwork for understanding your data by focusing on the details and characteristics of the specific group you’ve collected data from. 

On the other hand, inferential statistics act as bridges that connect your sample data to the broader population you’re truly interested in, helping you to draw conclusions in your research. Moreover, choosing the right inferential technique for your specific data and research questions is dependent on the initial insights from descriptive statistics, so both of these methods usually go hand-in-hand.

Descriptive Statistics Analysis

With sophisticated descriptive statistics, you can detect potential errors in your data by highlighting inconsistencies and outliers that might otherwise go unnoticed. Additionally, the characteristics revealed by descriptive statistics will help determine which inferential techniques are suitable for further analysis.

Measures in Descriptive Statistics

One of the key statistical tests used for descriptive statistics is central tendency . It consists of mean, median, and mode, telling you where most of your data points cluster:

• Mean: It refers to the “average” and is calculated by adding all the values in your data set and dividing by the number of values.
• Median: The middle value when your data is arranged in ascending or descending order. If you have an odd number of data points, the median is the exact middle value; with even numbers, it’s the average of the two middle values. 
• Mode: This refers to the most frequently occurring value in your data set, indicating the most common response or observation. Some data can have multiple modes (bimodal) or no mode at all.

Another statistic to test in descriptive analysis is the measures of dispersion , which involves range and standard deviation, revealing how spread out your data is relative to the central tendency measures:

• Range: It refers to the difference between the highest and lowest values in your data set. 
• Standard Deviation (SD): This tells you how the data is distributed within the range, revealing how much, on average, each data point deviates from the mean. Lower standard deviations indicate data points clustered closer to the mean, while higher standard deviations suggest a wider spread.

The shape of the distribution will then be measured through skewness. 

• Skewness: A statistic that indicates whether your data leans to one side (positive or negative) or is symmetrical (normal distribution). A positive skew suggests more data points concentrated on the lower end, while a negative skew indicates more data points on the higher end.

While the core measures mentioned above are fundamental, there are additional descriptive statistics used in specific contexts, including percentiles and interquartile range.

• Percentiles: This divides your data into 100 equal parts, revealing what percentage of data falls below a specific value. The 25th percentile (Q1) is the first quartile, the 50th percentile (Q2) is the median, and the 75th percentile (Q3) is the third quartile. Knowing these quartiles can help visualize the spread of your data.
• Interquartile Range (IQR): This measures the difference between Q3 and Q1, representing the middle 50% of your data.

Example of Descriptive Quantitative Data Analysis 

Let’s illustrate these concepts with a real-world example. Imagine a financial advisor analyzing a client’s portfolio. They have data on the client’s various holdings, including stock prices over the past year. With descriptive statistics they can obtain the following information:

• Central Tendency: The mean price for each stock reveals its average price over the year. The median price can further highlight if there were any significant price spikes or dips that skewed the mean.
• Measures of Dispersion: The standard deviation for each stock indicates its price volatility. A high standard deviation suggests the stock’s price fluctuated considerably, while a low standard deviation implies a more stable price history. This helps the advisor assess each stock’s risk profile.
• Shape of the Distribution: If data allows, analyzing skewness can be informative. A positive skew for a stock might suggest more frequent price drops, while a negative skew might indicate more frequent price increases.

By calculating these descriptive statistics, the advisor gains a quick understanding of the client’s portfolio performance and risk distribution. For instance, they could use correlation analysis to see if certain stock prices tend to move together, helping them identify expansion opportunities within the portfolio.

While descriptive statistics provide a foundational understanding, they should be followed by inferential analysis to uncover deeper insights that are crucial for making investment decisions.

Inferential Statistics Analysis

Inferential statistics analysis is particularly useful for hypothesis testing , as you can formulate predictions about group differences or potential relationships between variables , then use statistical tests to see if your sample data supports those hypotheses.

However, the power of inferential statistics hinges on one crucial factor: sample representativeness . If your sample doesn’t accurately reflect the population, your predictions won’t be very reliable. 

Statistical Tests for Inferential Statistics

Here are some of the commonly used tests for inferential statistics in commerce and finance, which can also be integrated to most analysis software:

• T-Tests: This compares the means, standard deviation, or skewness of two groups to assess if they’re statistically different, helping you determine if the observed difference is just a quirk within the sample or a significant reflection of the population.
• ANOVA (Analysis of Variance): While T-Tests handle comparisons between two groups, ANOVA focuses on comparisons across multiple groups, allowing you to identify potential variations and trends within the population.
• Correlation Analysis: This technique tests the relationship between two variables, assessing if one variable increases or decreases with the other. However, it’s important to note that just because two financial variables are correlated and move together, doesn’t necessarily mean one directly influences the other.
• Regression Analysis: Building on correlation, regression analysis goes a step further to verify the cause-and-effect relationships between the tested variables, allowing you to investigate if one variable actually influences the other.
• Cross-Tabulation: This breaks down the relationship between two categorical variables by displaying the frequency counts in a table format, helping you to understand how different groups within your data set might behave. The data in cross-tabulation can be mutually exclusive or have several connections with each other. 
• Trend Analysis: This examines how a variable in quantitative data changes over time, revealing upward or downward trends, as well as seasonal fluctuations. This can help you forecast future trends, and also lets you assess the effectiveness of the interventions in your marketing or investment strategy.
• MaxDiff Analysis: This is also known as the “best-worst” method. It evaluates customer preferences by asking respondents to choose the most and least preferred options from a set of products or services, allowing stakeholders to optimize product development or marketing strategies.
• Conjoint Analysis: Similar to MaxDiff, conjoint analysis gauges customer preferences, but it goes a step further by allowing researchers to see how changes in different product features (price, size, brand) influence overall preference.
• TURF Analysis (Total Unduplicated Reach and Frequency Analysis): This assesses a marketing campaign’s reach and frequency of exposure in different channels, helping businesses identify the most efficient channels to reach target audiences.
• Gap Analysis: This compares current performance metrics against established goals or benchmarks, using numerical data to represent the factors involved. This helps identify areas where performance falls short of expectations, serving as a springboard for developing strategies to bridge the gap and achieve those desired outcomes.
• SWOT Analysis (Strengths, Weaknesses, Opportunities, and Threats): This uses ratings or rankings to represent an organization’s internal strengths and weaknesses, along with external opportunities and threats. Based on this analysis, organizations can create strategic plans to capitalize on opportunities while minimizing risks.
• Text Analysis: This is an advanced method that uses specialized software to categorize and quantify themes, sentiment (positive, negative, neutral), and topics within textual data, allowing companies to obtain structured quantitative data from surveys, social media posts, or customer reviews.

Example of Inferential Quantitative Data Analysis

If you’re a financial analyst studying the historical performance of a particular stock, here are some predictions you can make with inferential statistics:

• The Differences between Groups: You can conduct T-Tests to compare the average returns of stocks in the technology sector with those in the healthcare sector. It can help assess if the observed difference in returns between these two sectors is simply due to random chance or if it’s statistically significant due to a significant difference in their performance.
• The Relationships between Variables: If you’re curious about the connection between a company’s price-to-earnings ratio (P/E ratios) and its future stock price movements, conducting correlation analysis can let you measure the strength and direction of this relationship. Is there a negative correlation, suggesting that higher P/E ratios might be associated with lower future stock prices? Or is there no significant correlation at all?

Understanding these inferential analysis techniques can help you uncover potential relationships and group differences that might not be readily apparent from descriptive statistics alone. Nonetheless, it’s important to remember that each technique has its own set of assumptions and limitations . Some methods are designed for parametric data with a normal distribution, while others are suitable for non-parametric data. 

Guide to Conduct Data Analysis in Quantitative Research

Now that we have discussed the types of data analysis techniques used in quantitative research, here’s a quick guide to help you choose the right method and grasp the essential steps of quantitative data analysis.

How to Choose the Right Quantitative Analysis Method?

Choosing between all these quantitative analysis methods may seem like a complicated task, but if you consider the 2 following factors, you can definitely choose the right technique:

Factor 1: Data Type

The data used in quantitative analysis can be categorized into two types, discrete data and continuous data, based on how they’re measured. They can also be further differentiated by their measurement scale. The four main types of measurement scales include: nominal, ordinal, interval or ratio. Understanding the distinctions between them is essential for choosing the appropriate statistical methods to interpret the results of your quantitative data analysis accurately.

Discrete data , which is also known as attribute data, represents whole numbers that can be easily counted and separated into distinct categories. It is often visualized using bar charts or pie charts, making it easy to see the frequency of each value. In the financial world, examples of discrete quantitative data include:

• The number of shares owned by an investor in a particular company
• The number of customer transactions processed by a bank per day
• Bond ratings (AAA, BBB, etc.) that represent discrete categories indicating the creditworthiness of a bond issuer
• The number of customers with different account types (checking, savings, investment) as seen in the pie chart below:

Discrete data usually use nominal or ordinal measurement scales, which can be then quantified to calculate their mode or median. Here are some examples:

• Nominal: This scale categorizes data into distinct groups with no inherent order. For instance, data on bank account types can be considered nominal data as it classifies customers in distinct categories which are independent of each other, either checking, savings, or investment accounts. and no inherent order or ranking implied by these account types.
• Ordinal: Ordinal data establishes a rank or order among categories. For example, investment risk ratings (low, medium, high) are ordered based on their perceived risk of loss, making it a type or ordinal data.

Conversely, continuous data can take on any value and fluctuate over time. It is usually visualized using line graphs, effectively showcasing how the values can change within a specific time frame. Examples of continuous data in the financial industry include:

• Interest rates set by central banks or offered by banks on loans and deposits
• Currency exchange rates which also fluctuate constantly throughout the day
• Daily trading volume of a particular stock on a specific day
• Stock prices that fluctuate throughout the day, as seen in the line graph below:

Source: Freepik

The measurement scale for continuous data is usually interval or ratio . Here is breakdown of their differences:

• Interval: This builds upon ordinal data by having consistent intervals between each unit, and its zero point doesn’t represent a complete absence of the variable. Let’s use credit score as an example. While the scale ranges from 300 to 850, the interval between each score rating is consistent (50 points), and a score of zero wouldn’t indicate an absence of credit history, but rather no credit score available. 
• Ratio: This scale has all the same characteristics of interval data but also has a true zero point, indicating a complete absence of the variable. Interest rates expressed as percentages are a classic example of ratio data. A 0% interest rate signifies the complete absence of any interest charged or earned, making it a true zero point.

Factor 2: Research Question

You also need to make sure that the analysis method aligns with your specific research questions. If you merely want to focus on understanding the characteristics of your data set, descriptive statistics might be all you need; if you need to analyze the connection between variables, then you have to include inferential statistics as well.

How to Analyze Quantitative Data 

Step 1: data collection  .

Depending on your research question, you might choose to conduct surveys or interviews. Distributing online or paper surveys can reach a broad audience, while interviews allow for deeper exploration of specific topics. You can also choose to source existing datasets from government agencies or industry reports.

Step 2: Data Cleaning

Raw data might contain errors, inconsistencies, or missing values, so data cleaning has to be done meticulously to ensure accuracy and consistency. This might involve removing duplicates, correcting typos, and handling missing information.

Furthermore, you should also identify the nature of your variables and assign them appropriate measurement scales , it could be nominal, ordinal, interval or ratio. This is important because it determines the types of descriptive statistics and analysis methods you can employ later. Once you categorize your data based on these measurement scales, you can arrange the data of each category in a proper order and organize it in a format that is convenient for you.

Step 3: Data Analysis

Based on the measurement scales of your variables, calculate relevant descriptive statistics to summarize your data. This might include measures of central tendency (mean, median, mode) and dispersion (range, standard deviation, variance). With these statistics, you can identify the pattern within your raw data. 

Then, these patterns can be analyzed further with inferential methods to test out the hypotheses you have developed. You may choose any of the statistical tests mentioned above, as long as they are compatible with the characteristics of your data.

Step 4. Data Interpretation and Communication 

Now that you have the results from your statistical analysis, you may draw conclusions based on the findings and incorporate them into your business strategies. Additionally, you should also transform your findings into clear and shareable information to facilitate discussion among stakeholders. Visualization techniques like tables, charts, or graphs can make complex data more digestible so that you can communicate your findings efficiently. 

Useful Quantitative Data Analysis Tools and Software 

We’ve compiled some commonly used quantitative data analysis tools and software. Choosing the right one depends on your experience level, project needs, and budget. Here’s a brief comparison: 

Quantitative Data in Finance and Investment

So how does this all affect the finance industry? Quantitative finance (or quant finance) has become a growing trend, with the quant fund market valued at $16,008.69 billion in 2023. This value is expected to increase at the compound annual growth rate of 10.09% and reach $31,365.94 billion by 2031, signifying its expanding role in the industry.

What is Quant Finance?

Quant finance is the process of using massive financial data and mathematical models to identify market behavior, financial trends, movements, and economic indicators, so that they can predict future trends.These calculated probabilities can be leveraged to find potential investment opportunities and maximize returns while minimizing risks.

Common Quantitative Investment Strategies

There are several common quantitative strategies, each offering unique approaches to help stakeholders navigate the market:

1. Statistical Arbitrage

This strategy aims for high returns with low volatility. It employs sophisticated algorithms to identify minuscule price discrepancies across the market, then capitalize on them at lightning speed, often generating short-term profits. However, its reliance on market efficiency makes it vulnerable to sudden market shifts, posing a risk of disrupting the calculations.

2. Factor Investing 

This strategy identifies and invests in assets based on factors like value, momentum, or quality. By analyzing these factors in quantitative databases , investors can construct portfolios designed to outperform the broader market. Overall, this method offers diversification and potentially higher returns than passive investing, but its success relies on the historical validity of these factors, which can evolve over time.

3. Risk Parity

This approach prioritizes portfolio balance above all else. Instead of allocating assets based on their market value, risk parity distributes them based on their risk contribution to achieve a desired level of overall portfolio risk, regardless of individual asset volatility. Although it is efficient in managing risks while potentially offering positive returns, it is important to note that this strategy’s complex calculations can be sensitive to unexpected market events.

4. Machine Learning & Artificial Intelligence (AI)

Quant analysts are beginning to incorporate these cutting-edge technologies into their strategies. Machine learning algorithms can act as data sifters, identifying complex patterns within massive datasets; whereas AI goes a step further, leveraging these insights to make investment decisions, essentially mimicking human-like decision-making with added adaptability. Despite the hefty development and implementation costs, its superior risk-adjusted returns and uncovering hidden patterns make this strategy a valuable asset.

Pros and Cons of Quantitative Data Analysis

Advantages of quantitative data analysis, minimum bias for reliable results.

Quantitative data analysis relies on objective, numerical data. This minimizes bias and human error, allowing stakeholders to make investment decisions without emotional intuitions that can cloud judgment. In turn, this offers reliable and consistent results for investment strategies.

Precise Calculations for Data-Driven Decisions

Quantitative analysis generates precise numerical results through statistical methods. This allows accurate comparisons between investment options and even predictions of future market behavior, helping investors make informed decisions about where to allocate their capital while managing potential risks.

Generalizability for Broader Insights 

By analyzing large datasets and identifying patterns, stakeholders can generalize the findings from quantitative analysis into broader populations, applying them to a wider range of investments for better portfolio construction and risk management

Efficiency for Extensive Research

Quantitative research is more suited to analyze large datasets efficiently, letting companies save valuable time and resources. The softwares used for quantitative analysis can automate the process of sifting through extensive financial data, facilitating quicker decision-making in the fast-paced financial environment.

Disadvantages of Quantitative Data Analysis

Limited scope .

By focusing on numerical data, quantitative analysis may provide a limited scope, as it can’t capture qualitative context such as emotions, motivations, or cultural factors. Although quantitative analysis provides a strong starting point, neglecting qualitative factors can lead to incomplete insights in the financial industry, impacting areas like customer relationship management and targeted marketing strategies.

Oversimplification 

Breaking down complex phenomena into numerical data could cause analysts to overlook the richness of the data, leading to the issue of oversimplification. Stakeholders who fail to understand the complexity of economic factors or market trends could face flawed investment decisions and missed opportunities.

Reliable Quantitative Data Solution 

In conclusion, quantitative data analysis offers a deeper insight into market trends and patterns, empowering you to make well-informed financial decisions. However, collecting comprehensive data and analyzing them can be a complex task that may divert resources from core investment activity. 

As a reliable provider, TEJ understands these concerns. Our TEJ Quantitative Investment Database offers high-quality financial and economic data for rigorous quantitative analysis. This data captures the true market conditions at specific points in time, enabling accurate backtesting of investment strategies.

Furthermore, TEJ offers diverse data sets that go beyond basic stock prices, encompassing various financial metrics, company risk attributes, and even broker trading information, all designed to empower your analysis and strategy development. Save resources and unlock the full potential of quantitative finance with TEJ’s data solutions today!

Subscribe to newsletter

• Data Analysis 108
• Market Research 48
• TQuant Lab 27
• Solution&DataSets
• Privacy Policy Statement
• Personal Data Policy
• Copyright Information
• Website licensing terms
• Information Security Policy 

• 11th Floor, No. 57, DongXing Road, Taipei 11070, Taiwan(R.O.C.)
• +886-2-8768-1088
• +886-2-8768-1336
• [email protected]

Quantitative Methods

• Living reference work entry
• First Online: 11 June 2021
• Cite this living reference work entry

• Juwel Rana 2 , 3 , 4 ,
• Patricia Luna Gutierrez 5 &
• John C. Oldroyd 6  

655 Accesses

2 Citations

Quantitative analysis ; Quantitative research methods ; Study design

Quantitative method is the collection and analysis of numerical data to answer scientific research questions. Quantitative method is used to summarize, average, find patterns, make predictions, and test causal associations as well as generalizing results to wider populations. It allows us to quantify effect sizes, determine the strength of associations, rank priorities, and weigh the strength of evidence of effectiveness.

Introduction

This entry aims to introduce the most common ways to use numbers and statistics to describe variables, establish relationships among variables, and build numerical understanding of a topic. In general, the quantitative research process uses a deductive approach (Neuman 2014 ; Leavy 2017 ), extrapolating from a particular case to the general situation (Babones 2016 ).

In practical ways, quantitative methods are an approach to studying a research topic. In research, the...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Babones S (2016) Interpretive quantitative methods for the social sciences. Sociology. https://doi.org/10.1177/0038038515583637

Balnaves M, Caputi P (2001) Introduction to quantitative research methods: an investigative approach. Sage, London

Book   Google Scholar  

Brenner PS (2020) Understanding survey methodology: sociological theory and applications. Springer, Boston

Google Scholar  

Creswell JW (2014) Research design: qualitative, quantitative, and mixed methods approaches. Sage, London

Leavy P (2017) Research design. The Gilford Press, New York

Mertens W, Pugliese A, Recker J (2018) Quantitative data analysis, research methods: information, systems, and contexts: second edition. https://doi.org/10.1016/B978-0-08-102220-7.00018-2

Neuman LW (2014) Social research methods: qualitative and quantitative approaches. Pearson Education Limited, Edinburgh

Treiman DJ (2009) Quantitative data analysis: doing social research to test ideas. Jossey-Bass, San Francisco

Download references

Author information

Authors and affiliations.

Department of Public Health, School of Health and Life Sciences, North South University, Dhaka, Bangladesh

Department of Biostatistics and Epidemiology, School of Health and Health Sciences, University of Massachusetts Amherst, MA, USA

Department of Research and Innovation, South Asia Institute for Social Transformation (SAIST), Dhaka, Bangladesh

Independent Researcher, Masatepe, Nicaragua

Patricia Luna Gutierrez

School of Behavioral and Health Sciences, Australian Catholic University, Fitzroy, VIC, Australia

John C. Oldroyd

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Juwel Rana .

Editor information

Editors and affiliations.

Florida Atlantic University, Boca Raton, FL, USA

Ali Farazmand

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this entry

Cite this entry.

Rana, J., Gutierrez, P.L., Oldroyd, J.C. (2021). Quantitative Methods. In: Farazmand, A. (eds) Global Encyclopedia of Public Administration, Public Policy, and Governance. Springer, Cham. https://doi.org/10.1007/978-3-319-31816-5_460-1

Download citation

DOI : https://doi.org/10.1007/978-3-319-31816-5_460-1

Received : 31 January 2021

Accepted : 14 February 2021

Published : 11 June 2021

Publisher Name : Springer, Cham

Print ISBN : 978-3-319-31816-5

Online ISBN : 978-3-319-31816-5

eBook Packages : Springer Reference Economics and Finance Reference Module Humanities and Social Sciences Reference Module Business, Economics and Social Sciences

• Publish with us

Policies and ethics

• Find a journal
• Track your research

Quantitative Data Analysis 101

By: Derek Jansen (MBA)  and Kerryn Warren (PhD) | December 2020

Overview: Quantitative Data Analysis 101

• What (exactly) is quantitative data analysis?
• When to use quantitative analysis
• How quantitative analysis works

The two “branches” of quantitative analysis

• Descriptive statistics 101
• Inferential statistics 101
• How to choose the right quantitative methods
• Recap & summary

What is quantitative data analysis?

Despite being a mouthful, quantitative data analysis simply means analysing data that is numbers-based – or data that can be easily “converted” into numbers without losing any meaning.

For example, category-based variables like gender, ethnicity, or native language could all be “converted” into numbers without losing meaning – for example, English could equal 1, French 2, etc.

This contrasts against qualitative data analysis, where the focus is on words, phrases and expressions that can’t be reduced to numbers. If you’re interested in learning about qualitative analysis, check out our post and video here .

What is quantitative analysis used for?

Quantitative analysis is generally used for three purposes.

• Firstly, it’s used to measure differences between groups . For example, the popularity of different clothing colours or brands.
• Secondly, it’s used to assess relationships between variables . For example, the relationship between weather temperature and voter turnout.
• And third, it’s used to test hypotheses in a scientifically rigorous way. For example, a hypothesis about the impact of a certain vaccine.

Again, this contrasts with qualitative analysis , which can be used to analyse people’s perceptions and feelings about an event or situation. In other words, things that can’t be reduced to numbers.

How does quantitative analysis work?

Well, since quantitative data analysis is all about analysing numbers , it’s no surprise that it involves statistics . Statistical analysis methods form the engine that powers quantitative analysis, and these methods can vary from pretty basic calculations (for example, averages and medians) to more sophisticated analyses (for example, correlations and regressions).

Sounds like gibberish? Don’t worry. We’ll explain all of that in this post. Importantly, you don’t need to be a statistician or math wiz to pull off a good quantitative analysis. We’ll break down all the technical mumbo jumbo in this post.

Need a helping hand?

As I mentioned, quantitative analysis is powered by statistical analysis methods . There are two main “branches” of statistical methods that are used – descriptive statistics and inferential statistics . In your research, you might only use descriptive statistics, or you might use a mix of both , depending on what you’re trying to figure out. In other words, depending on your research questions, aims and objectives . I’ll explain how to choose your methods later.

So, what are descriptive and inferential statistics?

Well, before I can explain that, we need to take a quick detour to explain some lingo. To understand the difference between these two branches of statistics, you need to understand two important words. These words are population and sample .

First up, population . In statistics, the population is the entire group of people (or animals or organisations or whatever) that you’re interested in researching. For example, if you were interested in researching Tesla owners in the US, then the population would be all Tesla owners in the US.

However, it’s extremely unlikely that you’re going to be able to interview or survey every single Tesla owner in the US. Realistically, you’ll likely only get access to a few hundred, or maybe a few thousand owners using an online survey. This smaller group of accessible people whose data you actually collect is called your sample .

So, to recap – the population is the entire group of people you’re interested in, and the sample is the subset of the population that you can actually get access to. In other words, the population is the full chocolate cake , whereas the sample is a slice of that cake.

So, why is this sample-population thing important?

Well, descriptive statistics focus on describing the sample , while inferential statistics aim to make predictions about the population, based on the findings within the sample. In other words, we use one group of statistical methods – descriptive statistics – to investigate the slice of cake, and another group of methods – inferential statistics – to draw conclusions about the entire cake. There I go with the cake analogy again…

With that out the way, let’s take a closer look at each of these branches in more detail.

Branch 1: Descriptive Statistics

Descriptive statistics serve a simple but critically important role in your research – to describe your data set – hence the name. In other words, they help you understand the details of your sample . Unlike inferential statistics (which we’ll get to soon), descriptive statistics don’t aim to make inferences or predictions about the entire population – they’re purely interested in the details of your specific sample .

When you’re writing up your analysis, descriptive statistics are the first set of stats you’ll cover, before moving on to inferential statistics. But, that said, depending on your research objectives and research questions , they may be the only type of statistics you use. We’ll explore that a little later.

So, what kind of statistics are usually covered in this section?

Some common statistical tests used in this branch include the following:

• Mean – this is simply the mathematical average of a range of numbers.
• Median – this is the midpoint in a range of numbers when the numbers are arranged in numerical order. If the data set makes up an odd number, then the median is the number right in the middle of the set. If the data set makes up an even number, then the median is the midpoint between the two middle numbers.
• Mode – this is simply the most commonly occurring number in the data set.
• In cases where most of the numbers are quite close to the average, the standard deviation will be relatively low.
• Conversely, in cases where the numbers are scattered all over the place, the standard deviation will be relatively high.
• Skewness . As the name suggests, skewness indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph, or do they skew to the left or right?

Feeling a bit confused? Let’s look at a practical example using a small data set.

First, we can see that the mean weight is 72.4 kilograms. In other words, the average weight across the sample is 72.4 kilograms. Straightforward.

Next, we can see that the median is very similar to the mean (the average). This suggests that this data set has a reasonably symmetrical distribution (in other words, a relatively smooth, centred distribution of weights, clustered towards the centre).

In terms of the mode , there is no mode in this data set. This is because each number is present only once and so there cannot be a “most common number”. If there were two people who were both 65 kilograms, for example, then the mode would be 65.

Next up is the standard deviation . 10.6 indicates that there’s quite a wide spread of numbers. We can see this quite easily by looking at the numbers themselves, which range from 55 to 90, which is quite a stretch from the mean of 72.4.

And lastly, the skewness of -0.2 tells us that the data is very slightly negatively skewed. This makes sense since the mean and the median are slightly different.

As you can see, these descriptive statistics give us some useful insight into the data set. Of course, this is a very small data set (only 10 records), so we can’t read into these statistics too much. Also, keep in mind that this is not a list of all possible descriptive statistics – just the most common ones. But why do all of these numbers matter?

While these descriptive statistics are all fairly basic, they’re important for a few reasons:

• Firstly, they help you get both a macro and micro-level view of your data. In other words, they help you understand both the big picture and the finer details.
• Secondly, they help you spot potential errors in the data – for example, if an average is way higher than you’d expect, or responses to a question are highly varied, this can act as a warning sign that you need to double-check the data.
• And lastly, these descriptive statistics help inform which inferential statistical techniques you can use, as those techniques depend on the skewness (in other words, the symmetry and normality) of the data.

Simply put, descriptive statistics are really important , even though the statistical techniques used are fairly basic. All too often at Grad Coach, we see students skimming over the descriptives in their eagerness to get to the more exciting inferential methods, and then landing up with some very flawed results.

Branch 2: Inferential Statistics

As I mentioned, while descriptive statistics are all about the details of your specific data set – your sample – inferential statistics aim to make inferences about the population . In other words, you’ll use inferential statistics to make predictions about what you’d expect to find in the full population.

What kind of predictions, you ask? Well, there are two common types of predictions that researchers try to make using inferential stats:

• Firstly, predictions about differences between groups – for example, height differences between children grouped by their favourite meal or gender.
• And secondly, relationships between variables – for example, the relationship between body weight and the number of hours a week a person does yoga.

In other words, inferential statistics (when done correctly), allow you to connect the dots and make predictions about what you expect to see in the real world population, based on what you observe in your sample data. For this reason, inferential statistics are used for hypothesis testing – in other words, to test hypotheses that predict changes or differences.

For example, if your population of interest is a mix of 50% male and 50% female , but your sample is 80% male , you can’t make inferences about the population based on your sample, since it’s not representative. This area of statistics is called sampling, but we won’t go down that rabbit hole here (it’s a deep one!) – we’ll save that for another post . What statistics are usually used in this branch?

There are many, many different statistical analysis methods within the inferential branch and it’d be impossible for us to discuss them all here. So we’ll just take a look at some of the most common inferential statistical methods so that you have a solid starting point.

First up are T-Tests . T-tests compare the means (the averages) of two groups of data to assess whether they’re statistically significantly different. In other words, do they have significantly different means, standard deviations and skewness.

This type of testing is very useful for understanding just how similar or different two groups of data are. For example, you might want to compare the mean blood pressure between two groups of people – one that has taken a new medication and one that hasn’t – to assess whether they are significantly different.

Kicking things up a level, we have ANOVA, which stands for “analysis of variance”. This test is similar to a T-test in that it compares the means of various groups, but ANOVA allows you to analyse multiple groups , not just two groups So it’s basically a t-test on steroids…

Next, we have correlation analysis . This type of analysis assesses the relationship between two variables. In other words, if one variable increases, does the other variable also increase, decrease or stay the same. For example, if the average temperature goes up, do average ice creams sales increase too? We’d expect some sort of relationship between these two variables intuitively , but correlation analysis allows us to measure that relationship scientifically .

Lastly, we have regression analysis – this is quite similar to correlation in that it assesses the relationship between variables, but it goes a step further to understand cause and effect between variables, not just whether they move together. In other words, does the one variable actually cause the other one to move, or do they just happen to move together naturally thanks to another force? Just because two variables correlate doesn’t necessarily mean that one causes the other. Stats overload…

I hear you. To make this all a little more tangible, let’s take a look at an example of a correlation in action.

How to choose the right analysis method

To choose the right statistical methods, you need to think about two important factors :

• The type of quantitative data you have (specifically, level of measurement and the shape of the data). And,
• Your research questions and hypotheses

Let’s take a closer look at each of these.

Factor 1 – Data type

The first thing you need to consider is the type of data you’ve collected (or the type of data you will collect). By data types, I’m referring to the four levels of measurement – namely, nominal, ordinal, interval and ratio. If you’re not familiar with this lingo, check out the video below.

Well, because different statistical methods and techniques require different types of data. This is one of the “assumptions” I mentioned earlier – every method has its assumptions regarding the type of data.

For example, some techniques work with categorical data (for example, yes/no type questions, or gender or ethnicity), while others work with continuous numerical data (for example, age, weight or income) – and, of course, some work with multiple data types.

If you try to use a statistical method that doesn’t support the data type you have, your results will be largely meaningless . So, make sure that you have a clear understanding of what types of data you’ve collected (or will collect). Once you have this, you can then check which statistical methods would support your data types here .

If you haven’t collected your data yet, you can work in reverse and look at which statistical method would give you the most useful insights, and then design your data collection strategy to collect the correct data types.

Another important factor to consider is the shape of your data . Specifically, does it have a normal distribution (in other words, is it a bell-shaped curve, centred in the middle) or is it very skewed to the left or the right? Again, different statistical techniques work for different shapes of data – some are designed for symmetrical data while others are designed for skewed data.

Factor 2: Your research questions

The next thing you need to consider is your specific research questions, as well as your hypotheses (if you have some). The nature of your research questions and research hypotheses will heavily influence which statistical methods and techniques you should use.

If you’re just interested in understanding the attributes of your sample (as opposed to the entire population), then descriptive statistics are probably all you need. For example, if you just want to assess the means (averages) and medians (centre points) of variables in a group of people.

On the other hand, if you aim to understand differences between groups or relationships between variables and to infer or predict outcomes in the population, then you’ll likely need both descriptive statistics and inferential statistics.

So, it’s really important to get very clear about your research aims and research questions, as well your hypotheses – before you start looking at which statistical techniques to use.

Never shoehorn a specific statistical technique into your research just because you like it or have some experience with it. Your choice of methods must align with all the factors we’ve covered here.

Time to recap…

You’re still with me? That’s impressive. We’ve covered a lot of ground here, so let’s recap on the key points:

• Quantitative data analysis is all about  analysing number-based data  (which includes categorical and numerical data) using various statistical techniques.
• The two main  branches  of statistics are  descriptive statistics  and  inferential statistics . Descriptives describe your sample, whereas inferentials make predictions about what you’ll find in the population.
• Common  descriptive statistical methods include  mean  (average),  median , standard  deviation  and  skewness .
• Common  inferential statistical methods include  t-tests ,  ANOVA ,  correlation  and  regression  analysis.
• To choose the right statistical methods and techniques, you need to consider the  type of data you’re working with , as well as your  research questions  and hypotheses.

Learn More About Quantitative:

Triangulation: The Ultimate Credibility Enhancer

Triangulation is one of the best ways to enhance the credibility of your research. Learn about the different options here.

Inferential Statistics 101: Simple Explainer (With Examples)

Quant Analysis 101: Inferential Statistics Everything You Need To Get Started (With...

Descriptive Statistics 101: Simple Explainer (With Examples)

Quant Analysis 101: Descriptive Statistics Everything You Need To Get Started (With...

Validity & Reliability: Explained Simply

Validity & Reliability In Research A Plain-Language Explanation (With Examples)By:...

Research Design 101: Qualitative & Quantitative

Learn about research design for both qualitative and quantitative studies. Includes plain-language explanations and examples.

📄 FREE TEMPLATES

Research Topic Ideation

Proposal Writing

Literature Review

Methodology & Analysis

Academic Writing

Referencing & Citing

Apps, Tools & Tricks

The Grad Coach Podcast

77 Comments

Hi, I have read your article. Such a brilliant post you have created.

Thank you for the feedback. Good luck with your quantitative analysis.

Thank you so much.

Thank you so much. I learnt much well. I love your summaries of the concepts. I had love you to explain how to input data using SPSS

Very useful, I have got the concept

Amazing and simple way of breaking down quantitative methods.

This is beautiful….especially for non-statisticians. I have skimmed through but I wish to read again. and please include me in other articles of the same nature when you do post. I am interested. I am sure, I could easily learn from you and get off the fear that I have had in the past. Thank you sincerely.

Send me every new information you might have.

i need every new information

Thank you for the blog. It is quite informative. Dr Peter Nemaenzhe PhD

It is wonderful. l’ve understood some of the concepts in a more compréhensive manner

Your article is so good! However, I am still a bit lost. I am doing a secondary research on Gun control in the US and increase in crime rates and I am not sure which analysis method I should use?

Based on the given learning points, this is inferential analysis, thus, use ‘t-tests, ANOVA, correlation and regression analysis’

Well explained notes. Am an MPH student and currently working on my thesis proposal, this has really helped me understand some of the things I didn’t know.

I like your page..helpful

wonderful i got my concept crystal clear. thankyou!!

This is really helpful , thank you

Thank you so much this helped

Wonderfully explained

thank u so much, it was so informative

THANKYOU, this was very informative and very helpful

This is great GRADACOACH I am not a statistician but I require more of this in my thesis

Include me in your posts.

This is so great and fully useful. I would like to thank you again and again.

Glad to read this article. I’ve read lot of articles but this article is clear on all concepts. Thanks for sharing.

Thank you so much. This is a very good foundation and intro into quantitative data analysis. Appreciate!

You have a very impressive, simple but concise explanation of data analysis for Quantitative Research here. This is a God-send link for me to appreciate research more. Thank you so much!

Avery good presentation followed by the write up. yes you simplified statistics to make sense even to a layman like me. Thank so much keep it up. The presenter did ell too. i would like more of this for Qualitative and exhaust more of the test example like the Anova.

This is a very helpful article, couldn’t have been clearer. Thank you.

Awesome and phenomenal information.Well done

The video with the accompanying article is super helpful to demystify this topic. Very well done. Thank you so much.

thank you so much, your presentation helped me a lot

I don’t know how should I express that ur article is saviour for me 🥺😍

It is well defined information and thanks for sharing. It helps me a lot in understanding the statistical data.

I gain a lot and thanks for sharing brilliant ideas, so wish to be linked on your email update.

Very helpful and clear .Thank you Gradcoach.

Thank for sharing this article, well organized and information presented are very clear.

VERY INTERESTING AND SUPPORTIVE TO NEW RESEARCHERS LIKE ME. AT LEAST SOME BASICS ABOUT QUANTITATIVE.

An outstanding, well explained and helpful article. This will help me so much with my data analysis for my research project. Thank you!

wow this has just simplified everything i was scared of how i am gonna analyse my data but thanks to you i will be able to do so

simple and constant direction to research. thanks

This is helpful

Great writing!! Comprehensive and very helpful.

Do you provide any assistance for other steps of research methodology like making research problem testing hypothesis report and thesis writing?

Thank you so much for such useful article!

Amazing article. So nicely explained. Wow

Very insightfull. Thanks

I am doing a quality improvement project to determine if the implementation of a protocol will change prescribing habits. Would this be a t-test?

The is a very helpful blog, however, I’m still not sure how to analyze my data collected. I’m doing a research on “Free Education at the University of Guyana”

tnx. fruitful blog!

So I am writing exams and would like to know how do establish which method of data analysis to use from the below research questions: I am a bit lost as to how I determine the data analysis method from the research questions.

Do female employees report higher job satisfaction than male employees with similar job descriptions across the South African telecommunications sector? – I though that maybe Chi Square could be used here. – Is there a gender difference in talented employees’ actual turnover decisions across the South African telecommunications sector? T-tests or Correlation in this one. – Is there a gender difference in the cost of actual turnover decisions across the South African telecommunications sector? T-tests or Correlation in this one. – What practical recommendations can be made to the management of South African telecommunications companies on leveraging gender to mitigate employee turnover decisions?

Your assistance will be appreciated if I could get a response as early as possible tomorrow

This was quite helpful. Thank you so much.

wow I got a lot from this article, thank you very much, keep it up

Thanks for yhe guidance. Can you send me this guidance on my email? To enable offline reading?

Thank you very much, this service is very helpful.

Every novice researcher needs to read this article as it puts things so clear and easy to follow. Its been very helpful.

Wonderful!!!! you explained everything in a way that anyone can learn. Thank you!!

I really enjoyed reading though this. Very easy to follow. Thank you

Many thanks for your useful lecture, I would be really appreciated if you could possibly share with me the PPT of presentation related to Data type?

Thank you very much for sharing, I got much from this article

This is a very informative write-up. Kindly include me in your latest posts.

Very interesting mostly for social scientists

Thank you so much, very helpfull

You’re welcome 🙂

woow, its great, its very informative and well understood because of your way of writing like teaching in front of me in simple languages.

I have been struggling to understand a lot of these concepts. Thank you for the informative piece which is written with outstanding clarity.

very informative article. Easy to understand

Beautiful read, much needed.

Always greet intro and summary. I learn so much from GradCoach

Quite informative. Simple and clear summary.

I thoroughly enjoyed reading your informative and inspiring piece. Your profound insights into this topic truly provide a better understanding of its complexity. I agree with the points you raised, especially when you delved into the specifics of the article. In my opinion, that aspect is often overlooked and deserves further attention.

Absolutely!!! Thank you

Thank you very much for this post. It made me to understand how to do my data analysis.

its nice work and excellent job ,you have made my work easier

Wow! So explicit. Well done.

Submit a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Submit Comment

• Print Friendly

Table of Contents

Types of statistical analysis, importance of statistical analysis, benefits of statistical analysis, statistical analysis process, statistical analysis methods, statistical analysis software, statistical analysis examples, career in statistical analysis, choose the right program, become proficient in statistics today, understanding statistical analysis: techniques and applications.

Statistical analysis is the process of collecting and analyzing data in order to discern patterns and trends. It is a method for removing bias from evaluating data by employing numerical analysis. This technique is useful for collecting the interpretations of research, developing statistical models, and planning surveys and studies.

Statistical analysis is a scientific tool in AI and ML that helps collect and analyze large amounts of data to identify common patterns and trends to convert them into meaningful information. In simple words, statistical analysis is a data analysis tool that helps draw meaningful conclusions from raw and unstructured data. 

The conclusions are drawn using statistical analysis facilitating decision-making and helping businesses make future predictions on the basis of past trends. It can be defined as a science of collecting and analyzing data to identify trends and patterns and presenting them. Statistical analysis involves working with numbers and is used by businesses and other institutions to make use of data to derive meaningful information. 

Given below are the 6 types of statistical analysis:

Descriptive Analysis

Descriptive statistical analysis involves collecting, interpreting, analyzing, and summarizing data to present them in the form of charts, graphs, and tables. Rather than drawing conclusions, it simply makes the complex data easy to read and understand.

Inferential Analysis

The inferential statistical analysis focuses on drawing meaningful conclusions on the basis of the data analyzed. It studies the relationship between different variables or makes predictions for the whole population.

Predictive Analysis

Predictive statistical analysis is a type of statistical analysis that analyzes data to derive past trends and predict future events on the basis of them. It uses machine learning algorithms, data mining , data modelling , and artificial intelligence to conduct the statistical analysis of data.

Prescriptive Analysis

The prescriptive analysis conducts the analysis of data and prescribes the best course of action based on the results. It is a type of statistical analysis that helps you make an informed decision. 

Exploratory Data Analysis

Exploratory analysis is similar to inferential analysis, but the difference is that it involves exploring the unknown data associations. It analyzes the potential relationships within the data. 

Causal Analysis

The causal statistical analysis focuses on determining the cause and effect relationship between different variables within the raw data. In simple words, it determines why something happens and its effect on other variables. This methodology can be used by businesses to determine the reason for failure. 

Statistical analysis eliminates unnecessary information and catalogs important data in an uncomplicated manner, making the monumental work of organizing inputs appear so serene. Once the data has been collected, statistical analysis may be utilized for a variety of purposes. Some of them are listed below:

• The statistical analysis aids in summarizing enormous amounts of data into clearly digestible chunks.
• The statistical analysis aids in the effective design of laboratory, field, and survey investigations.
• Statistical analysis may help with solid and efficient planning in any subject of study.
• Statistical analysis aid in establishing broad generalizations and forecasting how much of something will occur under particular conditions.
• Statistical methods, which are effective tools for interpreting numerical data, are applied in practically every field of study. Statistical approaches have been created and are increasingly applied in physical and biological sciences, such as genetics.
• Statistical approaches are used in the job of a businessman, a manufacturer, and a researcher. Statistics departments can be found in banks, insurance businesses, and government agencies.
• A modern administrator, whether in the public or commercial sector, relies on statistical data to make correct decisions.
• Politicians can utilize statistics to support and validate their claims while also explaining the issues they address.

Become a Data Science & Business Analytics Professional

• 11.5 M Expected New Jobs For Data Science And Analytics
• 28% Annual Job Growth By 2026
• $46K-$100K Average Annual Salary

Post Graduate Program in Data Analytics

• Post Graduate Program certificate and Alumni Association membership
• Exclusive hackathons and Ask me Anything sessions by IBM

Data Analyst

• Industry-recognized Data Analyst Master’s certificate from Simplilearn
• Dedicated live sessions by faculty of industry experts

Here's what learners are saying regarding our programs:

Felix Chong

Project manage , codethink.

After completing this course, I landed a new job & a salary hike of 30%. I now work with Zuhlke Group as a Project Manager.

Gayathri Ramesh

Associate data engineer , publicis sapient.

The course was well structured and curated. The live classes were extremely helpful. They made learning more productive and interactive. The program helped me change my domain from a data analyst to an Associate Data Engineer.

Statistical analysis can be called a boon to mankind and has many benefits for both individuals and organizations. Given below are some of the reasons why you should consider investing in statistical analysis:

• It can help you determine the monthly, quarterly, yearly figures of sales profits, and costs making it easier to make your decisions.
• It can help you make informed and correct decisions.
• It can help you identify the problem or cause of the failure and make corrections. For example, it can identify the reason for an increase in total costs and help you cut the wasteful expenses.
• It can help you conduct market research or analysis and make an effective marketing and sales strategy.
• It helps improve the efficiency of different processes.

Given below are the 5 steps to conduct a statistical analysis that you should follow:

• Step 1: Identify and describe the nature of the data that you are supposed to analyze.
• Step 2: The next step is to establish a relation between the data analyzed and the sample population to which the data belongs. 
• Step 3: The third step is to create a model that clearly presents and summarizes the relationship between the population and the data.
• Step 4: Prove if the model is valid or not.
• Step 5: Use predictive analysis to predict future trends and events likely to happen. 

Although there are various methods used to perform data analysis, given below are the 5 most used and popular methods of statistical analysis:

Mean or average mean is one of the most popular methods of statistical analysis. Mean determines the overall trend of the data and is very simple to calculate. Mean is calculated by summing the numbers in the data set together and then dividing it by the number of data points. Despite the ease of calculation and its benefits, it is not advisable to resort to mean as the only statistical indicator as it can result in inaccurate decision making. 

Standard Deviation

Standard deviation is another very widely used statistical tool or method. It analyzes the deviation of different data points from the mean of the entire data set. It determines how data of the data set is spread around the mean. You can use it to decide whether the research outcomes can be generalized or not. 

Regression is a statistical tool that helps determine the cause and effect relationship between the variables. It determines the relationship between a dependent and an independent variable. It is generally used to predict future trends and events.

Hypothesis Testing

Hypothesis testing can be used to test the validity or trueness of a conclusion or argument against a data set. The hypothesis is an assumption made at the beginning of the research and can hold or be false based on the analysis results. 

Sample Size Determination

Sample size determination or data sampling is a technique used to derive a sample from the entire population, which is representative of the population. This method is used when the size of the population is very large. You can choose from among the various data sampling techniques such as snowball sampling, convenience sampling, and random sampling. 

Everyone can't perform very complex statistical calculations with accuracy making statistical analysis a time-consuming and costly process. Statistical software has become a very important tool for companies to perform their data analysis. The software uses Artificial Intelligence and Machine Learning to perform complex calculations, identify trends and patterns, and create charts, graphs, and tables accurately within minutes. 

Look at the standard deviation sample calculation given below to understand more about statistical analysis.

The weights of 5 pizza bases in cms are as follows:

Calculation of Mean = (9+2+5+4+12)/5 = 32/5 = 6.4

Calculation of mean of squared mean deviation = (6.76+19.36+1.96+5.76+31.36)/5 = 13.04

Sample Variance = 13.04

Standard deviation = √13.04 = 3.611

A Statistical Analyst's career path is determined by the industry in which they work. Anyone interested in becoming a Data Analyst may usually enter the profession and qualify for entry-level Data Analyst positions right out of high school or a certificate program — potentially with a Bachelor's degree in statistics, computer science, or mathematics. Some people go into data analysis from a similar sector such as business, economics, or even the social sciences, usually by updating their skills mid-career with a statistical analytics course.

Statistical Analyst is also a great way to get started in the normally more complex area of data science. A Data Scientist is generally a more senior role than a Data Analyst since it is more strategic in nature and necessitates a more highly developed set of technical abilities, such as knowledge of multiple statistical tools, programming languages, and predictive analytics models.

Aspiring Data Scientists and Statistical Analysts generally begin their careers by learning a programming language such as R or SQL. Following that, they must learn how to create databases, do basic analysis, and make visuals using applications such as Tableau. However, not every Statistical Analyst will need to know how to do all of these things, but if you want to advance in your profession, you should be able to do them all.

Based on your industry and the sort of work you do, you may opt to study Python or R , become an expert at data cleaning, or focus on developing complicated statistical models.

You could also learn a little bit of everything, which might help you take on a leadership role and advance to the position of Senior Data Analyst. A Senior Statistical Analyst with vast and deep knowledge might take on a leadership role leading a team of other Statistical Analysts. Statistical Analysts with extra skill training may be able to advance to Data Scientists or other more senior data analytics positions.

Supercharge your career in AI and ML with Simplilearn's comprehensive courses. Gain the skills and knowledge to transform industries and unleash your true potential. Enroll now and unlock limitless possibilities!

Program Name AI Engineer Post Graduate Program In Artificial Intelligence Post Graduate Program In Artificial Intelligence Geo All Geos All Geos IN/ROW University Simplilearn Purdue Caltech Course Duration 11 Months 11 Months 11 Months Coding Experience Required Basic Basic No Skills You Will Learn 10+ skills including data structure, data manipulation, NumPy, Scikit-Learn, Tableau and more. 16+ skills including chatbots, NLP, Python, Keras and more. 8+ skills including Supervised & Unsupervised Learning Deep Learning Data Visualization, and more. Additional Benefits Get access to exclusive Hackathons, Masterclasses and Ask-Me-Anything sessions by IBM Applied learning via 3 Capstone and 12 Industry-relevant Projects Purdue Alumni Association Membership Free IIMJobs Pro-Membership of 6 months Resume Building Assistance Upto 14 CEU Credits Caltech CTME Circle Membership Cost $$ $$$$ $$$$ Explore Program Explore Program Explore Program

Hope this article assisted you in understanding the importance of statistical analysis in every sphere of life. Artificial Intelligence (AI) can help you perform statistical analysis and data analysis very effectively and efficiently. 

If you are a science wizard and fascinated by statistical analysis, check out this amazing Post Graduate Program In Data Analytics in collaboration with Purdue. With a comprehensive syllabus and real-life projects, this course is one of the most popular courses and will help you with all that you need to know about Artificial Intelligence. 

Data Science & Business Analytics Courses Duration and Fees

Data Science & Business Analytics programs typically range from a few weeks to several months, with fees varying based on program and institution.

Get Free Certifications with free video courses

Data Science & Business Analytics

Introduction to Data Analytics Course

Introduction to Data Science

Learn from Industry Experts with free Masterclasses

How Can You Master the Art of Data Analysis: Uncover the Path to Career Advancement

Develop Your Career in Data Analytics with Purdue University Professional Certificate

Career Masterclass: How to Get Qualified for a Data Analytics Career

Recommended Reads

Free eBook: Guide To The CCBA And CBAP Certifications

Understanding Statistical Process Control (SPC) and Top Applications

A Complete Guide on the Types of Statistical Studies

Digital Marketing Salary Guide 2021

What Is Data Analysis: A Comprehensive Guide

What Is Exploratory Data Analysis? Steps and Market Analysis

Get Affiliated Certifications with Live Class programs

• PMP, PMI, PMBOK, CAPM, PgMP, PfMP, ACP, PBA, RMP, SP, and OPM3 are registered marks of the Project Management Institute, Inc.

• Search Search Please fill out this field.
• Understanding QA
• Quantitative vs. Qualitative Analysis

Example of Quantitative Analysis in Finance

Drawbacks and limitations of quantitative analaysis, using quantitative finance outside of finance, the bottom line.

• Quantitative Analysis

Quantitative Analysis (QA): What It Is and How It's Used in Finance

Ariel Courage is an experienced editor, researcher, and former fact-checker. She has performed editing and fact-checking work for several leading finance publications, including The Motley Fool and Passport to Wall Street.

Investopedia / Hilary Allison

Quantitative analysis (QA) refers to methods used to understand the behavior of financial markets and make more informed investment or trading decisions. It involves the use of mathematical and statistical techniques to analyze financial data. For instance, by examining past stock prices, earnings reports, and other information, quantitative analysts, often called “ quants ,” aim to forecast where the market is headed.

Unlike fundamental analysis that might focus on a company's management team or industry conditions, quantitative analysis relies chiefly on crunching numbers and complex computations to derive actionable insights.

Quantitative analysis can be a powerful tool, especially in modern markets where data is abundant and computational tools are advanced, enabling a more precise examination of the financial landscape. However, many also believe that the raw numbers produced by quantitative analysis should be combined with the more in-depth understanding and nuance afforded by qualitative analysis .

Key Takeaways

• Quantitative analysis (QA) is a set of techniques that use mathematical and statistical modeling, measurement, and research to understand behavior.
• Quantitative analysis presents financial information in terms of a numerical value.
• It's used for the evaluation of financial instruments and for predicting real-world events such as changes in GDP.
• While powerful, quantitative analysis has some drawbacks that can be supplemented with qualitative analysis.

Understanding Quantitative Analysis

Quantitative analysis (QA) in finance refers to the use of mathematical and statistical techniques to analyze financial & economic data and make trading, investing, and risk management decisions.

QA starts with data collection, where quants gather a vast amount of financial data that might affect the market. This data can include anything from stock prices and company earnings to economic indicators like inflation or unemployment rates. They then use various mathematical models and statistical techniques to analyze this data, looking for trends, patterns, and potential investment opportunities. The outcome of this analysis can help investors decide where to allocate their resources to maximize returns or minimize risks.

Some key aspects of quantitative analysis in finance include:

• Statistical analysis - this aspect of quantitative analysis involves examining data to identify trends and relationships, build predictive models, and make forecasts. Techniques used can include regression analysis , which helps in understanding relationships between variables; time series analysis , which looks at data points collected or recorded at a specific time; and Monte Carlo simulations , a mathematical technique that allows you to account for uncertainty in your analyses and forecasts. Through statistical analysis, quants can uncover insights that may not be immediately apparent, helping investors and financial analysts make more informed decisions.
• Algorithmic trading - this entails using computer algorithms to automate the trading process. Algorithms can be programmed to carry out trades based on a variety of factors such as timing, price movements, liquidity changes, and other market signals. High-frequency trading (HFT), a type of algorithmic trading, involves making a large number of trades within fractions of a second to capitalize on small price movements. This automated approach to trading can lead to more efficient and often profitable trading strategies.
• Risk modeling - risk is an inherent part of financial markets. Risk modeling involves creating mathematical models to measure and quantify various risk exposures within a portfolio. Methods used in risk modeling include Value-at-Risk (VaR) models, scenario analysis , and stress testing . These tools help in understanding the potential downside and uncertainties associated with different investment scenarios, aiding in better risk management and mitigation strategies.
• Derivatives pricing - derivatives are financial contracts whose value is derived from other underlying assets like stocks or bonds. Derivatives pricing involves creating mathematical models to evaluate these contracts and determine their fair prices and risk profiles. A well-known model used in this domain is the Black-Scholes model , which helps in pricing options contracts . Accurate derivatives pricing is crucial for investors and traders to make sound financial decisions regarding buying, selling, or hedging with derivatives.
• Portfolio optimization - This is about constructing a portfolio in such a way that it yields the highest possible expected return for a given level of risk. Techniques like Modern Portfolio Theory (MPT) are employed to find the optimal allocation of assets within a portfolio. By analyzing various asset classes and their expected returns, risks, and correlations, quants can suggest the best mix of investments to achieve specific financial goals while minimizing risk.

The overall goal is to use data, math, statistics, and software to make more informed financial decisions, automate processes, and ultimately generate greater risk-adjusted returns.

Quantitative analysis is widely used in central banking, algorithmic trading, hedge fund management, and investment banking activities. Quantitative analysts, employ advanced skills in programming, statistics, calculus, linear algebra etc. to execute quantitative analysis.

Quantitative Analysis vs. Qualitative Analysis

Quantitative analysis relies heavily on numerical data and mathematical models to make decisions regarding investments and financial strategies. It focuses on the measurable, objective data that can be gathered about a company or a financial instrument.

But analysts also evaluate information that is not easily quantifiable or reduced to numeric values to get a better picture of a company's performance. This important qualitative data can include reputation, regulatory insights, or employee morale. Qualitative analysis thus focuses more on understanding the underlying qualities of a company or a financial instrument, which may not be immediately quantifiable.

Quantitative isn't the opposite of qualitative analysis. They're different and often complementary philosophies. They each provide useful information for informed decisions. When used together. better decisions can be made than using either one in isolation.

Some common uses of qualitative analysis include:

• Management Evaluation: Qualitative analysis is often better at evaluating a company's management team, their experience, and their ability to lead the company toward growth. While quantifiable metrics are useful, they often cannot capture the full picture of management's ability and potential. For example, the leadership skills, vision, and corporate culture instilled by management are intangible factors that can significantly impact a company's success, yet are difficult to measure with numbers alone.
• Industry Analysis: It also includes an analysis of the industry in which the company operates, the competition, and market conditions. For instance, it can explore how changes in technology or societal behaviors could impact the industry. Qualitative approaches can also better identify barriers to entry or exit, which can affect the level of competition and profitability within the industry.
• Brand Value and Company Reputation: The reputation of a company, its brand value, and customer loyalty are also significant factors considered in qualitative analysis. Understanding how consumers perceive the brand, their level of trust, and satisfaction can provide insights into customer loyalty and the potential for sustained revenue. This can be done through focus groups, surveys, or interviews.
• Regulatory Environment: The regulatory environment, potential legal issues, and other external factors that could impact a company are also analyzed qualitatively. Evaluating a company's compliance with relevant laws, regulations, and industry standards to ascertain its legal standing and the potential risk of legal issues. In addition, understanding a company's ethical practices and social responsibility initiatives, that can influence its relationship with stakeholders and the community at large.

Suppose you are interested in investing in a particular company, XYZ Inc. One way to evaluate its potential as an investment is by analyzing its past financial performance using quantitative analysis. Let's say, over the past five years, XYZ Inc. has been growing its revenue at an average rate of 8% per year. You decide to use regression analysis to forecast its future revenue growth. Regression analysis is a statistical method used to examine the relationship between variables.

After collecting the necessary data, you run a simple linear regression with the year as the independent variable and the revenue as the dependent variable. The output gives you a regression equation, let's say, R e v e n u e = 100 + 8 ( Y e a r ) Revenue=100+8(Year) R e v e n u e = 100 + 8 ( Y e a r ) . This equation suggests that for every year, the revenue of XYZ Inc. increases by $8 million, starting from a base of $100 million. This quantitative insight could be instrumental in helping you decide whether XYZ Inc. represents a good investment opportunity based on its historical revenue growth trend.

However, while you can quantify revenue growth for the firm and make predictions, the reasons for why may not be apparent from quantitative number crunching.

Augmenting with Qualitative Analysis

Qualitative analysis can provide a more nuanced understanding of XYZ Inc.'s potential. You decide to delve into the company's management and industry reputation. Through interviews, reviews, and industry reports, you find that the management team at XYZ Inc. is highly regarded with a track record of successful ventures. Moreover, the company has a strong brand value and a loyal customer base.

Additionally, you assess the industry in which XYZ Inc. operates and find it to be stable with a steady demand for the products that XYZ Inc. offers. The regulatory environment is also favorable, and the company has a good relationship with the local communities in which it operates.

By analyzing these qualitative factors, you obtain a more comprehensive understanding of the company's operational environment, the competence of its management team, and its reputation in the market. This qualitative insight complements the quantitative analysis, providing you with a well-rounded view of XYZ Inc.'s investment potential.

Combining both quantitative and qualitative analyses could therefore lead to a more informed investment decision regarding XYZ Inc.

Quantitative analysis, while powerful, comes with certain limitations:

• Data Dependency: Quantitative analysis is heavily dependent on the quality and availability of numerical data. If the data is inaccurate, outdated, or incomplete, the analysis and the subsequent conclusions drawn will be flawed. As they say, 'garbage-in, garbage-out'.
• Complexity: The methods and models used in quantitative analysis can be very complex, requiring a high level of expertise to develop, interpret, and act upon. This complexity can also make it difficult to communicate findings to individuals who lack a quantitative background.
• Lack of Subjectivity: Quantitative analysis often overlooks qualitative factors like management quality, brand reputation, and other subjective factors that can significantly affect a company's performance or a financial instrument's value. In other words, you may have the 'what' without the 'why' or 'how.' Qualitative analysis can augment this blind spot.
• Assumption-based Modeling: Many quantitative models are built on assumptions that may not hold true in real-world situations. For example, assumptions about normal distribution of returns or constant volatility may not reflect actual market conditions.
• Over-reliance on Historical Data: Quantitative analysis often relies heavily on historical data to make predictions about the future. However, past performance is not always indicative of future results, especially in rapidly changing markets or unforeseen situations like economic crises.
• Inability to Capture Human Emotion and Behavior: Markets are often influenced by human emotions and behaviors which can be erratic and hard to predict. Quantitative analysis, being number-driven, struggles to properly account for these human factors.
• Cost and Time Intensive: Developing accurate and reliable quantitative models can be time-consuming and expensive. It requires skilled personnel, sophisticated software tools, and often, extensive computational resources.
• Overfitting: There's a risk of overfitting , where a model might perform exceedingly well on past data but fails to predict future outcomes accurately because it's too tailored to past events.
• Lack of Flexibility: Quantitative models may lack the flexibility to adapt to new information or changing market conditions quickly, which can lead to outdated or incorrect analysis.
• Model Risk: There's inherent model risk involved where the model itself may have flaws or errors that can lead to incorrect analysis and potentially significant financial losses.

Understanding these drawbacks is crucial for analysts and decision-makers to interpret quantitative analysis results accurately and to balance them with qualitative insights for more holistic decision-making.

Quantitative analysis is a versatile tool that extends beyond the realm of finance into a variety of fields. In the domain of social sciences, for instance, it's used to analyze behavioral patterns, social trends, and the impact of policies on different demographics. Researchers employ statistical models to examine large datasets, enabling them to identify correlations, causations, and trends that can provide a deeper understanding of human behaviors and societal dynamics. Similarly, in the field of public policy, quantitative analysis plays a crucial role in evaluating the effectiveness of different policies, analyzing economic indicators, and forecasting the potential impacts of policy changes. By providing a method to measure and analyze data, it aids policymakers in making informed decisions based on empirical evidence.

In the arena of healthcare, quantitative analysis is employed for clinical trials, genetic research, and epidemiological studies to name a few areas. It assists in analyzing patient data, evaluating treatment outcomes, and understanding disease spread and its determinants. Meanwhile, in engineering and manufacturing, it's used to optimize processes, improve quality control, and enhance operational efficiency. By analyzing data related to production processes, material properties, and operational performance, engineers can identify bottlenecks, optimize workflows, and ensure the reliability and quality of products. Additionally, in the field of marketing, quantitative analysis is fundamental for market segmentation, advertising effectiveness, and consumer satisfaction studies. It helps marketers understand consumer preferences, the impact of advertising campaigns, and the market potential for new products. Through these diverse applications, quantitative analysis serves as a bedrock for data-driven decision-making, enabling professionals across different fields to derive actionable insights from complex data.

What Is Quantitative Analysis Used for in Finance?

Quantitative analysis is used by governments, investors, and businesses (in areas such as finance, project management, production planning, and marketing) to study a certain situation or event, measure it, predict outcomes, and thus help in decision-making. In finance, it's widely used for assessing investment opportunities and risks. For instance, before venturing into investments, analysts rely on quantitative analysis to understand the performance metrics of different financial instruments such as stocks, bonds, and derivatives. By delving into historical data and employing mathematical and statistical models, they can forecast potential future performance and evaluate the underlying risks. This practice isn't just confined to individual assets; it's also essential for portfolio management. By examining the relationships between different assets and assessing their risk and return profiles, investors can construct portfolios that are optimized for the highest possible returns for a given level of risk.

What Kind of Education Do You Need to Be a Quant?

Individuals pursuing a career in quantitative analysis usually have a strong educational background in quantitative fields like mathematics, statistics, computer science, finance, economics, or engineering. Advanced degrees (Master’s or Ph.D.) in quantitative disciplines are often preferred, and additional coursework or certifications in finance and programming can also be beneficial.

What Is the Difference Between Quantitative Analysis and Fundamental Analysis?

While both rely on the use of math and numbers, fundamental analysis takes a broader approach by examining the intrinsic value of a security. It dives into a company's financial statements, industry position, the competence of the management team, and the economic environment in which it operates. By evaluating factors like earnings, dividends, and the financial health of a company, fundamental analysts aim to ascertain the true value of a security and whether it is undervalued or overvalued in the market. This form of analysis is more holistic and requires a deep understanding of the company and the industry in which it operates.

How Does Artificial Intelligence (AI) Influence Quantitative Analysis?

Quantitative analysis often intersects with machine learning (ML) and other forms of artificial intelligence (AI). ML and AI can be employed to develop predictive models and algorithms based on the quantitative data. These technologies can automate the analysis process, handle large datasets, and uncover complex patterns or trends that might be difficult to detect through traditional quantitative methods.

Quantitative analysis is a mathematical approach that collects and evaluates measurable and verifiable data in order to evaluate performance, make better decisions, and predict trends. Unlike qualitative analysis, quantitative analysis uses numerical data to provide an explanation of "what" happened, but not "why" those events occurred.

DeFusco, R. A., McLeavey, D. W., Pinto, J. E., Runkle, D. E., & Anson, M. J. (2015). Quantitative investment analysis . John Wiley & Sons.

University of Sydney. " On Becoming a Quant ," Page 1

Linsmeier, Thomas J., and Neil D. Pearson. " Value at risk ." Financial analysts journal 56, no. 2 (2000): 47-67.

Fischer, Black, and Myron Scholes, " The Pricing of Options and Corporate Liabilities ." Journal of Political Economy, vol. 81, no. 3, 1974, pp. 637-654.

Francis, J. C., & Kim, D. (2013). Modern portfolio theory: Foundations, analysis, and new developments . John Wiley & Sons.

Kaczynski, D., Salmona, M., & Smith, T. (2014). " Qualitative research in finance ." Australian Journal of Management , 39 (1), 127-135.

• Terms of Service
• Editorial Policy
• Privacy Policy

Frequently asked questions

What is statistical analysis.

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

Frequently asked questions: Statistics

As the degrees of freedom increase, Student’s t distribution becomes less leptokurtic , meaning that the probability of extreme values decreases. The distribution becomes more and more similar to a standard normal distribution .

The three categories of kurtosis are:

• Mesokurtosis : An excess kurtosis of 0. Normal distributions are mesokurtic.
• Platykurtosis : A negative excess kurtosis. Platykurtic distributions are thin-tailed, meaning that they have few outliers .
• Leptokurtosis : A positive excess kurtosis. Leptokurtic distributions are fat-tailed, meaning that they have many outliers.

Probability distributions belong to two broad categories: discrete probability distributions and continuous probability distributions . Within each category, there are many types of probability distributions.

Probability is the relative frequency over an infinite number of trials.

For example, the probability of a coin landing on heads is .5, meaning that if you flip the coin an infinite number of times, it will land on heads half the time.

Since doing something an infinite number of times is impossible, relative frequency is often used as an estimate of probability. If you flip a coin 1000 times and get 507 heads, the relative frequency, .507, is a good estimate of the probability.

Categorical variables can be described by a frequency distribution. Quantitative variables can also be described by a frequency distribution, but first they need to be grouped into interval classes .

A histogram is an effective way to tell if a frequency distribution appears to have a normal distribution .

Plot a histogram and look at the shape of the bars. If the bars roughly follow a symmetrical bell or hill shape, like the example below, then the distribution is approximately normally distributed.

You can use the CHISQ.INV.RT() function to find a chi-square critical value in Excel.

For example, to calculate the chi-square critical value for a test with df = 22 and α = .05, click any blank cell and type:

=CHISQ.INV.RT(0.05,22)

You can use the qchisq() function to find a chi-square critical value in R.

For example, to calculate the chi-square critical value for a test with df = 22 and α = .05:

qchisq(p = .05, df = 22, lower.tail = FALSE)

You can use the chisq.test() function to perform a chi-square test of independence in R. Give the contingency table as a matrix for the “x” argument. For example:

m = matrix(data = c(89, 84, 86, 9, 8, 24), nrow = 3, ncol = 2)

chisq.test(x = m)

You can use the CHISQ.TEST() function to perform a chi-square test of independence in Excel. It takes two arguments, CHISQ.TEST(observed_range, expected_range), and returns the p value.

Chi-square goodness of fit tests are often used in genetics. One common application is to check if two genes are linked (i.e., if the assortment is independent). When genes are linked, the allele inherited for one gene affects the allele inherited for another gene.

Suppose that you want to know if the genes for pea texture (R = round, r = wrinkled) and color (Y = yellow, y = green) are linked. You perform a dihybrid cross between two heterozygous ( RY / ry ) pea plants. The hypotheses you’re testing with your experiment are:

• This would suggest that the genes are unlinked.
• This would suggest that the genes are linked.

You observe 100 peas:

• 78 round and yellow peas
• 6 round and green peas
• 4 wrinkled and yellow peas
• 12 wrinkled and green peas

Step 1: Calculate the expected frequencies

To calculate the expected values, you can make a Punnett square. If the two genes are unlinked, the probability of each genotypic combination is equal.

The expected phenotypic ratios are therefore 9 round and yellow: 3 round and green: 3 wrinkled and yellow: 1 wrinkled and green.

From this, you can calculate the expected phenotypic frequencies for 100 peas:

Step 2: Calculate chi-square

Χ 2 = 8.41 + 8.67 + 11.6 + 5.4 = 34.08

Step 3: Find the critical chi-square value

Since there are four groups (round and yellow, round and green, wrinkled and yellow, wrinkled and green), there are three degrees of freedom .

For a test of significance at α = .05 and df = 3, the Χ 2 critical value is 7.82.

Step 4: Compare the chi-square value to the critical value

Χ 2 = 34.08

Critical value = 7.82

The Χ 2 value is greater than the critical value .

Step 5: Decide whether the reject the null hypothesis

The Χ 2 value is greater than the critical value, so we reject the null hypothesis that the population of offspring have an equal probability of inheriting all possible genotypic combinations. There is a significant difference between the observed and expected genotypic frequencies ( p < .05).

The data supports the alternative hypothesis that the offspring do not have an equal probability of inheriting all possible genotypic combinations, which suggests that the genes are linked

You can use the chisq.test() function to perform a chi-square goodness of fit test in R. Give the observed values in the “x” argument, give the expected values in the “p” argument, and set “rescale.p” to true. For example:

chisq.test(x = c(22,30,23), p = c(25,25,25), rescale.p = TRUE)

You can use the CHISQ.TEST() function to perform a chi-square goodness of fit test in Excel. It takes two arguments, CHISQ.TEST(observed_range, expected_range), and returns the p value .

Both correlations and chi-square tests can test for relationships between two variables. However, a correlation is used when you have two quantitative variables and a chi-square test of independence is used when you have two categorical variables.

Both chi-square tests and t tests can test for differences between two groups. However, a t test is used when you have a dependent quantitative variable and an independent categorical variable (with two groups). A chi-square test of independence is used when you have two categorical variables.

The two main chi-square tests are the chi-square goodness of fit test and the chi-square test of independence .

A chi-square distribution is a continuous probability distribution . The shape of a chi-square distribution depends on its degrees of freedom , k . The mean of a chi-square distribution is equal to its degrees of freedom ( k ) and the variance is 2 k . The range is 0 to ∞.

As the degrees of freedom ( k ) increases, the chi-square distribution goes from a downward curve to a hump shape. As the degrees of freedom increases further, the hump goes from being strongly right-skewed to being approximately normal.

To find the quartiles of a probability distribution, you can use the distribution’s quantile function.

You can use the quantile() function to find quartiles in R. If your data is called “data”, then “quantile(data, prob=c(.25,.5,.75), type=1)” will return the three quartiles.

You can use the QUARTILE() function to find quartiles in Excel. If your data is in column A, then click any blank cell and type “=QUARTILE(A:A,1)” for the first quartile, “=QUARTILE(A:A,2)” for the second quartile, and “=QUARTILE(A:A,3)” for the third quartile.

You can use the PEARSON() function to calculate the Pearson correlation coefficient in Excel. If your variables are in columns A and B, then click any blank cell and type “PEARSON(A:A,B:B)”.

There is no function to directly test the significance of the correlation.

You can use the cor() function to calculate the Pearson correlation coefficient in R. To test the significance of the correlation, you can use the cor.test() function.

You should use the Pearson correlation coefficient when (1) the relationship is linear and (2) both variables are quantitative and (3) normally distributed and (4) have no outliers.

The Pearson correlation coefficient ( r ) is the most common way of measuring a linear correlation. It is a number between –1 and 1 that measures the strength and direction of the relationship between two variables.

This table summarizes the most important differences between normal distributions and Poisson distributions :

When the mean of a Poisson distribution is large (>10), it can be approximated by a normal distribution.

In the Poisson distribution formula, lambda (λ) is the mean number of events within a given interval of time or space. For example, λ = 0.748 floods per year.

The e in the Poisson distribution formula stands for the number 2.718. This number is called Euler’s constant. You can simply substitute e with 2.718 when you’re calculating a Poisson probability. Euler’s constant is a very useful number and is especially important in calculus.

The three types of skewness are:

• Right skew (also called positive skew ) . A right-skewed distribution is longer on the right side of its peak than on its left.
• Left skew (also called negative skew). A left-skewed distribution is longer on the left side of its peak than on its right.
• Zero skew. It is symmetrical and its left and right sides are mirror images.

Skewness and kurtosis are both important measures of a distribution’s shape.

• Skewness measures the asymmetry of a distribution.
• Kurtosis measures the heaviness of a distribution’s tails relative to a normal distribution .

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The t distribution was first described by statistician William Sealy Gosset under the pseudonym “Student.”

To calculate a confidence interval of a mean using the critical value of t , follow these four steps:

• Choose the significance level based on your desired confidence level. The most common confidence level is 95%, which corresponds to α = .05 in the two-tailed t table .
• Find the critical value of t in the two-tailed t table.
• Multiply the critical value of t by s / √ n .
• Add this value to the mean to calculate the upper limit of the confidence interval, and subtract this value from the mean to calculate the lower limit.

To test a hypothesis using the critical value of t , follow these four steps:

• Calculate the t value for your sample.
• Find the critical value of t in the t table .
• Determine if the (absolute) t value is greater than the critical value of t .
• Reject the null hypothesis if the sample’s t value is greater than the critical value of t . Otherwise, don’t reject the null hypothesis .

You can use the T.INV() function to find the critical value of t for one-tailed tests in Excel, and you can use the T.INV.2T() function for two-tailed tests.

You can use the qt() function to find the critical value of t in R. The function gives the critical value of t for the one-tailed test. If you want the critical value of t for a two-tailed test, divide the significance level by two.

You can use the RSQ() function to calculate R² in Excel. If your dependent variable is in column A and your independent variable is in column B, then click any blank cell and type “RSQ(A:A,B:B)”.

You can use the summary() function to view the R²  of a linear model in R. You will see the “R-squared” near the bottom of the output.

There are two formulas you can use to calculate the coefficient of determination (R²) of a simple linear regression .

The coefficient of determination (R²) is a number between 0 and 1 that measures how well a statistical model predicts an outcome. You can interpret the R² as the proportion of variation in the dependent variable that is predicted by the statistical model.

There are three main types of missing data .

Missing completely at random (MCAR) data are randomly distributed across the variable and unrelated to other variables .

Missing at random (MAR) data are not randomly distributed but they are accounted for by other observed variables.

Missing not at random (MNAR) data systematically differ from the observed values.

To tidy up your missing data , your options usually include accepting, removing, or recreating the missing data.

• Acceptance: You leave your data as is
• Listwise or pairwise deletion: You delete all cases (participants) with missing data from analyses
• Imputation: You use other data to fill in the missing data

Missing data are important because, depending on the type, they can sometimes bias your results. This means your results may not be generalizable outside of your study because your data come from an unrepresentative sample .

Missing data , or missing values, occur when you don’t have data stored for certain variables or participants.

In any dataset, there’s usually some missing data. In quantitative research , missing values appear as blank cells in your spreadsheet.

There are two steps to calculating the geometric mean :

• Multiply all values together to get their product.
• Find the n th root of the product ( n is the number of values).

Before calculating the geometric mean, note that:

• The geometric mean can only be found for positive values.
• If any value in the data set is zero, the geometric mean is zero.

The arithmetic mean is the most commonly used type of mean and is often referred to simply as “the mean.” While the arithmetic mean is based on adding and dividing values, the geometric mean multiplies and finds the root of values.

Even though the geometric mean is a less common measure of central tendency , it’s more accurate than the arithmetic mean for percentage change and positively skewed data. The geometric mean is often reported for financial indices and population growth rates.

The geometric mean is an average that multiplies all values and finds a root of the number. For a dataset with n numbers, you find the n th root of their product.

Outliers are extreme values that differ from most values in the dataset. You find outliers at the extreme ends of your dataset.

It’s best to remove outliers only when you have a sound reason for doing so.

Some outliers represent natural variations in the population , and they should be left as is in your dataset. These are called true outliers.

Other outliers are problematic and should be removed because they represent measurement errors , data entry or processing errors, or poor sampling.

You can choose from four main ways to detect outliers :

• Sorting your values from low to high and checking minimum and maximum values
• Visualizing your data with a box plot and looking for outliers
• Using the interquartile range to create fences for your data
• Using statistical procedures to identify extreme values

Outliers can have a big impact on your statistical analyses and skew the results of any hypothesis test if they are inaccurate.

These extreme values can impact your statistical power as well, making it hard to detect a true effect if there is one.

No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.

To find the slope of the line, you’ll need to perform a regression analysis .

Correlation coefficients always range between -1 and 1.

The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.

The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.

These are the assumptions your data must meet if you want to use Pearson’s r :

• Both variables are on an interval or ratio level of measurement
• Data from both variables follow normal distributions
• Your data have no outliers
• Your data is from a random or representative sample
• You expect a linear relationship between the two variables

A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.

Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.

There are various ways to improve power:

• Increase the potential effect size by manipulating your independent variable more strongly,
• Increase sample size,
• Increase the significance level (alpha),
• Reduce measurement error by increasing the precision and accuracy of your measurement devices and procedures,
• Use a one-tailed test instead of a two-tailed test for t tests and z tests.

A power analysis is a calculation that helps you determine a minimum sample size for your study. It’s made up of four main components. If you know or have estimates for any three of these, you can calculate the fourth component.

• Statistical power : the likelihood that a test will detect an effect of a certain size if there is one, usually set at 80% or higher.
• Sample size : the minimum number of observations needed to observe an effect of a certain size with a given power level.
• Significance level (alpha) : the maximum risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Expected effect size : a standardized way of expressing the magnitude of the expected result of your study, usually based on similar studies or a pilot study.

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

The risk of making a Type II error is inversely related to the statistical power of a test. Power is the extent to which a test can correctly detect a real effect when there is one.

To (indirectly) reduce the risk of a Type II error, you can increase the sample size or the significance level to increase statistical power.

The risk of making a Type I error is the significance level (or alpha) that you choose. That’s a value that you set at the beginning of your study to assess the statistical probability of obtaining your results ( p value ).

The significance level is usually set at 0.05 or 5%. This means that your results only have a 5% chance of occurring, or less, if the null hypothesis is actually true.

To reduce the Type I error probability, you can set a lower significance level.

In statistics, a Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s actually false.

In statistics, power refers to the likelihood of a hypothesis test detecting a true effect if there is one. A statistically powerful test is more likely to reject a false negative (a Type II error).

If you don’t ensure enough power in your study, you may not be able to detect a statistically significant result even when it has practical significance. Your study might not have the ability to answer your research question.

While statistical significance shows that an effect exists in a study, practical significance shows that the effect is large enough to be meaningful in the real world.

Statistical significance is denoted by p -values whereas practical significance is represented by effect sizes .

There are dozens of measures of effect sizes . The most common effect sizes are Cohen’s d and Pearson’s r . Cohen’s d measures the size of the difference between two groups while Pearson’s r measures the strength of the relationship between two variables .

Effect size tells you how meaningful the relationship between variables or the difference between groups is.

A large effect size means that a research finding has practical significance, while a small effect size indicates limited practical applications.

Using descriptive and inferential statistics , you can make two types of estimates about the population : point estimates and interval estimates.

• A point estimate is a single value estimate of a parameter . For instance, a sample mean is a point estimate of a population mean.
• An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate.

Both types of estimates are important for gathering a clear idea of where a parameter is likely to lie.

Standard error and standard deviation are both measures of variability . The standard deviation reflects variability within a sample, while the standard error estimates the variability across samples of a population.

The standard error of the mean , or simply standard error , indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.

To figure out whether a given number is a parameter or a statistic , ask yourself the following:

• Does the number describe a whole, complete population where every member can be reached for data collection ?
• Is it possible to collect data for this number from every member of the population in a reasonable time frame?

If the answer is yes to both questions, the number is likely to be a parameter. For small populations, data can be collected from the whole population and summarized in parameters.

If the answer is no to either of the questions, then the number is more likely to be a statistic.

The arithmetic mean is the most commonly used mean. It’s often simply called the mean or the average. But there are some other types of means you can calculate depending on your research purposes:

• Weighted mean: some values contribute more to the mean than others.
• Geometric mean : values are multiplied rather than summed up.
• Harmonic mean: reciprocals of values are used instead of the values themselves.

You can find the mean , or average, of a data set in two simple steps:

• Find the sum of the values by adding them all up.
• Divide the sum by the number of values in the data set.

This method is the same whether you are dealing with sample or population data or positive or negative numbers.

The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.

Because the median only uses one or two values, it’s unaffected by extreme outliers or non-symmetric distributions of scores. In contrast, the mean and mode can vary in skewed distributions.

To find the median , first order your data. Then calculate the middle position based on n , the number of values in your data set.

A data set can often have no mode, one mode or more than one mode – it all depends on how many different values repeat most frequently.

Your data can be:

• without any mode
• unimodal, with one mode,
• bimodal, with two modes,
• trimodal, with three modes, or
• multimodal, with four or more modes.

To find the mode :

• If your data is numerical or quantitative, order the values from low to high.
• If it is categorical, sort the values by group, in any order.

Then you simply need to identify the most frequently occurring value.

The interquartile range is the best measure of variability for skewed distributions or data sets with outliers. Because it’s based on values that come from the middle half of the distribution, it’s unlikely to be influenced by outliers .

The two most common methods for calculating interquartile range are the exclusive and inclusive methods.

The exclusive method excludes the median when identifying Q1 and Q3, while the inclusive method includes the median as a value in the data set in identifying the quartiles.

For each of these methods, you’ll need different procedures for finding the median, Q1 and Q3 depending on whether your sample size is even- or odd-numbered. The exclusive method works best for even-numbered sample sizes, while the inclusive method is often used with odd-numbered sample sizes.

While the range gives you the spread of the whole data set, the interquartile range gives you the spread of the middle half of a data set.

Homoscedasticity, or homogeneity of variances, is an assumption of equal or similar variances in different groups being compared.

This is an important assumption of parametric statistical tests because they are sensitive to any dissimilarities. Uneven variances in samples result in biased and skewed test results.

Statistical tests such as variance tests or the analysis of variance (ANOVA) use sample variance to assess group differences of populations. They use the variances of the samples to assess whether the populations they come from significantly differ from each other.

Variance is the average squared deviations from the mean, while standard deviation is the square root of this number. Both measures reflect variability in a distribution, but their units differ:

• Standard deviation is expressed in the same units as the original values (e.g., minutes or meters).
• Variance is expressed in much larger units (e.g., meters squared).

Although the units of variance are harder to intuitively understand, variance is important in statistical tests .

The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution :

• Around 68% of values are within 1 standard deviation of the mean.
• Around 95% of values are within 2 standard deviations of the mean.
• Around 99.7% of values are within 3 standard deviations of the mean.

The empirical rule is a quick way to get an overview of your data and check for any outliers or extreme values that don’t follow this pattern.

In a normal distribution , data are symmetrically distributed with no skew. Most values cluster around a central region, with values tapering off as they go further away from the center.

The measures of central tendency (mean, mode, and median) are exactly the same in a normal distribution.

The standard deviation is the average amount of variability in your data set. It tells you, on average, how far each score lies from the mean .

In normal distributions, a high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.

No. Because the range formula subtracts the lowest number from the highest number, the range is always zero or a positive number.

In statistics, the range is the spread of your data from the lowest to the highest value in the distribution. It is the simplest measure of variability .

While central tendency tells you where most of your data points lie, variability summarizes how far apart your points from each other.

Data sets can have the same central tendency but different levels of variability or vice versa . Together, they give you a complete picture of your data.

Variability is most commonly measured with the following descriptive statistics :

• Range : the difference between the highest and lowest values
• Interquartile range : the range of the middle half of a distribution
• Standard deviation : average distance from the mean
• Variance : average of squared distances from the mean

Variability tells you how far apart points lie from each other and from the center of a distribution or a data set.

Variability is also referred to as spread, scatter or dispersion.

While interval and ratio data can both be categorized, ranked, and have equal spacing between adjacent values, only ratio scales have a true zero.

For example, temperature in Celsius or Fahrenheit is at an interval scale because zero is not the lowest possible temperature. In the Kelvin scale, a ratio scale, zero represents a total lack of thermal energy.

A critical value is the value of the test statistic which defines the upper and lower bounds of a confidence interval , or which defines the threshold of statistical significance in a statistical test. It describes how far from the mean of the distribution you have to go to cover a certain amount of the total variation in the data (i.e. 90%, 95%, 99%).

If you are constructing a 95% confidence interval and are using a threshold of statistical significance of p = 0.05, then your critical value will be identical in both cases.

The t -distribution gives more probability to observations in the tails of the distribution than the standard normal distribution (a.k.a. the z -distribution).

In this way, the t -distribution is more conservative than the standard normal distribution: to reach the same level of confidence or statistical significance , you will need to include a wider range of the data.

A t -score (a.k.a. a t -value) is equivalent to the number of standard deviations away from the mean of the t -distribution .

The t -score is the test statistic used in t -tests and regression tests. It can also be used to describe how far from the mean an observation is when the data follow a t -distribution.

The t -distribution is a way of describing a set of observations where most observations fall close to the mean , and the rest of the observations make up the tails on either side. It is a type of normal distribution used for smaller sample sizes, where the variance in the data is unknown.

The t -distribution forms a bell curve when plotted on a graph. It can be described mathematically using the mean and the standard deviation .

In statistics, ordinal and nominal variables are both considered categorical variables .

Even though ordinal data can sometimes be numerical, not all mathematical operations can be performed on them.

Ordinal data has two characteristics:

• The data can be classified into different categories within a variable.
• The categories have a natural ranked order.

However, unlike with interval data, the distances between the categories are uneven or unknown.

Nominal and ordinal are two of the four levels of measurement . Nominal level data can only be classified, while ordinal level data can be classified and ordered.

Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable. These categories cannot be ordered in a meaningful way.

For example, for the nominal variable of preferred mode of transportation, you may have the categories of car, bus, train, tram or bicycle.

If your confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.

If your confidence interval for a correlation or regression includes zero, that means that if you run your experiment again there is a good chance of finding no correlation in your data.

In both of these cases, you will also find a high p -value when you run your statistical test, meaning that your results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.

If you want to calculate a confidence interval around the mean of data that is not normally distributed , you have two choices:

• Find a distribution that matches the shape of your data and use that distribution to calculate the confidence interval.
• Perform a transformation on your data to make it fit a normal distribution, and then find the confidence interval for the transformed data.

The standard normal distribution , also called the z -distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be converted into the standard normal distribution by turning the individual values into z -scores. In a z -distribution, z -scores tell you how many standard deviations away from the mean each value lies.

The z -score and t -score (aka z -value and t -value) show how many standard deviations away from the mean of the distribution you are, assuming your data follow a z -distribution or a t -distribution .

These scores are used in statistical tests to show how far from the mean of the predicted distribution your statistical estimate is. If your test produces a z -score of 2.5, this means that your estimate is 2.5 standard deviations from the predicted mean.

The predicted mean and distribution of your estimate are generated by the null hypothesis of the statistical test you are using. The more standard deviations away from the predicted mean your estimate is, the less likely it is that the estimate could have occurred under the null hypothesis .

To calculate the confidence interval , you need to know:

• The point estimate you are constructing the confidence interval for
• The critical values for the test statistic
• The standard deviation of the sample
• The sample size

Then you can plug these components into the confidence interval formula that corresponds to your data. The formula depends on the type of estimate (e.g. a mean or a proportion) and on the distribution of your data.

The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way.

The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.

For example, if you are estimating a 95% confidence interval around the mean proportion of female babies born every year based on a random sample of babies, you might find an upper bound of 0.56 and a lower bound of 0.48. These are the upper and lower bounds of the confidence interval. The confidence level is 95%.

The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average.

For data from skewed distributions, the median is better than the mean because it isn’t influenced by extremely large values.

The mode is the only measure you can use for nominal or categorical data that can’t be ordered.

The measures of central tendency you can use depends on the level of measurement of your data.

• For a nominal level, you can only use the mode to find the most frequent value.
• For an ordinal level or ranked data, you can also use the median to find the value in the middle of your data set.
• For interval or ratio levels, in addition to the mode and median, you can use the mean to find the average value.

Measures of central tendency help you find the middle, or the average, of a data set.

The 3 most common measures of central tendency are the mean, median and mode.

• The mode is the most frequent value.
• The median is the middle number in an ordered data set.
• The mean is the sum of all values divided by the total number of values.

Some variables have fixed levels. For example, gender and ethnicity are always nominal level data because they cannot be ranked.

However, for other variables, you can choose the level of measurement . For example, income is a variable that can be recorded on an ordinal or a ratio scale:

• At an ordinal level , you could create 5 income groupings and code the incomes that fall within them from 1–5.
• At a ratio level , you would record exact numbers for income.

If you have a choice, the ratio level is always preferable because you can analyze data in more ways. The higher the level of measurement, the more precise your data is.

The level at which you measure a variable determines how you can analyze your data.

Depending on the level of measurement , you can perform different descriptive statistics to get an overall summary of your data and inferential statistics to see if your results support or refute your hypothesis .

Levels of measurement tell you how precisely variables are recorded. There are 4 levels of measurement, which can be ranked from low to high:

• Nominal : the data can only be categorized.
• Ordinal : the data can be categorized and ranked.
• Interval : the data can be categorized and ranked, and evenly spaced.
• Ratio : the data can be categorized, ranked, evenly spaced and has a natural zero.

No. The p -value only tells you how likely the data you have observed is to have occurred under the null hypothesis .

If the p -value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.

The alpha value, or the threshold for statistical significance , is arbitrary – which value you use depends on your field of study.

In most cases, researchers use an alpha of 0.05, which means that there is a less than 5% chance that the data being tested could have occurred under the null hypothesis.

P -values are usually automatically calculated by the program you use to perform your statistical test. They can also be estimated using p -value tables for the relevant test statistic .

P -values are calculated from the null distribution of the test statistic. They tell you how often a test statistic is expected to occur under the null hypothesis of the statistical test, based on where it falls in the null distribution.

If the test statistic is far from the mean of the null distribution, then the p -value will be small, showing that the test statistic is not likely to have occurred under the null hypothesis.

A p -value , or probability value, is a number describing how likely it is that your data would have occurred under the null hypothesis of your statistical test .

The test statistic you use will be determined by the statistical test.

You can choose the right statistical test by looking at what type of data you have collected and what type of relationship you want to test.

The test statistic will change based on the number of observations in your data, how variable your observations are, and how strong the underlying patterns in the data are.

For example, if one data set has higher variability while another has lower variability, the first data set will produce a test statistic closer to the null hypothesis , even if the true correlation between two variables is the same in either data set.

The formula for the test statistic depends on the statistical test being used.

Generally, the test statistic is calculated as the pattern in your data (i.e. the correlation between variables or difference between groups) divided by the variance in the data (i.e. the standard deviation ).

• Univariate statistics summarize only one variable  at a time.
• Bivariate statistics compare two variables .
• Multivariate statistics compare more than two variables .

The 3 main types of descriptive statistics concern the frequency distribution, central tendency, and variability of a dataset.

• Distribution refers to the frequencies of different responses.
• Measures of central tendency give you the average for each response.
• Measures of variability show you the spread or dispersion of your dataset.

Descriptive statistics summarize the characteristics of a data set. Inferential statistics allow you to test a hypothesis or assess whether your data is generalizable to the broader population.

In statistics, model selection is a process researchers use to compare the relative value of different statistical models and determine which one is the best fit for the observed data.

The Akaike information criterion is one of the most common methods of model selection. AIC weights the ability of the model to predict the observed data against the number of parameters the model requires to reach that level of precision.

AIC model selection can help researchers find a model that explains the observed variation in their data while avoiding overfitting.

In statistics, a model is the collection of one or more independent variables and their predicted interactions that researchers use to try to explain variation in their dependent variable.

You can test a model using a statistical test . To compare how well different models fit your data, you can use Akaike’s information criterion for model selection.

The Akaike information criterion is calculated from the maximum log-likelihood of the model and the number of parameters (K) used to reach that likelihood. The AIC function is 2K – 2(log-likelihood) .

Lower AIC values indicate a better-fit model, and a model with a delta-AIC (the difference between the two AIC values being compared) of more than -2 is considered significantly better than the model it is being compared to.

The Akaike information criterion is a mathematical test used to evaluate how well a model fits the data it is meant to describe. It penalizes models which use more independent variables (parameters) as a way to avoid over-fitting.

AIC is most often used to compare the relative goodness-of-fit among different models under consideration and to then choose the model that best fits the data.

A factorial ANOVA is any ANOVA that uses more than one categorical independent variable . A two-way ANOVA is a type of factorial ANOVA.

Some examples of factorial ANOVAs include:

• Testing the combined effects of vaccination (vaccinated or not vaccinated) and health status (healthy or pre-existing condition) on the rate of flu infection in a population.
• Testing the effects of marital status (married, single, divorced, widowed), job status (employed, self-employed, unemployed, retired), and family history (no family history, some family history) on the incidence of depression in a population.
• Testing the effects of feed type (type A, B, or C) and barn crowding (not crowded, somewhat crowded, very crowded) on the final weight of chickens in a commercial farming operation.

In ANOVA, the null hypothesis is that there is no difference among group means. If any group differs significantly from the overall group mean, then the ANOVA will report a statistically significant result.

Significant differences among group means are calculated using the F statistic, which is the ratio of the mean sum of squares (the variance explained by the independent variable) to the mean square error (the variance left over).

If the F statistic is higher than the critical value (the value of F that corresponds with your alpha value, usually 0.05), then the difference among groups is deemed statistically significant.

The only difference between one-way and two-way ANOVA is the number of independent variables . A one-way ANOVA has one independent variable, while a two-way ANOVA has two.

• One-way ANOVA : Testing the relationship between shoe brand (Nike, Adidas, Saucony, Hoka) and race finish times in a marathon.
• Two-way ANOVA : Testing the relationship between shoe brand (Nike, Adidas, Saucony, Hoka), runner age group (junior, senior, master’s), and race finishing times in a marathon.

All ANOVAs are designed to test for differences among three or more groups. If you are only testing for a difference between two groups, use a t-test instead.

Multiple linear regression is a regression model that estimates the relationship between a quantitative dependent variable and two or more independent variables using a straight line.

Linear regression most often uses mean-square error (MSE) to calculate the error of the model. MSE is calculated by:

• measuring the distance of the observed y-values from the predicted y-values at each value of x;
• squaring each of these distances;
• calculating the mean of each of the squared distances.

Linear regression fits a line to the data by finding the regression coefficient that results in the smallest MSE.

Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.

For example, the relationship between temperature and the expansion of mercury in a thermometer can be modeled using a straight line: as temperature increases, the mercury expands. This linear relationship is so certain that we can use mercury thermometers to measure temperature.

A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables).

A regression model can be used when the dependent variable is quantitative, except in the case of logistic regression, where the dependent variable is binary.

A t-test should not be used to measure differences among more than two groups, because the error structure for a t-test will underestimate the actual error when many groups are being compared.

If you want to compare the means of several groups at once, it’s best to use another statistical test such as ANOVA or a post-hoc test.

A one-sample t-test is used to compare a single population to a standard value (for example, to determine whether the average lifespan of a specific town is different from the country average).

A paired t-test is used to compare a single population before and after some experimental intervention or at two different points in time (for example, measuring student performance on a test before and after being taught the material).

A t-test measures the difference in group means divided by the pooled standard error of the two group means.

In this way, it calculates a number (the t-value) illustrating the magnitude of the difference between the two group means being compared, and estimates the likelihood that this difference exists purely by chance (p-value).

Your choice of t-test depends on whether you are studying one group or two groups, and whether you care about the direction of the difference in group means.

If you are studying one group, use a paired t-test to compare the group mean over time or after an intervention, or use a one-sample t-test to compare the group mean to a standard value. If you are studying two groups, use a two-sample t-test .

If you want to know only whether a difference exists, use a two-tailed test . If you want to know if one group mean is greater or less than the other, use a left-tailed or right-tailed one-tailed test .

A t-test is a statistical test that compares the means of two samples . It is used in hypothesis testing , with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

Ask our team

Want to contact us directly? No problem.  We  are always here for you.

• Email [email protected]
• Start live chat
• Call +1 (510) 822-8066
• WhatsApp +31 20 261 6040

Our team helps students graduate by offering:

• A world-class citation generator
• Plagiarism Checker software powered by Turnitin
• Innovative Citation Checker software
• Professional proofreading services
• Over 300 helpful articles about academic writing, citing sources, plagiarism, and more

Scribbr specializes in editing study-related documents . We proofread:

• PhD dissertations
• Research proposals
• Personal statements
• Admission essays
• Motivation letters
• Reflection papers
• Journal articles
• Capstone projects

Scribbr’s Plagiarism Checker is powered by elements of Turnitin’s Similarity Checker , namely the plagiarism detection software and the Internet Archive and Premium Scholarly Publications content databases .

The add-on AI detector is powered by Scribbr’s proprietary software.

The Scribbr Citation Generator is developed using the open-source Citation Style Language (CSL) project and Frank Bennett’s citeproc-js . It’s the same technology used by dozens of other popular citation tools, including Mendeley and Zotero.

You can find all the citation styles and locales used in the Scribbr Citation Generator in our publicly accessible repository on Github .