dissertation statistical analysis

How To Write The Results/Findings Chapter

For quantitative studies (dissertations & theses).

By: Derek Jansen (MBA) | Expert Reviewed By: Kerryn Warren (PhD) | July 2021

So, you’ve completed your quantitative data analysis and it’s time to report on your findings. But where do you start? In this post, we’ll walk you through the results chapter (also called the findings or analysis chapter), step by step, so that you can craft this section of your dissertation or thesis with confidence. If you’re looking for information regarding the results chapter for qualitative studies, you can find that here .

Overview: Quantitative Results Chapter

• What exactly the results chapter is
• What you need to include in your chapter
• How to structure the chapter
• Tips and tricks for writing a top-notch chapter
• Free results chapter template

What exactly is the results chapter?

The results chapter (also referred to as the findings or analysis chapter) is one of the most important chapters of your dissertation or thesis because it shows the reader what you’ve found in terms of the quantitative data you’ve collected. It presents the data using a clear text narrative, supported by tables, graphs and charts. In doing so, it also highlights any potential issues (such as outliers or unusual findings) you’ve come across.

But how’s that different from the discussion chapter?

Well, in the results chapter, you only present your statistical findings. Only the numbers, so to speak – no more, no less. Contrasted to this, in the discussion chapter , you interpret your findings and link them to prior research (i.e. your literature review), as well as your research objectives and research questions . In other words, the results chapter presents and describes the data, while the discussion chapter interprets the data.

Let’s look at an example.

In your results chapter, you may have a plot that shows how respondents to a survey  responded: the numbers of respondents per category, for instance. You may also state whether this supports a hypothesis by using a p-value from a statistical test. But it is only in the discussion chapter where you will say why this is relevant or how it compares with the literature or the broader picture. So, in your results chapter, make sure that you don’t present anything other than the hard facts – this is not the place for subjectivity.

It’s worth mentioning that some universities prefer you to combine the results and discussion chapters. Even so, it is good practice to separate the results and discussion elements within the chapter, as this ensures your findings are fully described. Typically, though, the results and discussion chapters are split up in quantitative studies. If you’re unsure, chat with your research supervisor or chair to find out what their preference is.

What should you include in the results chapter?

Following your analysis, it’s likely you’ll have far more data than are necessary to include in your chapter. In all likelihood, you’ll have a mountain of SPSS or R output data, and it’s your job to decide what’s most relevant. You’ll need to cut through the noise and focus on the data that matters.

This doesn’t mean that those analyses were a waste of time – on the contrary, those analyses ensure that you have a good understanding of your dataset and how to interpret it. However, that doesn’t mean your reader or examiner needs to see the 165 histograms you created! Relevance is key.

How do I decide what’s relevant?

At this point, it can be difficult to strike a balance between what is and isn’t important. But the most important thing is to ensure your results reflect and align with the purpose of your study .  So, you need to revisit your research aims, objectives and research questions and use these as a litmus test for relevance. Make sure that you refer back to these constantly when writing up your chapter so that you stay on track.

As a general guide, your results chapter will typically include the following:

• Some demographic data about your sample
• Reliability tests (if you used measurement scales)
• Descriptive statistics
• Inferential statistics (if your research objectives and questions require these)
• Hypothesis tests (again, if your research objectives and questions require these)

We’ll discuss each of these points in more detail in the next section.

Importantly, your results chapter needs to lay the foundation for your discussion chapter . This means that, in your results chapter, you need to include all the data that you will use as the basis for your interpretation in the discussion chapter.

For example, if you plan to highlight the strong relationship between Variable X and Variable Y in your discussion chapter, you need to present the respective analysis in your results chapter – perhaps a correlation or regression analysis.

Need a helping hand?

How do I write the results chapter?

There are multiple steps involved in writing up the results chapter for your quantitative research. The exact number of steps applicable to you will vary from study to study and will depend on the nature of the research aims, objectives and research questions . However, we’ll outline the generic steps below.

Step 1 – Revisit your research questions

The first step in writing your results chapter is to revisit your research objectives and research questions . These will be (or at least, should be!) the driving force behind your results and discussion chapters, so you need to review them and then ask yourself which statistical analyses and tests (from your mountain of data) would specifically help you address these . For each research objective and research question, list the specific piece (or pieces) of analysis that address it.

At this stage, it’s also useful to think about the key points that you want to raise in your discussion chapter and note these down so that you have a clear reminder of which data points and analyses you want to highlight in the results chapter. Again, list your points and then list the specific piece of analysis that addresses each point. 

Next, you should draw up a rough outline of how you plan to structure your chapter . Which analyses and statistical tests will you present and in what order? We’ll discuss the “standard structure” in more detail later, but it’s worth mentioning now that it’s always useful to draw up a rough outline before you start writing (this advice applies to any chapter).

Step 2 – Craft an overview introduction

As with all chapters in your dissertation or thesis, you should start your quantitative results chapter by providing a brief overview of what you’ll do in the chapter and why . For example, you’d explain that you will start by presenting demographic data to understand the representativeness of the sample, before moving onto X, Y and Z.

This section shouldn’t be lengthy – a paragraph or two maximum. Also, it’s a good idea to weave the research questions into this section so that there’s a golden thread that runs through the document.

Step 3 – Present the sample demographic data

The first set of data that you’ll present is an overview of the sample demographics – in other words, the demographics of your respondents.

For example:

• What age range are they?
• How is gender distributed?
• How is ethnicity distributed?
• What areas do the participants live in?

The purpose of this is to assess how representative the sample is of the broader population. This is important for the sake of the generalisability of the results. If your sample is not representative of the population, you will not be able to generalise your findings. This is not necessarily the end of the world, but it is a limitation you’ll need to acknowledge.

Of course, to make this representativeness assessment, you’ll need to have a clear view of the demographics of the population. So, make sure that you design your survey to capture the correct demographic information that you will compare your sample to.

But what if I’m not interested in generalisability?

Well, even if your purpose is not necessarily to extrapolate your findings to the broader population, understanding your sample will allow you to interpret your findings appropriately, considering who responded. In other words, it will help you contextualise your findings . For example, if 80% of your sample was aged over 65, this may be a significant contextual factor to consider when interpreting the data. Therefore, it’s important to understand and present the demographic data.

 Step 4 – Review composite measures and the data “shape”.

Before you undertake any statistical analysis, you’ll need to do some checks to ensure that your data are suitable for the analysis methods and techniques you plan to use. If you try to analyse data that doesn’t meet the assumptions of a specific statistical technique, your results will be largely meaningless. Therefore, you may need to show that the methods and techniques you’ll use are “allowed”.

Most commonly, there are two areas you need to pay attention to:

#1: Composite measures

The first is when you have multiple scale-based measures that combine to capture one construct – this is called a composite measure .  For example, you may have four Likert scale-based measures that (should) all measure the same thing, but in different ways. In other words, in a survey, these four scales should all receive similar ratings. This is called “ internal consistency ”.

Internal consistency is not guaranteed though (especially if you developed the measures yourself), so you need to assess the reliability of each composite measure using a test. Typically, Cronbach’s Alpha is a common test used to assess internal consistency – i.e., to show that the items you’re combining are more or less saying the same thing. A high alpha score means that your measure is internally consistent. A low alpha score means you may need to consider scrapping one or more of the measures.

#2: Data shape

The second matter that you should address early on in your results chapter is data shape. In other words, you need to assess whether the data in your set are symmetrical (i.e. normally distributed) or not, as this will directly impact what type of analyses you can use. For many common inferential tests such as T-tests or ANOVAs (we’ll discuss these a bit later), your data needs to be normally distributed. If it’s not, you’ll need to adjust your strategy and use alternative tests.

To assess the shape of the data, you’ll usually assess a variety of descriptive statistics (such as the mean, median and skewness), which is what we’ll look at next.

Step 5 – Present the descriptive statistics

Now that you’ve laid the foundation by discussing the representativeness of your sample, as well as the reliability of your measures and the shape of your data, you can get started with the actual statistical analysis. The first step is to present the descriptive statistics for your variables.

For scaled data, this usually includes statistics such as:

• The mean – this is simply the mathematical average of a range of numbers.
• The median – this is the midpoint in a range of numbers when the numbers are arranged in order.
• The mode – this is the most commonly repeated number in the data set.
• Standard deviation – this metric indicates how dispersed a range of numbers is. In other words, how close all the numbers are to the mean (the average).
• Skewness – this 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 (this is called a normal or parametric distribution), or do they lean to the left or right (this is called a non-normal or non-parametric distribution).
• Kurtosis – this metric indicates whether the data are heavily or lightly-tailed, relative to the normal distribution. In other words, how peaked or flat the distribution is.

A large table that indicates all the above for multiple variables can be a very effective way to present your data economically. You can also use colour coding to help make the data more easily digestible.

For categorical data, where you show the percentage of people who chose or fit into a category, for instance, you can either just plain describe the percentages or numbers of people who responded to something or use graphs and charts (such as bar graphs and pie charts) to present your data in this section of the chapter.

When using figures, make sure that you label them simply and clearly , so that your reader can easily understand them. There’s nothing more frustrating than a graph that’s missing axis labels! Keep in mind that although you’ll be presenting charts and graphs, your text content needs to present a clear narrative that can stand on its own. In other words, don’t rely purely on your figures and tables to convey your key points: highlight the crucial trends and values in the text. Figures and tables should complement the writing, not carry it .

Depending on your research aims, objectives and research questions, you may stop your analysis at this point (i.e. descriptive statistics). However, if your study requires inferential statistics, then it’s time to deep dive into those .

Step 6 – Present the inferential statistics

Inferential statistics are used to make generalisations about a population , whereas descriptive statistics focus purely on the sample . Inferential statistical techniques, broadly speaking, can be broken down into two groups .

First, there are those that compare measurements between groups , such as t-tests (which measure differences between two groups) and ANOVAs (which measure differences between multiple groups). Second, there are techniques that assess the relationships between variables , such as correlation analysis and regression analysis. Within each of these, some tests can be used for normally distributed (parametric) data and some tests are designed specifically for use on non-parametric data.

There are a seemingly endless number of tests that you can use to crunch your data, so it’s easy to run down a rabbit hole and end up with piles of test data. Ultimately, the most important thing is to make sure that you adopt the tests and techniques that allow you to achieve your research objectives and answer your research questions .

In this section of the results chapter, you should try to make use of figures and visual components as effectively as possible. For example, if you present a correlation table, use colour coding to highlight the significance of the correlation values, or scatterplots to visually demonstrate what the trend is. The easier you make it for your reader to digest your findings, the more effectively you’ll be able to make your arguments in the next chapter.

Step 7 – Test your hypotheses

If your study requires it, the next stage is hypothesis testing. A hypothesis is a statement , often indicating a difference between groups or relationship between variables, that can be supported or rejected by a statistical test. However, not all studies will involve hypotheses (again, it depends on the research objectives), so don’t feel like you “must” present and test hypotheses just because you’re undertaking quantitative research.

The basic process for hypothesis testing is as follows:

• Specify your null hypothesis (for example, “The chemical psilocybin has no effect on time perception).
• Specify your alternative hypothesis (e.g., “The chemical psilocybin has an effect on time perception)
• Set your significance level (this is usually 0.05)
• Calculate your statistics and find your p-value (e.g., p=0.01)
• Draw your conclusions (e.g., “The chemical psilocybin does have an effect on time perception”)

Finally, if the aim of your study is to develop and test a conceptual framework , this is the time to present it, following the testing of your hypotheses. While you don’t need to develop or discuss these findings further in the results chapter, indicating whether the tests (and their p-values) support or reject the hypotheses is crucial.

Step 8 – Provide a chapter summary

To wrap up your results chapter and transition to the discussion chapter, you should provide a brief summary of the key findings . “Brief” is the keyword here – much like the chapter introduction, this shouldn’t be lengthy – a paragraph or two maximum. Highlight the findings most relevant to your research objectives and research questions, and wrap it up.

Some final thoughts, tips and tricks

Now that you’ve got the essentials down, here are a few tips and tricks to make your quantitative results chapter shine:

• When writing your results chapter, report your findings in the past tense . You’re talking about what you’ve found in your data, not what you are currently looking for or trying to find.
• Structure your results chapter systematically and sequentially . If you had two experiments where findings from the one generated inputs into the other, report on them in order.
• Make your own tables and graphs rather than copying and pasting them from statistical analysis programmes like SPSS. Check out the DataIsBeautiful reddit for some inspiration.
• Once you’re done writing, review your work to make sure that you have provided enough information to answer your research questions , but also that you didn’t include superfluous information.

If you’ve got any questions about writing up the quantitative results chapter, please leave a comment below. If you’d like 1-on-1 assistance with your quantitative analysis and discussion, check out our hands-on coaching service , or book a free consultation with a friendly coach.

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11 Tips For Writing a Dissertation Data Analysis

Since the evolution of the fourth industrial revolution – the Digital World; lots of data have surrounded us. There are terabytes of data around us or in data centers that need to be processed and used. The data needs to be appropriately analyzed to process it, and Dissertation data analysis forms its basis. If data analysis is valid and free from errors, the research outcomes will be reliable and lead to a successful dissertation. 

Considering the complexity of many data analysis projects, it becomes challenging to get precise results if analysts are not familiar with data analysis tools and tests properly. The analysis is a time-taking process that starts with collecting valid and relevant data and ends with the demonstration of error-free results.

So, in today’s topic, we will cover the need to analyze data, dissertation data analysis, and mainly the tips for writing an outstanding data analysis dissertation. If you are a doctoral student and plan to perform dissertation data analysis on your data, make sure that you give this article a thorough read for the best tips!

What is Data Analysis in Dissertation?

Dissertation Data Analysis  is the process of understanding, gathering, compiling, and processing a large amount of data. Then identifying common patterns in responses and critically examining facts and figures to find the rationale behind those outcomes.

Even f you have the data collected and compiled in the form of facts and figures, it is not enough for proving your research outcomes. There is still a need to apply dissertation data analysis on your data; to use it in the dissertation. It provides scientific support to the thesis and conclusion of the research.

Data Analysis Tools

There are plenty of indicative tests used to analyze data and infer relevant results for the discussion part. Following are some tests  used to perform analysis of data leading to a scientific conclusion:

11 Most Useful Tips for Dissertation Data Analysis

Doctoral students need to perform dissertation data analysis and then dissertation to receive their degree. Many Ph.D. students find it hard to do dissertation data analysis because they are not trained in it.

1. Dissertation Data Analysis Services

The first tip applies to those students who can afford to look for help with their dissertation data analysis work. It’s a viable option, and it can help with time management and with building the other elements of the dissertation with much detail.

Dissertation Analysis services are professional services that help doctoral students with all the basics of their dissertation work, from planning, research and clarification, methodology, dissertation data analysis and review, literature review, and final powerpoint presentation.

One great reference for dissertation data analysis professional services is Statistics Solutions , they’ve been around for over 22 years helping students succeed in their dissertation work. You can find the link to their website here .

For a proper dissertation data analysis, the student should have a clear understanding and statistical knowledge. Through this knowledge and experience, a student can perform dissertation analysis on their own. 

Following are some helpful tips for writing a splendid dissertation data analysis:

2. Relevance of Collected Data

If the data is irrelevant and not appropriate, you might get distracted from the point of focus. To show the reader that you can critically solve the problem, make sure that you write a theoretical proposition regarding the selection  and analysis of data.

3. Data Analysis

For analysis, it is crucial to use such methods that fit best with the types of data collected and the research objectives. Elaborate on these methods and the ones that justify your data collection methods thoroughly. Make sure to make the reader believe that you did not choose your method randomly. Instead, you arrived at it after critical analysis and prolonged research.

On the other hand,  quantitative analysis  refers to the analysis and interpretation of facts and figures – to build reasoning behind the advent of primary findings. An assessment of the main results and the literature review plays a pivotal role in qualitative and quantitative analysis.

The overall objective of data analysis is to detect patterns and inclinations in data and then present the outcomes implicitly.  It helps in providing a solid foundation for critical conclusions and assisting the researcher to complete the dissertation proposal. 

4. Qualitative Data Analysis

Qualitative data refers to data that does not involve numbers. You are required to carry out an analysis of the data collected through experiments, focus groups, and interviews. This can be a time-taking process because it requires iterative examination and sometimes demanding the application of hermeneutics. Note that using qualitative technique doesn’t only mean generating good outcomes but to unveil more profound knowledge that can be transferrable.

Presenting qualitative data analysis in a dissertation  can also be a challenging task. It contains longer and more detailed responses. Placing such comprehensive data coherently in one chapter of the dissertation can be difficult due to two reasons. Firstly, we cannot figure out clearly which data to include and which one to exclude. Secondly, unlike quantitative data, it becomes problematic to present data in figures and tables. Making information condensed into a visual representation is not possible. As a writer, it is of essence to address both of these challenges.

          Qualitative Data Analysis Methods

Following are the methods used to perform quantitative data analysis. 

•   Deductive Method

This method involves analyzing qualitative data based on an argument that a researcher already defines. It’s a comparatively easy approach to analyze data. It is suitable for the researcher with a fair idea about the responses they are likely to receive from the questionnaires.

•  Inductive Method

In this method, the researcher analyzes the data not based on any predefined rules. It is a time-taking process used by students who have very little knowledge of the research phenomenon.

5. Quantitative Data Analysis

Quantitative data contains facts and figures obtained from scientific research and requires extensive statistical analysis. After collection and analysis, you will be able to conclude. Generic outcomes can be accepted beyond the sample by assuming that it is representative – one of the preliminary checkpoints to carry out in your analysis to a larger group. This method is also referred to as the “scientific method”, gaining its roots from natural sciences.

The Presentation of quantitative data  depends on the domain to which it is being presented. It is beneficial to consider your audience while writing your findings. Quantitative data for  hard sciences  might require numeric inputs and statistics. As for  natural sciences , such comprehensive analysis is not required.

                Quantitative Analysis Methods

Following are some of the methods used to perform quantitative data analysis. 

• Trend analysis:  This corresponds to a statistical analysis approach to look at the trend of quantitative data collected over a considerable period.
• Cross-tabulation:  This method uses a tabula way to draw readings among data sets in research.  
• Conjoint analysis :   Quantitative data analysis method that can collect and analyze advanced measures. These measures provide a thorough vision about purchasing decisions and the most importantly, marked parameters.
• TURF analysis:  This approach assesses the total market reach of a service or product or a mix of both. 
• Gap analysis:  It utilizes the  side-by-side matrix  to portray quantitative data, which captures the difference between the actual and expected performance. 
• Text analysis:  In this method, innovative tools enumerate  open-ended data  into easily understandable data. 

6. Data Presentation Tools

Since large volumes of data need to be represented, it becomes a difficult task to present such an amount of data in coherent ways. To resolve this issue, consider all the available choices you have, such as tables, charts, diagrams, and graphs. 

Tables help in presenting both qualitative and quantitative data concisely. While presenting data, always keep your reader in mind. Anything clear to you may not be apparent to your reader. So, constantly rethink whether your data presentation method is understandable to someone less conversant with your research and findings. If the answer is “No”, you may need to rethink your Presentation. 

7. Include Appendix or Addendum

After presenting a large amount of data, your dissertation analysis part might get messy and look disorganized. Also, you would not be cutting down or excluding the data you spent days and months collecting. To avoid this, you should include an appendix part. 

The data you find hard to arrange within the text, include that in the  appendix part of a dissertation . And place questionnaires, copies of focus groups and interviews, and data sheets in the appendix. On the other hand, one must put the statistical analysis and sayings quoted by interviewees within the dissertation. 

8. Thoroughness of Data

It is a common misconception that the data presented is self-explanatory. Most of the students provide the data and quotes and think that it is enough and explaining everything. It is not sufficient. Rather than just quoting everything, you should analyze and identify which data you will use to approve or disapprove your standpoints. 

Thoroughly demonstrate the ideas and critically analyze each perspective taking care of the points where errors can occur. Always make sure to discuss the anomalies and strengths of your data to add credibility to your research.

9. Discussing Data

Discussion of data involves elaborating the dimensions to classify patterns, themes, and trends in presented data. In addition, to balancing, also take theoretical interpretations into account. Discuss the reliability of your data by assessing their effect and significance. Do not hide the anomalies. While using interviews to discuss the data, make sure you use relevant quotes to develop a strong rationale. 

It also involves answering what you are trying to do with the data and how you have structured your findings. Once you have presented the results, the reader will be looking for interpretation. Hence, it is essential to deliver the understanding as soon as you have submitted your data.

10. Findings and Results

Findings refer to the facts derived after the analysis of collected data. These outcomes should be stated; clearly, their statements should tightly support your objective and provide logical reasoning and scientific backing to your point. This part comprises of majority part of the dissertation. 

In the finding part, you should tell the reader what they are looking for. There should be no suspense for the reader as it would divert their attention. State your findings clearly and concisely so that they can get the idea of what is more to come in your dissertation.

11. Connection with Literature Review

At the ending of your data analysis in the dissertation, make sure to compare your data with other published research. In this way, you can identify the points of differences and agreements. Check the consistency of your findings if they meet your expectations—lookup for bottleneck position. Analyze and discuss the reasons behind it. Identify the key themes, gaps, and the relation of your findings with the literature review. In short, you should link your data with your research question, and the questions should form a basis for literature.

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Wrapping Up

Writing data analysis in the dissertation involves dedication, and its implementations demand sound knowledge and proper planning. Choosing your topic, gathering relevant data, analyzing it, presenting your data and findings correctly, discussing the results, connecting with the literature and conclusions are milestones in it. Among these checkpoints, the Data analysis stage is most important and requires a lot of keenness.

In this article, we thoroughly looked at the tips that prove valuable for writing a data analysis in a dissertation. Make sure to give this article a thorough read before you write data analysis in the dissertation leading to the successful future of your research.

Oxbridge Essays. Top 10 Tips for Writing a Dissertation Data Analysis.

Emidio Amadebai

As an IT Engineer, who is passionate about learning and sharing. I have worked and learned quite a bit from Data Engineers, Data Analysts, Business Analysts, and Key Decision Makers almost for the past 5 years. Interested in learning more about Data Science and How to leverage it for better decision-making in my business and hopefully help you do the same in yours.

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What is PhD Thesis Writing? | Beginner’s Guide

A data analysis dissertation is a complex and challenging project requiring significant time, effort, and expertise. Fortunately, it is possible to successfully complete a data analysis dissertation with careful planning and execution.

As a student, you must know how important it is to have a strong and well-written dissertation, especially regarding data analysis. Proper data analysis is crucial to the success of your research and can often make or break your dissertation.

To get a better understanding, you may review the data analysis dissertation examples listed below;

• Impact of Leadership Style on the Job Satisfaction of Nurses
• Effect of Brand Love on Consumer Buying Behaviour in Dietary Supplement Sector
• An Insight Into Alternative Dispute Resolution
• An Investigation of Cyberbullying and its Impact on Adolescent Mental Health in UK

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Types of data analysis for dissertation.

The various types of data Analysis in a Dissertation are as follows;

1.   Qualitative Data Analysis

Qualitative data analysis is a type of data analysis that involves analyzing data that cannot be measured numerically. This data type includes interviews, focus groups, and open-ended surveys. Qualitative data analysis can be used to identify patterns and themes in the data.

2.   Quantitative Data Analysis

Quantitative data analysis is a type of data analysis that involves analyzing data that can be measured numerically. This data type includes test scores, income levels, and crime rates. Quantitative data analysis can be used to test hypotheses and to look for relationships between variables.

3.   Descriptive Data Analysis

Descriptive data analysis is a type of data analysis that involves describing the characteristics of a dataset. This type of data analysis summarizes the main features of a dataset.

4.   Inferential Data Analysis

Inferential data analysis is a type of data analysis that involves making predictions based on a dataset. This type of data analysis can be used to test hypotheses and make predictions about future events.

5.   Exploratory Data Analysis

Exploratory data analysis is a type of data analysis that involves exploring a data set to understand it better. This type of data analysis can identify patterns and relationships in the data.

Time Period to Plan and Complete a Data Analysis Dissertation?

When planning dissertation data analysis, it is important to consider the dissertation methodology structure and time series analysis as they will give you an understanding of how long each stage will take. For example, using a qualitative research method, your data analysis will involve coding and categorizing your data.

This can be time-consuming, so allowing enough time in your schedule is important. Once you have coded and categorized your data, you will need to write up your findings. Again, this can take some time, so factor this into your schedule.

Finally, you will need to proofread and edit your dissertation before submitting it. All told, a data analysis dissertation can take anywhere from several weeks to several months to complete, depending on the project’s complexity. Therefore, starting planning early and allowing enough time in your schedule to complete the task is important.

Essential Strategies for Data Analysis Dissertation

A.   Planning

The first step in any dissertation is planning. You must decide what you want to write about and how you want to structure your argument. This planning will involve deciding what data you want to analyze and what methods you will use for a data analysis dissertation.

B.   Prototyping

Once you have a plan for your dissertation, it’s time to start writing. However, creating a prototype is important before diving head-first into writing your dissertation. A prototype is a rough draft of your argument that allows you to get feedback from your advisor and committee members. This feedback will help you fine-tune your argument before you start writing the final version of your dissertation.

C.   Executing

After you have created a plan and prototype for your data analysis dissertation, it’s time to start writing the final version. This process will involve collecting and analyzing data and writing up your results. You will also need to create a conclusion section that ties everything together.

D.   Presenting

The final step in acing your data analysis dissertation is presenting it to your committee. This presentation should be well-organized and professionally presented. During the presentation, you’ll also need to be ready to respond to questions concerning your dissertation.

Data Analysis Tools

Numerous suggestive tools are employed to assess the data and deduce pertinent findings for the discussion section. The tools used to analyze data and get a scientific conclusion are as follows:

a.     Excel

Excel is a spreadsheet program part of the Microsoft Office productivity software suite. Excel is a powerful tool that can be used for various data analysis tasks, such as creating charts and graphs, performing mathematical calculations, and sorting and filtering data.

b.     Google Sheets

Google Sheets is a free online spreadsheet application that is part of the Google Drive suite of productivity software. Google Sheets is similar to Excel in terms of functionality, but it also has some unique features, such as the ability to collaborate with other users in real-time.

c.     SPSS

SPSS is a statistical analysis software program commonly used in the social sciences. SPSS can be used for various data analysis tasks, such as hypothesis testing, factor analysis, and regression analysis.

d.     STATA

STATA is a statistical analysis software program commonly used in the sciences and economics. STATA can be used for data management, statistical modelling, descriptive statistics analysis, and data visualization tasks.

SAS is a commercial statistical analysis software program used by businesses and organizations worldwide. SAS can be used for predictive modelling, market research, and fraud detection.

R is a free, open-source statistical programming language popular among statisticians and data scientists. R can be used for tasks such as data wrangling, machine learning, and creating complex visualizations.

g.     Python

A variety of applications may be used using the distinctive programming language Python, including web development, scientific computing, and artificial intelligence. Python also has a number of modules and libraries that can be used for data analysis tasks, such as numerical computing, statistical modelling, and data visualization.

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Tips to Compose a Successful Data Analysis Dissertation

a.   Choose a Topic You’re Passionate About

The first step to writing a successful data analysis dissertation is to choose a topic you’re passionate about. Not only will this make the research and writing process more enjoyable, but it will also ensure that you produce a high-quality paper.

Choose a topic that is particular enough to be covered in your paper’s scope but not so specific that it will be challenging to obtain enough evidence to substantiate your arguments.

b.   Do Your Research

data analysis in research is an important part of academic writing. Once you’ve selected a topic, it’s time to begin your research. Be sure to consult with your advisor or supervisor frequently during this stage to ensure that you are on the right track. In addition to secondary sources such as books, journal articles, and reports, you should also consider conducting primary research through surveys or interviews. This will give you first-hand insights into your topic that can be invaluable when writing your paper.

c.   Develop a Strong Thesis Statement

After you’ve done your research, it’s time to start developing your thesis statement. It is arguably the most crucial part of your entire paper, so take care to craft a clear and concise statement that encapsulates the main argument of your paper.

Remember that your thesis statement should be arguable—that is, it should be capable of being disputed by someone who disagrees with your point of view. If your thesis statement is not arguable, it will be difficult to write a convincing paper.

d.   Write a Detailed Outline

Once you have developed a strong thesis statement, the next step is to write a detailed outline of your paper. This will offer you a direction to write in and guarantee that your paper makes sense from beginning to end.

Your outline should include an introduction, in which you state your thesis statement; several body paragraphs, each devoted to a different aspect of your argument; and a conclusion, in which you restate your thesis and summarize the main points of your paper.

e.   Write Your First Draft

With your outline in hand, it’s finally time to start writing your first draft. At this stage, don’t worry about perfecting your grammar or making sure every sentence is exactly right—focus on getting all of your ideas down on paper (or onto the screen). Once you have completed your first draft, you can revise it for style and clarity.

And there you have it! Following these simple tips can increase your chances of success when writing your data analysis dissertation. Just remember to start early, give yourself plenty of time to research and revise, and consult with your supervisor frequently throughout the process.

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Studying the above examples gives you valuable insight into the structure and content that should be included in your own data analysis dissertation. You can also learn how to effectively analyze and present your data and make a lasting impact on your readers.

In addition to being a useful resource for completing your dissertation, these examples can also serve as a valuable reference for future academic writing projects. By following these examples and understanding their principles, you can improve your data analysis skills and increase your chances of success in your academic career.

You may also contact Premier Dissertations to develop your data analysis dissertation.

For further assistance, some other resources in the dissertation writing section are shared below;

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How to Write Data Analysis For A Dissertation?

How to Develop a Conceptual Framework in Dissertation?

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• Cookies & Privacy
• GETTING STARTED
• Introduction
• FUNDAMENTALS

Getting to the main article

Choosing your route

Setting research questions/ hypotheses

Assessment point

Building the theoretical case

Setting your research strategy

Data collection

Data analysis

CONSIDERATION ONE

The data analysis process.

The data analysis process involves three steps : (STEP ONE) select the correct statistical tests to run on your data; (STEP TWO) prepare and analyse the data you have collected using a relevant statistics package; and (STEP THREE) interpret the findings properly so that you can write up your results (i.e., usually in Chapter Four: Results ). The basic idea behind each of these steps is relatively straightforward, but the act of analysing your data (i.e., by selecting statistical tests, preparing your data and analysing it, and interpreting the findings from these tests) can be time consuming and challenging. We have tried to make this process as easy as possible by providing comprehensive, step-by-step guides in the Data Analysis part of Lærd Dissertation, but you should leave time at least one week to analyse your data.

STEP ONE Select the correct statistical tests to run on your data

It is common that dissertation students collect good data, but then report the wrong findings because of selecting the incorrect statistical tests to run in the first place. Selecting the correct statistical tests to perform on the data that you have collected will depend on (a) the research questions/hypotheses you have set, together with the research design you have adopted, and (b) the type and nature of your data:

The research questions/hypotheses you have set, together with the research design you have adopted

Your research questions/hypotheses and research design explain what variables you are measuring and how you plan to measure these variables. These highlight whether you want to (a) predict a score or a membership of a group, (b) find out differences between groups or treatments, or (c) explore associations/relationships between variables. These different aims determine the statistical tests that may be appropriate to run on your data. We highlight the word may because the most appropriate test that is identified based on your research questions/hypotheses and research design can change depending on the type and nature of the data you collect; something we discuss next.

The type and nature of the data you collected

Data is not all the same. As you will have identified by now, not all variables are measured in the same way; variables can be dichotomous, ordinal, or continuous. In addition, not all data is normal , as term we explain the Data Analysis section, nor is the data you have collected when comparing groups necessarily equal for each group. As a result, you might think that running a particular statistical test is correct (e.g., a dependent t-test), based on the research questions/hypotheses you have set, but the data you have collected fails certain assumptions that are important to this statistical test (i.e., normality and homogeneity of variance ). As a result, you have to run another statistical test (e.g., a Mann-Whitney U instead of a dependent t-test).

To select the correct statistical tests to run on the data in your dissertation, we have created a Statistical Test Selector to help guide you through the various options.

STEP TWO Prepare and analyse your data using a relevant statistics package

The preparation and analysis of your data is actually a much more practical step than many students realise. Most of the time required to get the results that you will present in your write up (i.e., usually in Chapter Four: Results ) comes from knowing (a) how to enter data into a statistics package (e.g., SPSS) so that it can be analysed correctly, and (b) what buttons to press in the statistics package to correctly run the statistical tests you need:

Entering data is not just about knowing what buttons to press, but: (a) how to code your data correctly to recognise the types of variables that you have, as well as issues such as reverse coding ; (b) how to filter your dataset to take into account missing data and outliers ; (c) how to split files (i.e., in SPSS) when analysing the data for separate subgroups (e.g., males and females) using the same statistical tests; (d) how to weight and unweight data you have collected; and (e) other things you need to consider when entering data. What you have to do when it comes to entering data (i.e., in terms of coding, filtering, splitting files, and weighting/unweighting data) will depend on the statistical tests you plan to run. Therefore, entering data starts with using the Statistical Test Selector to help guide you through the various options. In the Data Analysis section, we help you to understand what you need to know about entering data in the context of your dissertation.

Running statistical tests

Statistics packages do the hard work of statistically analysing your data, but they rely on you making a number of choices. This is not simply about selecting the correct statistical test, but knowing, when you have selected a given test to run on your data, what buttons to press to: (a) test for the assumptions underlying the statistical test; (b) test whether corrections can be made when assumptions are violated ; (c) take into account outliers and missing data ; (d) choose between the different numerical and graphical ways to approach your analysis; and (e) other standard and more advanced tips. In the Data Analysis section, we explain what these considerations are (i.e., assumptions, corrections, outliers and missing data, numerical and graphical analysis) so that you can apply them to your own dissertation. We also provide comprehensive , step-by-step instructions with screenshots that show you how to enter data and run a wide range of statistical tests using the statistics package, SPSS. We do this on the basis that you probably have little or no knowledge of SPSS.

STEP THREE Interpret the findings properly

SPSS produces many tables of output for the typical tests you will run. In addition, SPSS has many new methods of presenting data using its Model viewer. You need to know which of these tables is important for your analysis and what the different figures/numbers mean. Interpreting these findings properly and communicating your results is one of the most important aspects of your dissertation. In the Data Analysis section, we show you how to understand these tables of output, what part of this output you need to look at, and how to write up the results in an appropriate format (i.e., so that you can answer you research hypotheses).

Raw Data to Excellence: Master Dissertation Analysis

Discover the secrets of successful dissertation data analysis. Get practical advice and useful insights from experienced experts now!

Have you ever found yourself knee-deep in a dissertation, desperately seeking answers from the data you’ve collected? Or have you ever felt clueless with all the data that you’ve collected but don’t know where to start? Fear not, in this article we are going to discuss a method that helps you come out of this situation and that is Dissertation Data Analysis.

Dissertation data analysis is like uncovering hidden treasures within your research findings. It’s where you roll up your sleeves and explore the data you’ve collected, searching for patterns, connections, and those “a-ha!” moments. Whether you’re crunching numbers, dissecting narratives, or diving into qualitative interviews, data analysis is the key that unlocks the potential of your research.

Dissertation Data Analysis

Dissertation data analysis plays a crucial role in conducting rigorous research and drawing meaningful conclusions. It involves the systematic examination, interpretation, and organization of data collected during the research process. The aim is to identify patterns, trends, and relationships that can provide valuable insights into the research topic.

The first step in dissertation data analysis is to carefully prepare and clean the collected data. This may involve removing any irrelevant or incomplete information, addressing missing data, and ensuring data integrity. Once the data is ready, various statistical and analytical techniques can be applied to extract meaningful information.

Descriptive statistics are commonly used to summarize and describe the main characteristics of the data, such as measures of central tendency (e.g., mean, median) and measures of dispersion (e.g., standard deviation, range). These statistics help researchers gain an initial understanding of the data and identify any outliers or anomalies.

Furthermore, qualitative data analysis techniques can be employed when dealing with non-numerical data, such as textual data or interviews. This involves systematically organizing, coding, and categorizing qualitative data to identify themes and patterns.

Types of Research

When considering research types in the context of dissertation data analysis, several approaches can be employed:

1. Quantitative Research

This type of research involves the collection and analysis of numerical data. It focuses on generating statistical information and making objective interpretations. Quantitative research often utilizes surveys, experiments, or structured observations to gather data that can be quantified and analyzed using statistical techniques.

2. Qualitative Research

In contrast to quantitative research, qualitative research focuses on exploring and understanding complex phenomena in depth. It involves collecting non-numerical data such as interviews, observations, or textual materials. Qualitative data analysis involves identifying themes, patterns, and interpretations, often using techniques like content analysis or thematic analysis.

3. Mixed-Methods Research

This approach combines both quantitative and qualitative research methods. Researchers employing mixed-methods research collect and analyze both numerical and non-numerical data to gain a comprehensive understanding of the research topic. The integration of quantitative and qualitative data can provide a more nuanced and comprehensive analysis, allowing for triangulation and validation of findings.

Primary vs. Secondary Research

Primary research.

Primary research involves the collection of original data specifically for the purpose of the dissertation. This data is directly obtained from the source, often through surveys, interviews, experiments, or observations. Researchers design and implement their data collection methods to gather information that is relevant to their research questions and objectives. Data analysis in primary research typically involves processing and analyzing the raw data collected.

Secondary Research

Secondary research involves the analysis of existing data that has been previously collected by other researchers or organizations. This data can be obtained from various sources such as academic journals, books, reports, government databases, or online repositories. Secondary data can be either quantitative or qualitative, depending on the nature of the source material. Data analysis in secondary research involves reviewing, organizing, and synthesizing the available data.

If you wanna deepen into Methodology in Research, also read: What is Methodology in Research and How Can We Write it?

Types of Analysis 

Various types of analysis techniques can be employed to examine and interpret the collected data. Of all those types, the ones that are most important and used are:

• Descriptive Analysis: Descriptive analysis focuses on summarizing and describing the main characteristics of the data. It involves calculating measures of central tendency (e.g., mean, median) and measures of dispersion (e.g., standard deviation, range). Descriptive analysis provides an overview of the data, allowing researchers to understand its distribution, variability, and general patterns.
• Inferential Analysis: Inferential analysis aims to draw conclusions or make inferences about a larger population based on the collected sample data. This type of analysis involves applying statistical techniques, such as hypothesis testing, confidence intervals, and regression analysis, to analyze the data and assess the significance of the findings. Inferential analysis helps researchers make generalizations and draw meaningful conclusions beyond the specific sample under investigation.
• Qualitative Analysis: Qualitative analysis is used to interpret non-numerical data, such as interviews, focus groups, or textual materials. It involves coding, categorizing, and analyzing the data to identify themes, patterns, and relationships. Techniques like content analysis, thematic analysis, or discourse analysis are commonly employed to derive meaningful insights from qualitative data.
• Correlation Analysis: Correlation analysis is used to examine the relationship between two or more variables. It determines the strength and direction of the association between variables. Common correlation techniques include Pearson’s correlation coefficient, Spearman’s rank correlation, or point-biserial correlation, depending on the nature of the variables being analyzed.

Basic Statistical Analysis

When conducting dissertation data analysis, researchers often utilize basic statistical analysis techniques to gain insights and draw conclusions from their data. These techniques involve the application of statistical measures to summarize and examine the data. Here are some common types of basic statistical analysis used in dissertation research:

• Descriptive Statistics
• Frequency Analysis
• Cross-tabulation
• Chi-Square Test
• Correlation Analysis

Advanced Statistical Analysis

In dissertation data analysis, researchers may employ advanced statistical analysis techniques to gain deeper insights and address complex research questions. These techniques go beyond basic statistical measures and involve more sophisticated methods. Here are some examples of advanced statistical analysis commonly used in dissertation research:

Regression Analysis

• Analysis of Variance (ANOVA)
• Factor Analysis
• Cluster Analysis
• Structural Equation Modeling (SEM)
• Time Series Analysis

Examples of Methods of Analysis

Regression analysis is a powerful tool for examining relationships between variables and making predictions. It allows researchers to assess the impact of one or more independent variables on a dependent variable. Different types of regression analysis, such as linear regression, logistic regression, or multiple regression, can be used based on the nature of the variables and research objectives.

Event Study

An event study is a statistical technique that aims to assess the impact of a specific event or intervention on a particular variable of interest. This method is commonly employed in finance, economics, or management to analyze the effects of events such as policy changes, corporate announcements, or market shocks.

Vector Autoregression

Vector Autoregression is a statistical modeling technique used to analyze the dynamic relationships and interactions among multiple time series variables. It is commonly employed in fields such as economics, finance, and social sciences to understand the interdependencies between variables over time.

Preparing Data for Analysis

1. become acquainted with the data.

It is crucial to become acquainted with the data to gain a comprehensive understanding of its characteristics, limitations, and potential insights. This step involves thoroughly exploring and familiarizing oneself with the dataset before conducting any formal analysis by reviewing the dataset to understand its structure and content. Identify the variables included, their definitions, and the overall organization of the data. Gain an understanding of the data collection methods, sampling techniques, and any potential biases or limitations associated with the dataset.

2. Review Research Objectives

This step involves assessing the alignment between the research objectives and the data at hand to ensure that the analysis can effectively address the research questions. Evaluate how well the research objectives and questions align with the variables and data collected. Determine if the available data provides the necessary information to answer the research questions adequately. Identify any gaps or limitations in the data that may hinder the achievement of the research objectives.

3. Creating a Data Structure

This step involves organizing the data into a well-defined structure that aligns with the research objectives and analysis techniques. Organize the data in a tabular format where each row represents an individual case or observation, and each column represents a variable. Ensure that each case has complete and accurate data for all relevant variables. Use consistent units of measurement across variables to facilitate meaningful comparisons.

4. Discover Patterns and Connections

In preparing data for dissertation data analysis, one of the key objectives is to discover patterns and connections within the data. This step involves exploring the dataset to identify relationships, trends, and associations that can provide valuable insights. Visual representations can often reveal patterns that are not immediately apparent in tabular data. 

Qualitative Data Analysis

Qualitative data analysis methods are employed to analyze and interpret non-numerical or textual data. These methods are particularly useful in fields such as social sciences, humanities, and qualitative research studies where the focus is on understanding meaning, context, and subjective experiences. Here are some common qualitative data analysis methods:

Thematic Analysis

The thematic analysis involves identifying and analyzing recurring themes, patterns, or concepts within the qualitative data. Researchers immerse themselves in the data, categorize information into meaningful themes, and explore the relationships between them. This method helps in capturing the underlying meanings and interpretations within the data.

Content Analysis

Content analysis involves systematically coding and categorizing qualitative data based on predefined categories or emerging themes. Researchers examine the content of the data, identify relevant codes, and analyze their frequency or distribution. This method allows for a quantitative summary of qualitative data and helps in identifying patterns or trends across different sources.

Grounded Theory

Grounded theory is an inductive approach to qualitative data analysis that aims to generate theories or concepts from the data itself. Researchers iteratively analyze the data, identify concepts, and develop theoretical explanations based on emerging patterns or relationships. This method focuses on building theory from the ground up and is particularly useful when exploring new or understudied phenomena.

Discourse Analysis

Discourse analysis examines how language and communication shape social interactions, power dynamics, and meaning construction. Researchers analyze the structure, content, and context of language in qualitative data to uncover underlying ideologies, social representations, or discursive practices. This method helps in understanding how individuals or groups make sense of the world through language.

Narrative Analysis

Narrative analysis focuses on the study of stories, personal narratives, or accounts shared by individuals. Researchers analyze the structure, content, and themes within the narratives to identify recurring patterns, plot arcs, or narrative devices. This method provides insights into individuals’ live experiences, identity construction, or sense-making processes.

Applying Data Analysis to Your Dissertation

Applying data analysis to your dissertation is a critical step in deriving meaningful insights and drawing valid conclusions from your research. It involves employing appropriate data analysis techniques to explore, interpret, and present your findings. Here are some key considerations when applying data analysis to your dissertation:

Selecting Analysis Techniques

Choose analysis techniques that align with your research questions, objectives, and the nature of your data. Whether quantitative or qualitative, identify the most suitable statistical tests, modeling approaches, or qualitative analysis methods that can effectively address your research goals. Consider factors such as data type, sample size, measurement scales, and the assumptions associated with the chosen techniques.

Data Preparation

Ensure that your data is properly prepared for analysis. Cleanse and validate your dataset, addressing any missing values, outliers, or data inconsistencies. Code variables, transform data if necessary, and format it appropriately to facilitate accurate and efficient analysis. Pay attention to ethical considerations, data privacy, and confidentiality throughout the data preparation process.

Execution of Analysis

Execute the selected analysis techniques systematically and accurately. Utilize statistical software, programming languages, or qualitative analysis tools to carry out the required computations, calculations, or interpretations. Adhere to established guidelines, protocols, or best practices specific to your chosen analysis techniques to ensure reliability and validity.

Interpretation of Results

Thoroughly interpret the results derived from your analysis. Examine statistical outputs, visual representations, or qualitative findings to understand the implications and significance of the results. Relate the outcomes back to your research questions, objectives, and existing literature. Identify key patterns, relationships, or trends that support or challenge your hypotheses.

Drawing Conclusions

Based on your analysis and interpretation, draw well-supported conclusions that directly address your research objectives. Present the key findings in a clear, concise, and logical manner, emphasizing their relevance and contributions to the research field. Discuss any limitations, potential biases, or alternative explanations that may impact the validity of your conclusions.

Validation and Reliability

Evaluate the validity and reliability of your data analysis by considering the rigor of your methods, the consistency of results, and the triangulation of multiple data sources or perspectives if applicable. Engage in critical self-reflection and seek feedback from peers, mentors, or experts to ensure the robustness of your data analysis and conclusions.

In conclusion, dissertation data analysis is an essential component of the research process, allowing researchers to extract meaningful insights and draw valid conclusions from their data. By employing a range of analysis techniques, researchers can explore relationships, identify patterns, and uncover valuable information to address their research objectives.

Turn Your Data Into Easy-To-Understand And Dynamic Stories

Decoding data is daunting and you might end up in confusion. Here’s where infographics come into the picture. With visuals, you can turn your data into easy-to-understand and dynamic stories that your audience can relate to. Mind the Graph is one such platform that helps scientists to explore a library of visuals and use them to amplify their research work. Sign up now to make your presentation simpler. 

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Statistical Analysis in a Dissertation: 4 Expert Tips for Academic Success

Are you looking to Conduct Statistical Analysis in a Dissertation? In this article. we offer top tips, tricks, and triumphs for success. Master the art of data analysis and take your dissertation to the next level with our expert guidance at Houston Essays.

Statistical analysis is an integral part of conducting a dissertation, playing a crucial role in deriving meaningful insights from research data. Whether you are studying social sciences, business, or any other field, understanding how to effectively conduct statistical analysis can greatly enhance the credibility of your research findings. In this article, we will explore the process of conducting statistical analysis in a dissertation, providing you with pro tips and tricks along the way.

Statistical analysis involves the application of various mathematical and computational techniques to analyze and interpret data. In the context of a dissertation, statistical analysis helps researchers draw conclusions, validate research hypotheses, and make informed decisions based on empirical evidence. It allows for a deeper understanding of the relationships and patterns within the data, enabling researchers to uncover valuable insights.

The examination of trends, structures, and correlations using quantitative data is known as statistical analysis. It is a crucial research instrument utilized by academics, government, corporations, and other groups.

Statistical Analysis in a Dissertation assists doctorate students with all the fundamental components of their dissertation work, including planning, researching and clarifying, methodology, dissertation data statistical analysis or evaluation, review of literature, and the final PowerPoint presentation. One of a dissertation’s most crucial elements, the statistical analysis section, is where you showcase your original research skills.

It can be challenging at first to analyze data and deal with statistics while writing your dissertation. However, there are several guidelines you can adhere to conduct statistical analysis in a dissertation.

In this article, we will discuss how to conduct statistical analysis in a dissertation.

Here’s what we’ll cover:

How to conduct statistical analysis in a dissertation, 1. selecting the appropriate statistical test.

Depending on the variables being examined and the nature/type of the queries that need to be resolved, we assist in choosing the most suitable statistical test. Whether category or numerical data is being evaluated also makes a difference. When deciding on a statistical test to use for an SPSS analysis, the following factors are frequently taken into account:

• Type and distribution of the information that was gathered:  Checking the distribution of the data is crucial before choosing the type of test to apply to it. When data is reliable, parametric tests are conducted; however, if the data has a non-normal distribution, non-parametric testing is selected. Using tools like the histogram, Q-plots, and graphical representations of the values, we test the normality of the data distribution. On nominal, ordinal, and discrete types of data, non-parametric testing is also employed. Continuous data can be analyzed using both parametric and non-parametric tests.
• Study goals and objectives:  The kind of statistical tests to use depends on the goal and objectives of a study. Depending on what the student wishes to accomplish before submitting the dissertation, our data analysis services may employ statistical tests, including regression analysis, chi-squared, t-tests, ANOVA, as well as correlations.

2. Preparing Your Data for Statistical Analysis

Before you start statistically analyzing your data, there are a few things you need to do, regardless of whether they are on paper or in a computer file (or both).

• First, ensure they don’t contain any information that might be used to identify specific participants.
• Secondly, make sure they don’t contain any data that might be used to identify specific participants.  Unless the information is extremely sensitive, a secured space or computer with a password is generally sufficient. Make copies of your data or create backup files, and store them in another safe place, at least until the work is finished.
• The next step is to verify that your raw data are complete and seem to have been recorded appropriately. You might discover at this point that there are unreadable, missing, or blatantly misunderstood responses. You must determine whether these issues are severe enough to render a participant’s data useless. You might need to remove that participant’s data from the analysis if details about the key independent or dependent variable are absent or if numerous responses are missing or questionable. Don’t throw away or erase any data that you do want to exclude because you or another researcher could need to access them in the future. Set them away temporarily, and make notes on why you chose to do so—you’ll need to report this data.

You can now prepare your data for statistical analysis if it already exists in a computer database or enter it in a spreadsheet program if it isn’t. Prepare your data for analysis or create your data file using the appropriate software, such as SPSS, SAS, or R.

3. Conducting the Statistical Analysis

You have reached the stage of statistical analysis where all of the data that has been helpful up to this point will be interpreted. It becomes challenging to present so much data in a cohesive way since large quantities of data need to be displayed. Think about all your options, including tables, graphs, diagrams, and charts, to address this problem.

Tables aid in the concise presentation of both quantitative and qualitative information. Keep your reader in mind at all times when presenting data. Anything that is obvious to you might not be to your reader. Therefore, keep in mind that someone who is unfamiliar with your research and conclusions may not be able to understand your data presentation style. If “No” is the response, you might want to reconsider your presentation.

Your dissertation’s analysis section could become unorganized and messy after providing a lot of data. If it does, you should add an appendix to prevent this. Include any information that is difficult for you to incorporate inside the main body text in the dissertation’s appendix section. Additionally, add data sheets, questions, and records of interviews and focus groups to the appendix. The statistical analysis and quotes from interviews, on the other hand, must be included in the dissertation.

4. Validity and Reliability Of Statistical Analysis

The idea that the information provided is self-explanatory is a prevalent one. The majority of students who use statistics and citations believe that this is sufficient for explaining everything. It is not enough. Instead of just repeating everything, you should study the information and decide whether facts will support or contradict your viewpoints. Indicates whether the data you use are reliable and dependable.

Demonstrate the concepts in full detail and critically evaluate each viewpoint, taking care to address any potential fault spots. If you want to give your research more credibility, you should always talk about the weaknesses and strengths of your data.

Importance of Statistical Analysis in a Dissertation

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• 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.

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• Knowledge Base

The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organisations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organise and summarise the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalise your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalising your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organising data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. 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 false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

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.

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• What is Effect Size and Why Does It Matter? (Examples)
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Usually there is no good way to write a statistic. It rarely sounds good, and often interrupts the structure or flow of your writing. Oftentimes the best way to write descriptive statistics is to be direct. If you are citing several statistics about the same topic, it may be best to include them all in the same paragraph or section.

The mean of exam two is 77.7. The median is 75, and the mode is 79. Exam two had a standard deviation of 11.6.

Overall the company had another excellent year. We shipped 14.3 tons of fertilizer for the year, and averaged 1.7 tons of fertilizer during the summer months. This is an increase over last year, where we shipped only 13.1 tons of fertilizer, and averaged only 1.4 tons during the summer months. (Standard deviations were as followed: this summer .3 tons, last summer .4 tons).

Some fields prefer to put means and standard deviations in parentheses like this:

If you have lots of statistics to report, you should strongly consider presenting them in tables or some other visual form. You would then highlight statistics of interest in your text, but would not report all of the statistics. See the section on statistics and visuals for more details.

If you have a data set that you are using (such as all the scores from an exam) it would be unusual to include all of the scores in a paper or article. One of the reasons to use statistics is to condense large amounts of information into more manageable chunks; presenting your entire data set defeats this purpose.

At the bare minimum, if you are presenting statistics on a data set, it should include the mean and probably the standard deviation. This is the minimum information needed to get an idea of what the distribution of your data set might look like. How much additional information you include is entirely up to you. In general, don't include information if it is irrelevant to your argument or purpose. If you include statistics that many of your readers would not understand, consider adding the statistics in a footnote or appendix that explains it in more detail.

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Mathematics and Statistics Theses and Dissertations

Theses/dissertations from 2023 2023.

Classification of Finite Topological Quandles and Shelves via Posets , Hitakshi Lahrani

Applied Analysis for Learning Architectures , Himanshu Singh

Rational Functions of Degree Five That Permute the Projective Line Over a Finite Field , Christopher Sze

Theses/Dissertations from 2022 2022

New Developments in Statistical Optimal Designs for Physical and Computer Experiments , Damola M. Akinlana

Advances and Applications of Optimal Polynomial Approximants , Raymond Centner

Data-Driven Analytical Predictive Modeling for Pancreatic Cancer, Financial & Social Systems , Aditya Chakraborty

On Simultaneous Similarity of d-tuples of Commuting Square Matrices , Corey Connelly

Symbolic Computation of Lump Solutions to a Combined (2+1)-dimensional Nonlinear Evolution Equation , Jingwei He

Boundary behavior of analytic functions and Approximation Theory , Spyros Pasias

Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function , Daniel Siebel-Cortopassi

A Functional Optimization Approach to Stochastic Process Sampling , Ryan Matthew Thurman

Theses/Dissertations from 2021 2021

Riemann-Hilbert Problems for Nonlocal Reverse-Time Nonlinear Second-order and Fourth-order AKNS Systems of Multiple Components and Exact Soliton Solutions , Alle Adjiri

Zeros of Harmonic Polynomials and Related Applications , Azizah Alrajhi

Combination of Time Series Analysis and Sentiment Analysis for Stock Market Forecasting , Hsiao-Chuan Chou

Uncertainty Quantification in Deep and Statistical Learning with applications in Bio-Medical Image Analysis , K. Ruwani M. Fernando

Data-Driven Analytical Modeling of Multiple Myeloma Cancer, U.S. Crop Production and Monitoring Process , Lohuwa Mamudu

Long-time Asymptotics for mKdV Type Reduced Equations of the AKNS Hierarchy in Weighted L 2 Sobolev Spaces , Fudong Wang

Online and Adjusted Human Activities Recognition with Statistical Learning , Yanjia Zhang

Theses/Dissertations from 2020 2020

Bayesian Reliability Analysis of The Power Law Process and Statistical Modeling of Computer and Network Vulnerabilities with Cybersecurity Application , Freeh N. Alenezi

Discrete Models and Algorithms for Analyzing DNA Rearrangements , Jasper Braun

Bayesian Reliability Analysis for Optical Media Using Accelerated Degradation Test Data , Kun Bu

On the p(x)-Laplace equation in Carnot groups , Robert D. Freeman

Clustering methods for gene expression data of Oxytricha trifallax , Kyle Houfek

Gradient Boosting for Survival Analysis with Applications in Oncology , Nam Phuong Nguyen

Global and Stochastic Dynamics of Diffusive Hindmarsh-Rose Equations in Neurodynamics , Chi Phan

Restricted Isometric Projections for Differentiable Manifolds and Applications , Vasile Pop

On Some Problems on Polynomial Interpolation in Several Variables , Brian Jon Tuesink

Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L -Ensemble of O ( n ) Model Type for n = 2 and n = 3 , Xiankui Yang

Non-Associative Algebraic Structures in Knot Theory , Emanuele Zappala

Theses/Dissertations from 2019 2019

Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries , Maryam Bagherian

Probabilistic Modeling of Democracy, Corruption, Hemophilia A and Prediabetes Data , A. K. M. Raquibul Bashar

Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras , Amine Ben Abdeljelil

Fractional Random Weighted Bootstrapping for Classification on Imbalanced Data with Ensemble Decision Tree Methods , Sean Charles Carter

Hierarchical Self-Assembly and Substitution Rules , Daniel Alejandro Cruz

Statistical Learning of Biomedical Non-Stationary Signals and Quality of Life Modeling , Mahdi Goudarzi

Probabilistic and Statistical Prediction Models for Alzheimer’s Disease and Statistical Analysis of Global Warming , Maryam Ibrahim Habadi

Essays on Time Series and Machine Learning Techniques for Risk Management , Michael Kotarinos

The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact , Daviel Leyva

Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms , Ozan Pirbudak

Analyses of Unorthodox Overlapping Gene Segments in Oxytricha Trifallax , Shannon Stich

An Optimal Medium-Strength Regularity Algorithm for 3-uniform Hypergraphs , John Theado

Power Graphs of Quasigroups , DayVon L. Walker

Theses/Dissertations from 2018 2018

Groups Generated by Automata Arising from Transformations of the Boundaries of Rooted Trees , Elsayed Ahmed

Non-equilibrium Phase Transitions in Interacting Diffusions , Wael Al-Sawai

A Hybrid Dynamic Modeling of Time-to-event Processes and Applications , Emmanuel A. Appiah

Lump Solutions and Riemann-Hilbert Approach to Soliton Equations , Sumayah A. Batwa

Developing a Model to Predict Prevalence of Compulsive Behavior in Individuals with OCD , Lindsay D. Fields

Generalizations of Quandles and their cohomologies , Matthew J. Green

Hamiltonian structures and Riemann-Hilbert problems of integrable systems , Xiang Gu

Optimal Latin Hypercube Designs for Computer Experiments Based on Multiple Objectives , Ruizhe Hou

Human Activity Recognition Based on Transfer Learning , Jinyong Pang

Signal Detection of Adverse Drug Reaction using the Adverse Event Reporting System: Literature Review and Novel Methods , Minh H. Pham

Statistical Analysis and Modeling of Cyber Security and Health Sciences , Nawa Raj Pokhrel

Machine Learning Methods for Network Intrusion Detection and Intrusion Prevention Systems , Zheni Svetoslavova Stefanova

Orthogonal Polynomials With Respect to the Measure Supported Over the Whole Complex Plane , Meng Yang

Theses/Dissertations from 2017 2017

Modeling in Finance and Insurance With Levy-It'o Driven Dynamic Processes under Semi Markov-type Switching Regimes and Time Domains , Patrick Armand Assonken Tonfack

Prevalence of Typical Images in High School Geometry Textbooks , Megan N. Cannon

On Extending Hansel's Theorem to Hypergraphs , Gregory Sutton Churchill

Contributions to Quandle Theory: A Study of f-Quandles, Extensions, and Cohomology , Indu Rasika U. Churchill

Linear Extremal Problems in the Hardy Space H p for 0 p , Robert Christopher Connelly

Statistical Analysis and Modeling of Ovarian and Breast Cancer , Muditha V. Devamitta Perera

Statistical Analysis and Modeling of Stomach Cancer Data , Chao Gao

Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings , Kumar Vijay Garapati

Dynamics of Multicultural Social Networks , Kristina B. Hilton

Cybersecurity: Stochastic Analysis and Modelling of Vulnerabilities to Determine the Network Security and Attackers Behavior , Pubudu Kalpani Kaluarachchi

Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations , Morgan Ashley McAnally

Patterns in Words Related to DNA Rearrangements , Lukas Nabergall

Time Series Online Empirical Bayesian Kernel Density Segmentation: Applications in Real Time Activity Recognition Using Smartphone Accelerometer , Shuang Na

Schreier Graphs of Thompson's Group T , Allen Pennington

Cybersecurity: Probabilistic Behavior of Vulnerability and Life Cycle , Sasith Maduranga Rajasooriya

Bayesian Artificial Neural Networks in Health and Cybersecurity , Hansapani Sarasepa Rodrigo

Real-time Classification of Biomedical Signals, Parkinson’s Analytical Model , Abolfazl Saghafi

Lump, complexiton and algebro-geometric solutions to soliton equations , Yuan Zhou

Theses/Dissertations from 2016 2016

A Statistical Analysis of Hurricanes in the Atlantic Basin and Sinkholes in Florida , Joy Marie D'andrea

Statistical Analysis of a Risk Factor in Finance and Environmental Models for Belize , Sherlene Enriquez-Savery

Putnam's Inequality and Analytic Content in the Bergman Space , Matthew Fleeman

On the Number of Colors in Quandle Knot Colorings , Jeremy William Kerr

Statistical Modeling of Carbon Dioxide and Cluster Analysis of Time Dependent Information: Lag Target Time Series Clustering, Multi-Factor Time Series Clustering, and Multi-Level Time Series Clustering , Doo Young Kim

Some Results Concerning Permutation Polynomials over Finite Fields , Stephen Lappano

Hamiltonian Formulations and Symmetry Constraints of Soliton Hierarchies of (1+1)-Dimensional Nonlinear Evolution Equations , Solomon Manukure

Modeling and Survival Analysis of Breast Cancer: A Statistical, Artificial Neural Network, and Decision Tree Approach , Venkateswara Rao Mudunuru

Generalized Phase Retrieval: Isometries in Vector Spaces , Josiah Park

Leonard Systems and their Friends , Jonathan Spiewak

Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations , Yue Sun

Statistical Analysis and Modeling Health Data: A Longitudinal Study , Bhikhari Prasad Tharu

Global Attractors and Random Attractors of Reaction-Diffusion Systems , Junyi Tu

Time Dependent Kernel Density Estimation: A New Parameter Estimation Algorithm, Applications in Time Series Classification and Clustering , Xing Wang

On Spectral Properties of Single Layer Potentials , Seyed Zoalroshd

Theses/Dissertations from 2015 2015

Analysis of Rheumatoid Arthritis Data using Logistic Regression and Penalized Approach , Wei Chen

Active Tile Self-assembly and Simulations of Computational Systems , Daria Karpenko

Nearest Neighbor Foreign Exchange Rate Forecasting with Mahalanobis Distance , Vindya Kumari Pathirana

Statistical Learning with Artificial Neural Network Applied to Health and Environmental Data , Taysseer Sharaf

Radial Versus Othogonal and Minimal Projections onto Hyperplanes in l_4^3 , Richard Alan Warner

Ensemble Learning Method on Machine Maintenance Data , Xiaochuang Zhao

Theses/Dissertations from 2014 2014

Properties of Graphs Used to Model DNA Recombination , Ryan Arredondo

Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability , Jonathan Burns

On the Classification of Groups Generated by Automata with 4 States over a 2-Letter Alphabet , Louis Caponi

Statistical Analysis, Modeling, and Algorithms for Pharmaceutical and Cancer Systems , Bong-Jin Choi

Topological Data Analysis of Properties of Four-Regular Rigid Vertex Graphs , Grant Mcneil Conine

Trend Analysis and Modeling of Health and Environmental Data: Joinpoint and Functional Approach , Ram C. Kafle

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Statistical Methods for Analyzing Interval-Censored Data

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• Affiliation: Gillings School of Global Public Health, Department of Biostatistics
• Interval-censored data arise when the event of interest is not directly observed, but rather known to occur within a time interval. The fact that none of the event times is exactly observed makes the regression analysis and model diagnosis challenging. This dissertation develops novel statistical methods for interval-censored data analysis in three projects. In the first project, we study the nonparametric maximum pseudo-likelihood estimation of marginal proportional hazards models for multivariate interval-censored data. We fit the models by maximizing the nonparametric maximum pseudo-likelihood under the working assumption that the event times are independent. We prove that the resulting estimators for the regression parameters are consistent and asymptotically normal with a covariance matrix that can be consistently estimated by a sandwich estimator. We evaluate the performance of the proposed methods through simulation studies and an application to the Atherosclerosis Risk in Communities Study. The second project extends the first project by considering recurrent events under interval censoring. We formulate the effects of covariates on multiple types of recurrent events through proportional rates models. We employ nonparametric maximum pseudo-likelihood estimation under the working assumptions that all types of events are independent and each type of event is a nonhomogeneous Poisson process. We show that the resulting estimators for the regression parameters are consistent and asymptotically normal, with a covariance matrix that can be estimated consistently by a sandwich estimator. We evaluate the performance of the proposed methods through simulation studies and analysis of a skin cancer clinical trial. In the third project, we present a framework for checking the adequacy of the Cox model with interval-censored data. We construct certain stochastic processes that are informative about various aspects of the model. We show that these stochastic processes can be viewed as the score statistics for testing zero regression parameters under some extended models and establish their weak convergence to Gaussian processes. We approximate the limiting distributions by Monte Carlo simulation and develop graphical and numerical procedures to check model assumptions. We evaluate the performance of the proposed methods through simulation studies and an application to the Atherosclerosis Risk in Communities Study.
• Model misspecification
• Public health
• Mathematics
• Interval censoring
• EM algorithm
• Survival analysis
• Profile likelihood
• https://doi.org/10.17615/drky-gr25
• Dissertation
• In Copyright - Educational Use Permitted
• Zeng, Dongling
• Hudgens, Michael
• Howard, Annie Green
• Avery, Christy
• Doctor of Philosophy
• University of North Carolina at Chapel Hill Graduate School

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Innovative Statistics Project Ideas for Insightful Analysis

Table of contents

• 1.1 AP Statistics Topics for Project
• 1.2 Statistics Project Topics for High School Students
• 1.3 Statistical Survey Topics
• 1.4 Statistical Experiment Ideas
• 1.5 Easy Stats Project Ideas
• 1.6 Business Ideas for Statistics Project
• 1.7 Socio-Economic Easy Statistics Project Ideas
• 1.8 Experiment Ideas for Statistics and Analysis
• 2 Conclusion: Navigating the World of Data Through Statistics

Diving into the world of data, statistics presents a unique blend of challenges and opportunities to uncover patterns, test hypotheses, and make informed decisions. It is a fascinating field that offers many opportunities for exploration and discovery. This article is designed to inspire students, educators, and statistics enthusiasts with various project ideas. We will cover:

• Challenging concepts suitable for advanced placement courses.
• Accessible ideas that are engaging and educational for younger students.
• Ideas for conducting surveys and analyzing the results.
• Topics that explore the application of statistics in business and socio-economic areas.

Each category of topics for the statistics project provides unique insights into the world of statistics, offering opportunities for learning and application. Let’s dive into these ideas and explore the exciting world of statistical analysis.

Top Statistics Project Ideas for High School

Statistics is not only about numbers and data; it’s a unique lens for interpreting the world. Ideal for students, educators, or anyone with a curiosity about statistical analysis, these project ideas offer an interactive, hands-on approach to learning. These projects range from fundamental concepts suitable for beginners to more intricate studies for advanced learners. They are designed to ignite interest in statistics by demonstrating its real-world applications, making it accessible and enjoyable for people of all skill levels.

Need help with statistics project? Get your paper written by a professional writer Get Help Reviews.io 4.9/5

AP Statistics Topics for Project

• Analyzing Variance in Climate Data Over Decades.
• The Correlation Between Economic Indicators and Standard of Living.
• Statistical Analysis of Voter Behavior Patterns.
• Probability Models in Sports: Predicting Outcomes.
• The Effectiveness of Different Teaching Methods: A Statistical Study.
• Analysis of Demographic Data in Public Health.
• Time Series Analysis of Stock Market Trends.
• Investigating the Impact of Social Media on Academic Performance.
• Survival Analysis in Clinical Trial Data.
• Regression Analysis on Housing Prices and Market Factors.

Statistics Project Topics for High School Students

• The Mathematics of Personal Finance: Budgeting and Spending Habits.
• Analysis of Class Performance: Test Scores and Study Habits.
• A Statistical Comparison of Local Public Transportation Options.
• Survey on Dietary Habits and Physical Health Among Teenagers.
• Analyzing the Popularity of Various Music Genres in School.
• The Impact of Sleep on Academic Performance: A Statistical Approach.
• Statistical Study on the Use of Technology in Education.
• Comparing Athletic Performance Across Different Sports.
• Trends in Social Media Usage Among High School Students.
• The Effect of Part-Time Jobs on Student Academic Achievement.

Statistical Survey Topics

• Public Opinion on Environmental Conservation Efforts.
• Consumer Preferences in the Fast Food Industry.
• Attitudes Towards Online Learning vs. Traditional Classroom Learning.
• Survey on Workplace Satisfaction and Productivity.
• Public Health: Attitudes Towards Vaccination.
• Trends in Mobile Phone Usage and Preferences.
• Community Response to Local Government Policies.
• Consumer Behavior in Online vs. Offline Shopping.
• Perceptions of Public Safety and Law Enforcement.
• Social Media Influence on Political Opinions.

Statistical Experiment Ideas

• The Effect of Light on Plant Growth.
• Memory Retention: Visual vs. Auditory Information.
• Caffeine Consumption and Cognitive Performance.
• The Impact of Exercise on Stress Levels.
• Testing the Efficacy of Natural vs. Chemical Fertilizers.
• The Influence of Color on Mood and Perception.
• Sleep Patterns: Analyzing Factors Affecting Sleep Quality.
• The Effectiveness of Different Types of Water Filters.
• Analyzing the Impact of Room Temperature on Concentration.
• Testing the Strength of Different Brands of Batteries.

Easy Stats Project Ideas

• Average Daily Screen Time Among Students.
• Analyzing the Most Common Birth Months.
• Favorite School Subjects Among Peers.
• Average Time Spent on Homework Weekly.
• Frequency of Public Transport Usage.
• Comparison of Pet Ownership in the Community.
• Favorite Types of Movies or TV Shows.
• Daily Water Consumption Habits.
• Common Breakfast Choices and Their Nutritional Value.
• Steps Count: A Week-Long Study.

Business Ideas for Statistics Project

• Analyzing Customer Satisfaction in Retail Stores.
• Market Analysis of a New Product Launch.
• Employee Performance Metrics and Organizational Success.
• Sales Data Analysis for E-commerce Websites.
• Impact of Advertising on Consumer Buying Behavior.
• Analysis of Supply Chain Efficiency.
• Customer Loyalty and Retention Strategies.
• Trend Analysis in Social Media Marketing.
• Financial Risk Assessment in Investment Decisions.
• Market Segmentation and Targeting Strategies.

Socio-Economic Easy Statistics Project Ideas

• Income Inequality and Its Impact on Education.
• The Correlation Between Unemployment Rates and Crime Levels.
• Analyzing the Effects of Minimum Wage Changes.
• The Relationship Between Public Health Expenditure and Population Health.
• Demographic Analysis of Housing Affordability.
• The Impact of Immigration on Local Economies.
• Analysis of Gender Pay Gap in Different Industries.
• Statistical Study of Homelessness Causes and Solutions.
• Education Levels and Their Impact on Job Opportunities.
• Analyzing Trends in Government Social Spending.

Experiment Ideas for Statistics and Analysis

• Multivariate Analysis of Global Climate Change Data.
• Time-Series Analysis in Predicting Economic Recessions.
• Logistic Regression in Medical Outcome Prediction.
• Machine Learning Applications in Statistical Modeling.
• Network Analysis in Social Media Data.
• Bayesian Analysis of Scientific Research Data.
• The Use of Factor Analysis in Psychology Studies.
• Spatial Data Analysis in Geographic Information Systems (GIS).
• Predictive Analysis in Customer Relationship Management (CRM).
• Cluster Analysis in Market Research.

Conclusion: Navigating the World of Data Through Statistics

In this exploration of good statistics project ideas, we’ve ventured through various topics, from the straightforward to the complex, from personal finance to global climate change. These ideas are gateways to understanding the world of data and statistics, and platforms for cultivating critical thinking and analytical skills. Whether you’re a high school student, a college student, or a professional, engaging in these projects can deepen your appreciation of how statistics shapes our understanding of the world around us. These projects encourage exploration, inquiry, and a deeper engagement with the world of numbers, trends, and patterns – the essence of statistics.

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