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Methodology

Guide to Experimental Design | Overview, Steps, & Examples

Guide to Experimental Design | Overview, 5 steps & Examples

Published on December 3, 2019 by Rebecca Bevans . Revised on June 21, 2023.

Experiments are used to study causal relationships . You manipulate one or more independent variables and measure their effect on one or more dependent variables.

Experimental design create a set of procedures to systematically test a hypothesis . A good experimental design requires a strong understanding of the system you are studying.

There are five key steps in designing an experiment:

Consider your variables and how they are related
Write a specific, testable hypothesis
Design experimental treatments to manipulate your independent variable
Assign subjects to groups, either between-subjects or within-subjects
Plan how you will measure your dependent variable

For valid conclusions, you also need to select a representative sample and control any extraneous variables that might influence your results. If random assignment of participants to control and treatment groups is impossible, unethical, or highly difficult, consider an observational study instead. This minimizes several types of research bias, particularly sampling bias , survivorship bias , and attrition bias as time passes.

Step 1: define your variables, step 2: write your hypothesis, step 3: design your experimental treatments, step 4: assign your subjects to treatment groups, step 5: measure your dependent variable, other interesting articles, frequently asked questions about experiments.

You should begin with a specific research question . We will work with two research question examples, one from health sciences and one from ecology:

To translate your research question into an experimental hypothesis, you need to define the main variables and make predictions about how they are related.

Start by simply listing the independent and dependent variables .

Research question	Independent variable	Dependent variable
Phone use and sleep	Minutes of phone use before sleep	Hours of sleep per night
Temperature and soil respiration	Air temperature just above the soil surface	CO2 respired from soil

Then you need to think about possible extraneous and confounding variables and consider how you might control them in your experiment.

	Extraneous variable	How to control
Phone use and sleep	in sleep patterns among individuals.	measure the average difference between sleep with phone use and sleep without phone use rather than the average amount of sleep per treatment group.
Temperature and soil respiration	also affects respiration, and moisture can decrease with increasing temperature.	monitor soil moisture and add water to make sure that soil moisture is consistent across all treatment plots.

Finally, you can put these variables together into a diagram. Use arrows to show the possible relationships between variables and include signs to show the expected direction of the relationships.

Diagram of the relationship between variables in a sleep experiment

Here we predict that increasing temperature will increase soil respiration and decrease soil moisture, while decreasing soil moisture will lead to decreased soil respiration.

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Now that you have a strong conceptual understanding of the system you are studying, you should be able to write a specific, testable hypothesis that addresses your research question.

	Null hypothesis (H )	Alternate hypothesis (H )
Phone use and sleep	Phone use before sleep does not correlate with the amount of sleep a person gets.	Increasing phone use before sleep leads to a decrease in sleep.
Temperature and soil respiration	Air temperature does not correlate with soil respiration.	Increased air temperature leads to increased soil respiration.

The next steps will describe how to design a controlled experiment . In a controlled experiment, you must be able to:

Systematically and precisely manipulate the independent variable(s).
Precisely measure the dependent variable(s).
Control any potential confounding variables.

If your study system doesn’t match these criteria, there are other types of research you can use to answer your research question.

How you manipulate the independent variable can affect the experiment’s external validity – that is, the extent to which the results can be generalized and applied to the broader world.

First, you may need to decide how widely to vary your independent variable.

just slightly above the natural range for your study region.
over a wider range of temperatures to mimic future warming.
over an extreme range that is beyond any possible natural variation.

Second, you may need to choose how finely to vary your independent variable. Sometimes this choice is made for you by your experimental system, but often you will need to decide, and this will affect how much you can infer from your results.

a categorical variable : either as binary (yes/no) or as levels of a factor (no phone use, low phone use, high phone use).
a continuous variable (minutes of phone use measured every night).

How you apply your experimental treatments to your test subjects is crucial for obtaining valid and reliable results.

First, you need to consider the study size : how many individuals will be included in the experiment? In general, the more subjects you include, the greater your experiment’s statistical power , which determines how much confidence you can have in your results.

Then you need to randomly assign your subjects to treatment groups . Each group receives a different level of the treatment (e.g. no phone use, low phone use, high phone use).

You should also include a control group , which receives no treatment. The control group tells us what would have happened to your test subjects without any experimental intervention.

When assigning your subjects to groups, there are two main choices you need to make:

A completely randomized design vs a randomized block design .
A between-subjects design vs a within-subjects design .

Randomization

An experiment can be completely randomized or randomized within blocks (aka strata):

In a completely randomized design , every subject is assigned to a treatment group at random.
In a randomized block design (aka stratified random design), subjects are first grouped according to a characteristic they share, and then randomly assigned to treatments within those groups.

	Completely randomized design	Randomized block design
Phone use and sleep	Subjects are all randomly assigned a level of phone use using a random number generator.	Subjects are first grouped by age, and then phone use treatments are randomly assigned within these groups.
Temperature and soil respiration	Warming treatments are assigned to soil plots at random by using a number generator to generate map coordinates within the study area.	Soils are first grouped by average rainfall, and then treatment plots are randomly assigned within these groups.

Sometimes randomization isn’t practical or ethical , so researchers create partially-random or even non-random designs. An experimental design where treatments aren’t randomly assigned is called a quasi-experimental design .

Between-subjects vs. within-subjects

In a between-subjects design (also known as an independent measures design or classic ANOVA design), individuals receive only one of the possible levels of an experimental treatment.

In medical or social research, you might also use matched pairs within your between-subjects design to make sure that each treatment group contains the same variety of test subjects in the same proportions.

In a within-subjects design (also known as a repeated measures design), every individual receives each of the experimental treatments consecutively, and their responses to each treatment are measured.

Within-subjects or repeated measures can also refer to an experimental design where an effect emerges over time, and individual responses are measured over time in order to measure this effect as it emerges.

Counterbalancing (randomizing or reversing the order of treatments among subjects) is often used in within-subjects designs to ensure that the order of treatment application doesn’t influence the results of the experiment.

	Between-subjects (independent measures) design	Within-subjects (repeated measures) design
Phone use and sleep	Subjects are randomly assigned a level of phone use (none, low, or high) and follow that level of phone use throughout the experiment.	Subjects are assigned consecutively to zero, low, and high levels of phone use throughout the experiment, and the order in which they follow these treatments is randomized.
Temperature and soil respiration	Warming treatments are assigned to soil plots at random and the soils are kept at this temperature throughout the experiment.	Every plot receives each warming treatment (1, 3, 5, 8, and 10C above ambient temperatures) consecutively over the course of the experiment, and the order in which they receive these treatments is randomized.

Finally, you need to decide how you’ll collect data on your dependent variable outcomes. You should aim for reliable and valid measurements that minimize research bias or error.

Some variables, like temperature, can be objectively measured with scientific instruments. Others may need to be operationalized to turn them into measurable observations.

Ask participants to record what time they go to sleep and get up each day.
Ask participants to wear a sleep tracker.

How precisely you measure your dependent variable also affects the kinds of statistical analysis you can use on your data.

Experiments are always context-dependent, and a good experimental design will take into account all of the unique considerations of your study system to produce information that is both valid and relevant to your research question.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

Student’s t -distribution
Normal distribution
Null and Alternative Hypotheses
Chi square tests
Confidence interval
Cluster sampling
Stratified sampling
Data cleansing
Reproducibility vs Replicability
Peer review
Likert scale

Research bias

Implicit bias
Framing effect
Cognitive bias
Placebo effect
Hawthorne effect
Hindsight bias
Affect heuristic

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

A testable hypothesis
At least one independent variable that can be precisely manipulated
At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

How you will manipulate the variable(s)
How you will control for any potential confounding variables
How many subjects or samples will be included in the study
How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

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A Comprehensive Guide to Design of Experiments: Concepts, Techniques, and Case Study Analysis

Nilimesh Halder, PhD

Introduction: The Importance of Design of Experiments in Data Science

Design of Experiments (DOE) is a powerful statistical methodology that enables researchers and practitioners to systematically plan, design, and analyze experiments in a controlled manner. By carefully structuring and analyzing experimental data, DOE allows for the identification of significant factors, interactions, and optimal settings that influence a response variable. In this extensive article, we will discuss the fundamental concepts of DOE, delve into various DOE techniques, and analyze a case study to illustrate the application of these concepts in practice.

1. Fundamental Concepts of Design of Experiments

1.1 factors and levels.

In the context of DOE, factors are the variables or conditions that can be controlled or manipulated during an experiment. Levels represent the different values or settings of these factors. For example, when testing the effectiveness of a drug, the factors could be dosage and administration frequency, with each factor having multiple levels.

1.2 Response Variables

Written by Nilimesh Halder, PhD

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A previous course in basic statistical methods. The required background is introduced and reviewed as needed throughout the course.

What you'll learn

Plan, design and conduct experiments efficiently and effectively, and analyze the resulting data to obtain valid objective conclusions.

Use response surface methods for system optimization as a follow-up to successful screening.

Use experimental design tools for computer experiments, both deterministic and stochastic computer models.

Use software tools to create custom designs based on optimal design methodology for situations where standard designs are not easily applicable.

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Learn modern experimental strategy, including factorial and fractional factorial experimental designs, designs for screening many factors, designs for optimization experiments, and designs for complex experiments such as those with hard-to-change factors and unusual responses. There is thorough coverage of modern data analysis techniques for experimental design, including software. Applications include electronics and semiconductors, automotive and aerospace, chemical and process industries, pharmaceutical and bio-pharm, medical devices, and many others.

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Participants will complete a project that is typically based around their own work environment, and can use this to effectively demonstrate the application of experimental design methodology. The structure of the course and the step-by-stem process taught in the course is designed to ensure participant success.

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By the end of this course, you will be able to:

Approach complex industrial and business research problems and address them through a rigorous, statistically sound experimental strategy

Use modern software to effectively plan experiments

Analyze the resulting data of an experiment, and communicate the results effectively to decision-makers.

Factorial and Fractional Factorial Designs

Conduct a factorial experiment in blocks and construct and analyze a fractional factorial design

Apply the factorial concept to experiments with several factors

Use the analysis of variance for factorial designs

Use the 2^k system of factorial designs

Response Surfaces, Mixtures, and Model Building

Conduct experiments w/computer models and understand how least squares regression is used to build an empirical model from experimental design data

Understand the response surface methodology strategy to conduct experiments where system optimization is the objective

Recognize how the response surface approach can be used for experiments where the factors are the components of a mixture

Recognize where the objective of the experiment is to minimize the variability transmitted into the response from uncontrollable factors

Random Models, Nested and Split-plot Designs

Design and analyze experiments where some of the factors are random

Design and analyze experiments where there are nested factors or hard-to-change factors

Analyze experiments with covariates

Design and analyze experiments with nonnormal response distributions

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Frequently asked questions

How long does it take to complete the specialization.

There are 15 modules, spread across 4 courses. Each module is based on one chapter of the textbook. The specialization can be completed in approximately 4 months.

What background knowledge is necessary?

Knowledge of basic statistical methods, although the background knowledge is introduced and reviewed throughout the course as needed.

Do I need to take the courses in a specific order?

It is not necessary to take the courses in a specific order, but we recommend taking the courses in the order presented, as each subsequent course will build on material from previous courses.

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Design efficient and effective experiments to solve a wide variety of problems in science, engineering, and business where data collection and analysis is essential to success.

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Lesson 1: introduction to design of experiments, overview section .

In this course we will pretty much cover the textbook - all of the concepts and designs included. I think we will have plenty of examples to look at and experience to draw from.

Please note: the main topics listed in the syllabus follow the chapters in the book.

A word of advice regarding the analyses. The prerequisite for this course is STAT 501 - Regression Methods and STAT 502 - Analysis of Variance . However, the focus of the course is on the design and not on the analysis. Thus, one can successfully complete this course without these prerequisites, with just STAT 500 - Applied Statistics for instance, but it will require much more work, and for the analysis less appreciation of the subtleties involved. You might say it is more conceptual than it is math oriented.

Text Reference: Montgomery, D. C. (2019). Design and Analysis of Experiments , 10th Edition, John Wiley & Sons. ISBN 978-1-119-59340-9

What is the Scientific Method? Section

Do you remember learning about this back in high school or junior high even? What were those steps again?

Decide what phenomenon you wish to investigate. Specify how you can manipulate the factor and hold all other conditions fixed, to insure that these extraneous conditions aren't influencing the response you plan to measure.

Then measure your chosen response variable at several (at least two) settings of the factor under study. If changing the factor causes the phenomenon to change, then you conclude that there is indeed a cause-and-effect relationship at work.

How many factors are involved when you do an experiment? Some say two - perhaps this is a comparative experiment? Perhaps there is a treatment group and a control group? If you have a treatment group and a control group then, in this case, you probably only have one factor with two levels.

How many of you have baked a cake? What are the factors involved to ensure a successful cake? Factors might include preheating the oven, baking time, ingredients, amount of moisture, baking temperature, etc.-- what else? You probably follow a recipe so there are many additional factors that control the ingredients - i.e., a mixture. In other words, someone did the experiment in advance! What parts of the recipe did they vary to make the recipe a success? Probably many factors, temperature and moisture, various ratios of ingredients, and presence or absence of many additives. Now, should one keep all the factors involved in the experiment at a constant level and just vary one to see what would happen? This is a strategy that works but is not very efficient. This is one of the concepts that we will address in this course.

understand the issues and principles of Design of Experiments (DOE),
understand experimentation is a process,
list the guidelines for designing experiments, and
recognize the key historical figures in DOE.

Design of Experiments

Credit hours:, learning objective:, description:.

A thorough and practical course in design and analysis of experiments for experimental workers and applied statisticians. SAS statistical software is used for analysis. Taken by graduate students from many fields. F2018 STAT514 Syllabus

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Prerequisites:, applied / theory:, web address:, web content:, computer requirements:, other requirements:, proed minimum requirements:.

Design and Analysis of Experiments

Description.

Explore innovative strategies for constructing and executing experiments—including factorial and fractional factorial designs—that can be applied across the physical, chemical, biological, medical, social, psychological, economic, engineering, and industrial sciences. Over the course of five days, you’ll enhance your ability to conduct cost-effective, efficient experiments, and analyze the data that they yield in order to derive maximal value for your organization.

Course Overview

THIS COURSE MAY BE TAKEN INDIVIDUALLY OR As part of THE PROFESSIONAL CERTIFICATE PROGRAM IN BIOTECHNOLOGY & LIFE SCIENCES .

This program is planned for those interested in the design, conduct, and analysis of experiments in the physical, chemical, biological, medical, social, psychological, economic, engineering, or industrial sciences. The course will examine how to design experiments, carry them out, and analyze the data they yield. Various designs are discussed and their respective differences, advantages, and disadvantages are noted. In particular, factorial and fractional factorial designs are discussed in greater detail. These are designs in which two or more factors are varied simultaneously; the experimenter wishes to study not only the effect of each factor, but also how the effect of one factor changes as the levels of other factors change. The latter is generally referred to as an interaction effect among factors.

The fractional factorial design has been chosen for extra-detailed study in view of its considerable record of success over the last 30 years. It has been found to allow cost reduction, increase efficiency of experimentation, and often reveal the essential nature of a process. In addition, it is readily understood by those who are conducting the experiments, as well as those to whom the results are reported.

The program will be elementary in terms of mathematics. The course includes a review of the modest probability and statistics background necessary for conducting and analyzing scientific experimentation. With this background, we first discuss the logic of hypothesis testing and, in particular, the statistical techniques generally referred to as Analysis of Variance. A variety of software packages are illustrated, including Excel, SPSS, JMP, and other more specialized packages.

Throughout the program we emphasize applications, using real examples from the areas mentioned above, including such relatively new areas as experimentation in the social and economic sciences.

We discuss Taguchi methods and compare and contrast them with more traditional techniques. These methods, originating in Japan, have engendered significant interest in the United States.

All participants receive a copy of the text, Experimental Design: with applications in management, engineering and the sciences , Duxbury Press, 2002, co-authored by Paul D. Berger and Robert E. Maurer, in addition to extensive PowerPoint notes.

Participant Takeaways

Describe how to design experiments, carry them out, and analyze the data they yield.
Understand the process of designing an experiment including factorial and fractional factorial designs.
Examine how a factorial design allows cost reduction, increases efficiency of experimentation, and reveals the essential nature of a process; and discuss its advantages to those who conduct the experiments as well as those to whom the results are reported.
Investigate the logic of hypothesis testing, including analysis of variance and the detailed analysis of experimental data.
Formulate understanding of the subject using real examples, including experimentation in the social and economic sciences.
Introduce Taguchi methods, and compare and contrast them with more traditional techniques.
Learn the technique of regression analysis, and how it compares and contrasts with other techniques studied in the course.
Understand the role of response surface methodology and its basic underpinnings.
Gain an understanding of how the analysis of experimental design data is carried out using the most common software packages.
Be able to apply what you have learned immediately upon return to your company.

Who Should Attend

This course is appropriate for anyone interested in designing, conducting, and analyzing experiments in the biological, chemical, economic, engineering, industrial, medical, physical, psychological, or social sciences. Applicants need only have interest in experimentation. No previous training in probability and statistics is required, but any experience in these areas will be useful.

Program Outline

Class runs 9:00 am - 5:00 pm every day.

Introduction to Experimental Design
Hypothesis Testing
ANOVA I, Assumptions, Software
Multiple Comparison Testing
ANOVA II, Interaction Effects
Latin Squares and Graeco-Latin Squares
2K Designs (continued)
Confounding/Blocking Designs
Confounding/Blocking Designs (continued)
2k-p Fractional-Factorial Designs
2k-p Fractional-Factorial Designs (continued)
Taguchi Designs
Taguchi Designs (continued)
Orthogonality and Orthogonal contrasts
3K Factorial Designs
Regression Analysis I
Regression Analysis II
Regression Analysis III & Introduction to Response Surface Modeling
Response Surface Modeling (continued), Literature Review, Course Summary

AMONG THE SUBJECTS TO BE DISCUSSED ARE:

The logic of complete two-level factorial designs
Detailed discussion of interaction among studied factors
Large versus small experiments
Simultaneous study of several factors versus study of one factor at a time
Fractional experimental designs; construction and examples
The application of hypothesis testing to analyzing experiments
The important role of orthogonality in modern experimental design
Single degree-of-freedom analysis; pinpointing sources of variability
The trade-off between interaction and replication
Response surface experimentation
Yates' forward algorithm
The reliability of estimates in factorial designs
The usage of software in design and analysis of experiments
Latin and Graeco-Latin squares as fractional designs; examples
Designs with all studied factors at three levels
The role of fractional designs in response surface experimentation
Taguchi designs
Incomplete study of many factors versus intensive study of a few factors
Multivariate linear regression models
The book and journal literature on experimental design

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Biotechnology & Life Sciences

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Design and Analysis of Experiments

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Course Overview

THIS COURSE MAY BE TAKEN INDIVIDUALLY OR As part of THE PROFESSIONAL CERTIFICATE PROGRAM IN BIOTECHNOLOGY & LIFE SCIENCES .

Throughout the program we emphasize applications, using real examples from the areas mentioned above, including such relatively new areas as experimentation in the social and economic sciences.

We discuss Taguchi methods and compare and contrast them with more traditional techniques. These methods, originating in Japan, have engendered significant interest in the United States.

Participant Takeaways

Describe how to design experiments, carry them out, and analyze the data they yield.
Understand the process of designing an experiment including factorial and fractional factorial designs.
Examine how a factorial design allows cost reduction, increases efficiency of experimentation, and reveals the essential nature of a process; and discuss its advantages to those who conduct the experiments as well as those to whom the results are reported.
Investigate the logic of hypothesis testing, including analysis of variance and the detailed analysis of experimental data.
Formulate understanding of the subject using real examples, including experimentation in the social and economic sciences.
Introduce Taguchi methods, and compare and contrast them with more traditional techniques.
Learn the technique of regression analysis, and how it compares and contrasts with other techniques studied in the course.
Understand the role of response surface methodology and its basic underpinnings.
Gain an understanding of how the analysis of experimental design data is carried out using the most common software packages.
Be able to apply what you have learned immediately upon return to your company.

Who Should Attend

Program Outline

Class runs 9:00 am - 5:00 pm every day.

Introduction to Experimental Design
Hypothesis Testing
ANOVA I, Assumptions, Software
Multiple Comparison Testing
ANOVA II, Interaction Effects
Latin Squares and Graeco-Latin Squares
2K Designs (continued)
Confounding/Blocking Designs
Confounding/Blocking Designs (continued)
2k-p Fractional-Factorial Designs
2k-p Fractional-Factorial Designs (continued)
Taguchi Designs
Taguchi Designs (continued)
Orthogonality and Orthogonal contrasts
3K Factorial Designs
Regression Analysis I
Regression Analysis II
Regression Analysis III & Introduction to Response Surface Modeling
Response Surface Modeling (continued), Literature Review, Course Summary

AMONG THE SUBJECTS TO BE DISCUSSED ARE:

The logic of complete two-level factorial designs
Detailed discussion of interaction among studied factors
Large versus small experiments
Simultaneous study of several factors versus study of one factor at a time
Fractional experimental designs; construction and examples
The application of hypothesis testing to analyzing experiments
The important role of orthogonality in modern experimental design
Single degree-of-freedom analysis; pinpointing sources of variability
The trade-off between interaction and replication
Response surface experimentation
Yates' forward algorithm
The reliability of estimates in factorial designs
The usage of software in design and analysis of experiments
Latin and Graeco-Latin squares as fractional designs; examples
Designs with all studied factors at three levels
The role of fractional designs in response surface experimentation
Taguchi designs
Incomplete study of many factors versus intensive study of a few factors
Multivariate linear regression models
The book and journal literature on experimental design

Testimonials

The type of content you will learn in this course, whether it's a foundational understanding of the subject, the hottest trends and developments in the field, or suggested practical applications for industry.

How the course is taught, from traditional classroom lectures and riveting discussions to group projects to engaging and interactive simulations and exercises with your peers.

What level of expertise and familiarity the material in this course assumes you have. The greater the amount of introductory material taught in the course, the less you will need to be familiar with when you attend.

General & Introductory Industrial Engineering

Design and Analysis of Experiments, 10th Edition

ISBN: 978-1-119-49244-3

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Douglas C. Montgomery

Design and Analysis of Experiments provides a rigorous introduction to product and process design improvement through quality and performance optimization. Clear demonstration of widely practiced techniques and procedures allows readers to master fundamental concepts, develop design and analysis skills, and use experimental models and results in real-world applications. Detailed coverage of factorial and fractional factorial design, response surface techniques, regression analysis, biochemistry and biotechnology, single factor experiments, and other critical topics offer highly-relevant guidance through the complexities of the field.

Stressing the importance of both conceptual knowledge and practical skills, this text adopts a balanced approach to theory and application. Extensive discussion of modern software tools integrate data from real-world studies, while examples illustrate the efficacy of designed experiments across industry lines, from service and transactional organizations to heavy industry and biotechnology. Broad in scope yet deep in detail, this text is both an essential student resource and an invaluable reference for professionals in engineering, science, manufacturing, statistics, and business management.

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Design and Analysis of Experiments and Observational Studies using R : A Volume in the Chapman & Hall/CRC Texts in Statistical Science Series

This website is free to use, and is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License .

About the Author

Nathan Taback is an Associate Professor, Teaching Stream in the Department of Statistical Sciences, University of Toronto

Organization of the book

The structure of each chapter presents concepts or methods followed by a section that shows readers how to implement these in R. These sections are labeled “ Computational Lab: Topic ”, where “ Topic ” is the topic that is implemented in R.

Software information and conventions

One of the unique features of this book is the emphasis on simulation and computation using R. R is wonderful because of the many open source packages available, but this can also lead to confusion about which packages to use for a task. I have tried to minimize the number of packages used in the book. The set of packages loaded on startup by default is

plus base . If a function from a non-default library is used, then this is indicated by pkg::name instead of

This should make it clear which package a user needs to load before using a function.

Information on the R version used to write this book is below.

The packages used in writing this book are:

Whenever possible the R code developed in this book is written as a function instead of a series of statements. “Functions allow you to automate common tasks in a more powerful and general way than copy-and-pasting.” 1 In fact, I have taken the approach that whenever I’ve copied and pasted a block of code more than twice then it’s time to write a function.

The value an R function returns is the last value evaluated. return() can be used to return a value before the last value. Many of the functions in this book use return() to make code easier to read even when the last value of the function is returned.

R 4.1.0 now provides a simple native forward pipe syntax |> . The simple form of the forward pipe inserts the left-hand side as the first argument in the right-hand side call. The pipe syntax used in this book is %>% from the magrittr library. Most of the code in this book should work with the native pipe |> , although this has not been thoroughly tested.

The data sets used in this book are available in the R package scidesignR , and can be installed by running install.packages("scidesignR") .

Acknowledgments

I would like to thank all the students and instructors who used my notes and provided valuable feedback. Michael Moon provided excellent assistance with helping me develop many of the exercises. Monika, Adam, and Oliver, as usual, provided sustained support throughout this project.

Montgomery:

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The past and present of thought experiments’ research at Glancy: bibliometric review and analysis

Open access
Published: 07 September 2024
Volume 3 , article number 142 , ( 2024 )

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Hartono Bancong 1

In the development of physical theories, thought experiments play a crucial role. Research on this topic began in 1976 and has continued to the present. This study aims to provide a more complete picture of the progress of thought experiments over the past two decades. To achieve this, this study employs bibliometric mapping methods. A total of 679 published papers were analyzed, including articles (504), conference papers (92), and book chapters (83). This data was retrieved from the Scopus database. The study's findings reveal that research and publications on thought experiments are highly valued and have received significant attention over the past eight years. According to the findings, 90% of the top 20 source titles contributing to thought experiments are from journals in the first and second quartiles (Q1 and Q2). This quartile ranking shows the quality and significant influence of a journal. The geographical distribution indicates that the United States contributes the most to thought experiments research, with 213 documents, 2592 citations, and 47 links. We also identified several prospective keywords that could be the focus of future research, including artificial intelligence, physics education, fiction, God, theology, productive imagination, technology, speculative design, and critical design. Therefore, this study provides a thorough picture of thought experiment research trends and future directions of potential topics that can be the focus of future researchers.

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1 Introduction

Thought experiments (TEs) have a long history in science. Since Ernst Mach, the term TEs, a direct translation of the phrase Gedankenexperimente , has been widely discussed in the philosophy of science [ 18 ]. Thought and experiments are two components of TEs [ 4 , 18 , 29 ]. The thought element involves visualizing an imaginary world based on theory and experience, whereas the experimental aspect entails practical tasks in a physical laboratory, such as manipulating items and related variables. While some authors consider TEs to be mere arguments [ 24 ], others believe TEs are a form of fiction since their function is comparable to literary fiction in that both have a narrative framework by creating scenarios of occurrences from beginning to end [ 13 , 22 ]. However, unlike fiction, which frequently provides contradictory discourses, we believe that TEs should be logically and conceptually cohesive. TEs are structured imaginative actions based on the theory and experience of thought experimenters to achieve certain goals.

The contributions of TEs to the growth of scientific theories, particularly in physics, are essential. Physicists have employed TEs several times throughout history to either come up with new hypotheses or disprove previous ones. As the most representative examples, Newton used the TEs of cannonballs to support his hypothesis that the force of gravity is universal and the principal force of planetary motion, or Galileo used the TEs of free-falling bodies to disprove Aristotle's theory of gravity, which stated that the speed of falling objects is proportional to their weight. Galileo’s falling body, Newton's bucket and cannon, Maxwell's demon, and Schrodinger’s cat are just a few of the well-known TEs in physics [ 4 ]. These are only a few examples of the significant role TEs played in the development of scientific theories.

In the past 10 years, several works have studied TEs from the perspectives of history and philosophy of science [ 7 , 8 , 10 , 30 , 33 ]. Because most existing historical work on TEs focuses on individual TEs or individual accounts of TEs, reassessing the history of the philosophical debate on TEs becomes essential [ 33 ]. In the philosophy of science, historical debates regarding interactions between various philosophers or philosophical explanations across time in developed TEs are sometimes disregarded. Several studies have also used TEs as an imaginative tool in the classroom to teach science subjects. Velentzas and Halkia [ 37 ], for example, used TEs from Newton's Cannon to teach satellite physics. They then assert that TEs, as a teaching tool, can assist students in strengthening their syllogistic abilities and help them conceive scenarios beyond their everyday experience [ 37 ]. El Skaf and Palacios [ 12 ] have also systematically analyzed the epistemic role of TEs from Wheeler's demon and Geroch's engine, which gave rise to black hole thermodynamics. Recently, Bancong et al. [ 2 ] reported that physics teachers in Indonesia have a high awareness of the importance of TEs in learning physics, especially atomic theory and relativity, even though they lack skills in the pedagogic aspects of TEs. Therefore, Indonesian physics teachers also suggest using technology such as virtual reality to help visualize an imaginary world when performing TEs.

Although a number of studies on TEs from various perspectives have been conducted, no study has yet completely examined this field to look at the trend of this topic in recent years. Therefore, it becomes essential to conduct a bibliometric study of TEs over time based on authoritative databases like Scopus. Because of Scopus's comprehensive coverage of scholarly articles in the field of education [ 23 , 27 , 34 ], it was chosen as the database for this study. Scopus is also a popular resource for bibliometric research [ 23 , 28 ]. For this reason, we use data sources from the Scopus database to carry out the bibliometric method. Our study covers journal articles, conference papers, and book chapters from the last 20 years to provide a more complete view.

To highlight the significance of TEs research, we compare its growth to other scientific topics. While many scientific fields have seen growth over the past two decades, TEs research has also shown a unique and sustained increase in interest and publications. This trend contrasts sharply with the decline in research focus on traditional physics experiments [ 41 ]. Similarly, other topics in physics education, such as methodological issues, textbook analysis, and pre-service physics teachers, are also experiencing reduced research interest [ 25 ]. Additionally, the integration of TEs with emerging technologies, such as artificial intelligence, underscores their evolving relevance and potential for future research [ 21 ].

Therefore, this study aims to provide an up-to-date overview of trends in TEs research. The research questions in this study are as follows:

How is the growth of research output on the topic of TEs over the last 20 years?

Which source titles have contributed the most to the publication of papers on TEs in the last 20 years?

Who are the most prominent authors on the topic of TEs in the last 20 years?

Which countries have published the most articles on TEs over the past 20 years?

What are the most relevant keywords that can be found in the studies of TEs over the last 20 years?

2.1 Research design

This study aims to analyze the trends in TEs research over the past 20 years by using a bibliometric mapping method. To ensure a thorough analysis of recent trends and developments, this study focused on studies published between 2003 and 2022. This period was chosen because of significant advancements in research methodologies and bibliometric analysis tools in the early 2000s, as well as the consistent growth and comprehensive coverage of the Scopus database since that time. Bibliometric analysis is a well-known statistical method for examining and analyzing a large amount of scientific data on a certain topic [ 26 , 39 ]. Metrics studied in bibliometric research include annual publications, source titles, authors, institutions, nations, and keywords, covering data from primary, secondary, and tertiary journals over a specific time period. It should be noted that no ethical approval was required for this study as it did not involve humans or animals.

2.2 Data collection

In this study, data were gathered from the Scopus database ( https://www.scopus.com ). Scopus was chosen because it covers a wider range of documents than any other scientific database [ 23 , 28 , 35 ]. Scopus is the world's largest abstracting and indexing database, with 84 million records containing over 18.0 million open access items, including gold, hybrid gold, green, and bronze, as well as 10.9 million conference papers, 25.8 thousand active peer-reviewed journals, and over 7000 publishers [ 14 ]. In addition, Scopus covers a wider range of educational disciplines than other databases, such as the Web of Science (WoS) [ 23 , 27 , 34 ]. As a result, using the Scopus database enables researchers to shed light on areas that may not be covered in WoS.

Electronic data search and retrieval were conducted on February 25, 2023. Keyword search was set to include title, abstract, and keywords. The keyword search was set to include the title, abstract, and keywords. The combination of search strings, operators, and filters used in this study was TITLE-ABS-KEY ("Thought-experiments" AND "Science" OR "Physics"). Quotation marks were used to focus on documents containing this exact phrase, thus ensuring high relevance to the study's scope. The Scopus database retrieved 898 documents related to these keywords with full bibliographical information, including articles (67.04%), paper proceedings (10.13%), book chapters (10.02%), and other types of documents (12.81%). By using the Scopus filter, other types of publications (12.81%), including review articles, were excluded from the list of documents. The exclusion of review articles was intentional to focus on original research contributions that advance the field of TEs directly. Including reviews could confound the analysis as they often summarize existing research rather than introduce new findings. Therefore, concentrating on the three most prevalent types of documents—articles, conference papers, and book chapters—allowed for a clearer interpretation of trends and patterns in original research outputs over the specified period. Additionally, we limited the year of publication to studies published within the last 20 years (2003–2022) to ensure the relevance and currency of our analysis. After using a filtering process to eliminate papers that did not meet the inclusion and exclusion criteria, a total of 679 articles were identified for bibliometric analysis. These articles included 504 articles, 92 book chapters, and 83 conference papers.

2.3 Data analysis

The data analysis process began with acquiring the necessary raw data by downloading it from the Scopus database in either comma-separated value (CSV) or research information system (RIS) format. For data analysis and visualization, we used VOSviewer and Microsoft Excel. VOSviewer, a sophisticated mapping tool, was employed to create collaborative networks for various variables and keywords, while Microsoft Excel was used for descriptive analysis, such as determining the number of articles published each year and identifying the most prolific source titles.

The network graphs in this study were generated using VOSviewer, based on co-authorship, co-occurrence, and citation data from Scopus. The analysis type focused on the co-occurrence of keywords and co-authorship, with a full counting method. Keywords with a minimum of four occurrences were included. The visualization settings in VOSviewer were mainly default, with the attraction parameter set to 2 and the repulsion parameter set to 0. These settings ensured that the most relevant and frequently occurring terms were highlighted, providing a clear overview of research trends and collaborations in the field of TEs over the past 20 years.

In this study, we explored the most productive publishers, the most referenced articles, the most productive authors, the most productive nations, and author keyword occurrences across time. An analysis of co-authorship and co-occurrence was performed at this stage. The analysis of co-authorship provides insights into the interactions between authors. This methodology was also used for metrics related to countries. For country attribution, we included all the countries of all authors involved in each publication, not just the corresponding author. This method ensures that all co-authors' contributions are acknowledged and provides a comprehensive representation of the global distribution of research. Co-occurrence analysis was employed as a means of investigating current keywords and their interrelationships with other phrases associated with TEs. Within this particular framework, the term “node size” refers to the frequency at which a certain keyword appears in comparison to other words. Additionally, interconnected nodes are visually represented by lines known as connections. The link establishes a connection between two nodes, while the width of the link signifies the intensity or potency of the connection between the aforementioned nodes [ 36 , 39 ].

In the context of network map visualization, nodes that exhibit a high degree of association are categorized into clusters. The clustering of items was performed using the Louvain algorithm, a popular method for community detection in large networks due to its efficiency and accuracy in handling large datasets [ 36 , 39 ]. This algorithm was chosen for its ability to uncover modular structures within large networks, which is particularly useful for identifying distinct research themes and collaboration groups in bibliometric data. Subsequently, a distinct color code was assigned to each cluster, wherein nodes within the same cluster exhibit a high degree of homogeneity. Therefore, this bibliometric mapping approach enabled researchers to discern patterns and emerging areas of interest throughout the timeframe spanning from 2003 to 2022. Figure 1 shows the stages in the process of collecting and analyzing data in this study.

The steps in collecting and analyzing the data

3.1 Statistics analysis

In this analysis, we use statistical data to observe differences in the number of articles published each year. The goal is to determine whether the quantity of publications on the topic of TEs has increased or decreased annually. Figure 2 illustrates the number of papers published over the last 20 years (2003–2022). As we can see, there has been an increase in the interest and attention of researchers, scholars, and experts in researching TEs. The growth started in 2004 and continued until 2006. The number of papers published then fluctuated between 2006 and 2015. The increase started again in 2015 and continued until 2021. The number of publications increased significantly in 2021, with 69 articles published. This growth demonstrates that research and publications on TEs are in high demand and have garnered significant attention globally in the last eight years despite a reduction in 2022. Although studies in this area are still ongoing, these findings indicate an annual growth in the writing and publication of TEs on Scopus.

Number of articles published each year

Statistical data are also used to see the number of source titles that have made the greatest contributions to TEs during the last 20 years. A total of 679 papers have been published from various sources with different types of documents in the form of articles (504), conference papers (92), and book chapters (83). According to statistical data in the Scopus database, publication in journals is very significant in publishing research on the topic of TEs, while publication in proceedings and book chapters with the main scope of TEs is not very significant. Therefore, researchers, academics, and experts are advised to submit their articles focused on TEs to journals rather than proceedings and chapter books. Table 1 lists the top 20 sources of scientific research publications covering the topic of TEs from 2003 to 2022.

As seen in Table 1 , 90% of the source titles contributing to the TEs topic are journals, with only one publishing conference proceedings. Philosophical studies ranks first, with 17 documents published in the last 20 years. This is followed by the AIP Conference Proceedings with 15 documents. The American Journal of Physics, Science and Education, and Studies in History and Philosophy of Science Part A have published 11 documents each. Other source titles, such as Synthese (10), Foundations of Science (9), Physics Teacher (9), Journal for General Philosophy of Science (8), and Philosophy of Science (8), also contributed to publishing TEs topics. Minds and Machines and Physics Education each published seven documents. Erkenntnis, European Journal of Physics, Physics Essays, and Religions each published six documents, Acta Analytica published five documents, while Axiomathes, Boston Studies in the Philosophy of and History of Science, and European Journal for Philosophy of Science each published four documents.

3.2 Bibliometric analysis

3.2.1 contributions of authors.

Table 2 shows the 10 most prolific authors based on the total number of published articles from 2003 to 2022. As shown in this list, Stuart is the most significant author with 7 papers (51 citations), followed by Bancong from Universitas Muhammadiyah Makassar, Indonesia, with 5 papers (15 citations). Following Bancong, Fehige from the University of Toronto, Canada, has also published 5 articles. The majority of Fehige’s research focuses on TEs in the context of religion. In contrast to Fehige, Brown, also from the University of Toronto in Canada, has studied TEs through the lens of history and philosophy of science in several of his works (4 documents, 52 citations). Similarly, Buzzoni (3 documents, 15 citations) and El Skaf (3 documents, 29 citations) from Italy, discuss TEs from historical and philosophical perspectives of science. Meanwhile, Halkia and Velentzas from the University of Athens, Greece, have analyzed TEs thoroughly from an educational standpoint, with the number of documents being 4 and 86 citations.

3.2.2 Contributions of country

In the context of the leading countries, authors from 64 different countries/territories published a total of 679 documents. Table 3 lists the top 20 countries in terms of TE contributions based on the number of papers published. As shown, the United States contributes the most to TEs research, with 213 documents, 2592 citations, and 47 links. The number of papers is about three times that of the United Kingdom, which comes second (75 documents, 1016 citations, and 31 links). European countries continue to hold third to sixth place, with Germany publishing 50 documents with 634 citations, followed by Canada (43 documents, 410 citations, and 17 links), Italy (33 documents, 96 citations, 6 links), and the Netherlands (28 documents, 342 citations, and 12 links). This suggests that countries in America and Europe contribute the most to TEs. The Asian country that has contributed the most to TEs is China, with 18 documents, 286 citations, and 11 links, followed by India (14 documents), Japan (12 documents), and South Korea (12 documents), with 97, 111, and 27 citations, respectively. The three countries below these are European countries, with Austria having issued 10 documents related to TEs with a total of 135 citations, followed by Finland (9 documents, 31 citations) and Spain (9 documents, 47 citations).

3.2.3 Keywords

The results of a keyword analysis can be used in further investigation of the topic at hand. This study employs a minimum threshold of two occurrences of keywords in all research articles that were examined using VOSviewer. Figure 3 displays the 253 authors' keywords detected from 1990, which may be categorized into six distinct clusters. Cluster 1 is characterized by a red color, Cluster 2 by a green color, while Cluster 3 is distinguished by a blue color. In addition, Cluster 4 is characterized by a yellow color, Cluster 5 has a purple hue, and Cluster 6 is distinguished by a light blue shade. Each cluster is comprised of interconnected keywords that are visually represented by the same colors. It is important to note that the size and shape of the node are indicative of the frequency of its occurrences [ 36 , 39 ]. In other words, there is a positive correlation between the size of the node and the frequency of occurrences of these terms. Clustering is employed as a means to gain insights or a comprehensive understanding of bibliometric groupings, whereas image mapping serves the purpose of obtaining a holistic depiction of a bibliometric network.

Network visualization of TEs

Figure 3 shows Cluster 1 (red) with 68 items such as thought experiments, intuition, Science, Kant, Aristotle, Galileo, Platonism, personal identity, theology, fiction narrative, moral motivation, and neuroscience. Cluster 2 (green) consists of 57 categories, such as science fiction, philosophy of science, philosophy of physics, philosophical thought, epistemology, knowledge, scientific reasoning, experiments, models, and realism. Cluster 3 (blue) contains 41 items, such as consciousness, Maxwell's demon, Schrodinger's cat, quantum theory, entropy, uncertainty principle, quantum entanglement, quantum information, quantum physics, and Newton's bucket. Furthermore, cluster 4 (yellow) consists of 30 items: physics education, science education, visualization, special theory of relativity, history of physics, problem-solving, exploration, Einstein, relativity, and falsification. Cluster 5 (purple) consists of 29 items: imagination, ontology, physics, truth time, algorithm of discovery, artificial intelligence, ethics, nanotechnology, fiction, philosophy, and technology. Finally, cluster 6 (light blue) contains 16 categories, including popular science, fictionality, narrative, construction, sensation, a priori, story, Mach, memory, productive imagination, and schema.

Keywords in clusters 1 and 2 have a high number of occurrences and a high total link strength. The term thought experiment ranks first with 85 occurrences and a total link strength of 91. This is followed by the term thought experiment with 60 occurrences, a total link strength of 98, and several other keywords. The high number of occurrences and high total link strength indicate that scientific research publications on the topic of TEs in the 2003–2022 range indexed by Scopus have a strong and direct relationship with these keywords. Table 4 displays the ten keywords with the highest occurrence and overall link strength in the last 20 years on the topic of TEs.

VOSviewer, on the other hand, is also used to visualize the progress of keywords over a certain period. Figure 4 illustrates the overlay visualization of the TEs topic in the time range 2003 to 2022.

Overlay visualization of TEs

Figure 4 depicts the annual distribution of the number of articles containing keywords. The various colors represent the publication dates of the related papers where these keywords appear together. The data in Fig. 4 indicate that the most frequently used topics related to TEs from 2010 to 2014 were quantum theory, ethical naturalism, ethical naturalism, quantum mechanics, scientific discovery, and mental models. Then, from 2014 to 2018, keywords such as scientific reasoning, intuition, science education, computer simulation, history of science, and science fiction began to appear in the TEs topic. The hottest topics in TEs research are shown in yellow color, including fiction, artificial intelligence, God, theology, speculative design, critical design, and methods of case. These findings indicate that these keywords have gained popularity in recent years. It can be concluded that scholars have increasingly turned to research on the mentioned topics in recent years.

4 Discussion

The goal of this study is to use the bibliometric mapping method to examine the trend of studies on TEs during the last 20 years (2003–2022). According to the findings of the study, there has been an increase in the interest and attention of researchers, scholars, and professionals in studying TEs. Although research in this area is ongoing, these findings indicate an annual growth in the writing and publication of TEs on Scopus. This growth demonstrates that research and publications on TEs are in high demand and receive significant global attention.

Interestingly, 90% of the top 20 source titles contributing to TEs research are journals in the first quartile (Q1) and second quartile (Q2). Among these, 10 journals are in the highest quartile, Q1, and 8 journals are in Q2. The quartile level indicates that these journals have the highest quality and the greatest influence [ 39 , 40 ]. Furthermore, 7 source titles (Philosophical Studies, Synthese, Foundations of Science, Minds and Machines, Erkenntnis, Acta Analytica, and Axiomathes) that publish TEs topics focus on the field of philosophy. When studying TEs from a philosophical standpoint, researchers, scholars, and professionals have the option of submitting their articles to these journals. Alternatively, if TEs are studied from a historical perspective, journals such as Science and Education, Studies in History and Philosophy of Science Part A, Journal for General Philosophy of Science, Philosophy of Science, Boston Studies in the Philosophy and History of Science, and European Journal for Philosophy of Science are appropriate. Meanwhile, if TEs are studied from an educational perspective, Physics Teacher, Science and Education, Physics Education, American Journal of Physics, and European Journal of Physics are ideal choices for publishing articles. These journals regularly publish articles in physics education studies.

If we look at the authors who have made the greatest contributions to the topic of TEs in the previous 20 years (2003–2022), Stuart is the most significant author with 7 articles (51 citations). Stuart’s work focuses on the history and philosophy of TEs [ 31 , 32 , 33 ], with the first publication in 2014 in the journal Perspectives of Science. In contrast to Stuart, Bancong's work, which ranks second, investigates various TEs from an educational standpoint. His first work, published in 2018, examined TEs in high school physics textbooks [ 3 ], followed by an investigation of how students construct TEs collaboratively [ 4 ], and an identification of factors influencing TEs during problem-solving activities [ 5 ]. Following Bancong, Fehige from the University of Toronto, Canada, has also published 5 articles. Most of his work examines TEs in religious contexts, such as thought experiments, Christianity and science in novalis [ 15 ], thought experiments and theology [ 16 ], and the book of job as a thought experiment: on science, religion, and literature [ 17 ] which was published in the journal Religions in 2019. Brown examines TEs in several of his works in light of the history and philosophy of science [ 6 , 7 ], as do Buzzoni and El Skaf from Italy, who mostly discuss TEs in light of the history and philosophy of science [ 8 , 12 ]. Meanwhile, Halkia and Velentzas from the University of Athens, Greece, have discussed TEs from an educational perspective, such as using TEs from Newton's Cannon for teaching satellite physics [ 37 ] and using TEs from the theory of relativity for teaching relativity theories [ 38 ].

Over the past two decades, authors have examined TEs from diverse perspectives, including history, philosophy, education, and religion. This variety highlights a significant shift in the disciplinary landscape of TE research, which is historically rooted in the philosophy of science [ 18 , 24 ]. The true strength of TEs lies in their adaptability across disciplines, rather than in resolving philosophical disputes. Although TEs were traditionally centered on history and philosophy of science (HPS), recent trends show a growing application in education and technology, particularly in artificial intelligence and speculative design. This shift indicates that TEs have not lost their significance but have instead found new areas of relevance. In HPS, the focus has moved toward understanding the methodological and epistemological implications of TEs, confirming their essential role in scientific reasoning [ 7 , 30 ]. Additionally, in fields such as physics education, TEs are increasingly utilized to explore complex theoretical concepts and enhance educational methodologies [ 2 , 12 ].

Based on the most commonly used keywords in the last 20 years, research on TEs has mostly focused on understanding TEs from a philosophical perspective in the first five years (2003–2007). Thought experiments rethought and reperceived [ 19 ], on thought experiments: is there more to the argument? [ 24 ] and thought experiments [ 9 ] are a few examples. Then, over the next five years (2008–2012), many studies looked at how TEs contributed to physical theories, including the special theory of relativity and quantum theory. The keywords that emerged frequently during this period were quantum theory, scientific discovery, methodology, quantum mechanics, twin earths, falling bodies, and others. In the last ten years, TEs have been studied from various perspectives. For example, in 2013, Velentzas and Halkia [ 38 ] also used TEs as a didactic tool in teaching physics to upper-secondary students. Fehige, on the other hand, began to connect TEs to theology, with a specific focus on the interaction between Christianity and science [ 15 , 16 ]. There are also researchers who continue to study the existence of TEs from a philosophical point of view and claim that TEs are science fiction [ 1 , 20 ]. In recent years, TEs have become increasingly popular in education and have been linked to artificial intelligence. Artificial intelligence, physics education, productive imagination, technology, and speculative design are some of the keywords that appear frequently. This is not surprising because TEs, as experimental activities using mental models, are not easy for students to perform on their own [ 4 , 5 ]. Therefore, technology that can assist students in creating an imaginative world for constructing TEs is required.

Since no studies have charted the trends in TEs research so far, it is difficult to compare the research results obtained with those of others. Nevertheless, several studies that examine trends in physics education reveal that although research on experiments is declining in physics education, TEs are still important to physics teaching and learning [ 41 ]. Hallswoth et al. [ 21 ] have also used artificial intelligence technologies to support TEs in the field of wet biology research, which is dominated by experiments on microbial growth and survival. The use of artificial intelligence in learning is based on the growing interest in artificial intelligence methods in science, technology, and education [ 11 ]. Overall, our study contributes to a more comprehensive understanding of TEs research trends during the last 20 years. In addition, this research also contributes to providing an overview of several potential topics that can be the focus of future researchers, such as the use of artificial intelligence in TEs. By situating our findings within the broader context of previous studies, we provide a clearer picture of how TE research has evolved and where it is heading.

5 Conclusions

This study aims to present a more comprehensive understanding of the trend of studies on TEs during the last 20 years (2003–2022). Research on this topic began in 1976, and its progress has continued to the present. A total of 679 published papers from various sources, including articles (504), conference papers (92), and book chapters (83), were analyzed. The results of the study show that research and publications on TEs are of interest and have received a lot of attention during the last eight years. A significant increase occurred in 2021, with 69 published articles. According to the findings, 95% of the top 20 source titles contributing to TEs are from journals in the first and second quartiles (Q1 and Q2). This quartile ranking shows the quality and significant influence of a journal. The geographical distribution reveals that the United States contributes the most to TEs research, with 213 documents, 2592 citations, and 47 links. We also identified several prospective keywords that could be the focus of future research, including artificial intelligence, physics education, fiction, God, theology, productive imagination, technology, speculative design, and critical design. Therefore, this study contributes to providing a thorough picture of thought experiment research trends and future directions of potential topics that can be the focus of future researchers.

This research has several limitations. The exclusive source of publication data utilized in this study is the Scopus database, which is recognized as one of the most extensive databases in the field. However, it is worth noting that future research endeavors may consider including publication data from other prominent sources such as WoS and Google Scholar. Furthermore, the utilization of the search function in the TITLE-ABS-KEY field, specifically employing the terms "Thought-experiments" AND "Science" OR "Physics," was used for the purpose of data retrieval. However, it is important to acknowledge that this approach is not infallible, as there is a potential for some papers to be overlooked, making the process less than completely accurate. Despite its limitations, this research is often regarded as a pioneering contribution to the field of bibliometric studies on the subject of TEs during the past two decades.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Abstract: This work is devoted to inverse problems for elliptic partial differential equations in an Euclidean domain, in which the boundary and/or interior conditions are given merely on some accessible portion of the boundary and/or inside the domain, the goal being the efficient construction of an approximation for the unknown solution in the remaining part of the domain; such inverse problems are usually called data-completion problems or inverse Cauchy problems. They have been intensively studied in the past decades, but due to their severe instability it has remained an up-to-date challenge to derive both theoretical and numerical methods that can efficiently treat such inverse problems in general settings, especially in high dimensions or in which the solution or the domain exhibit singularities or complex geometries. In this paper we establish a fundamental probabilistic framework in which such inverse problems can be analyzed both theoretically and numerically in terms of the geometry of the domain and the structure of the coefficients. The methods we develop are different from what has been previously proposed in the literature, and are designed to accurately quantify the instability of the inverse problem, as well as to construct a natural subspace of approximate solutions given the available measurements, by simulating the spectrum of the direct problem and performing a singular value decomposition.The approach is based on elliptic measures in conjunction with probabilistic representations and parallel Monte Carlo simulations. The proposed methods are accompanied by a full probabilistic error analysis, showing the convergence of the approximations and providing explicit error bounds. The complexity of the methods is also taken into discussion.We provide thorough numerical simulations performed on graphical processing units, in dimensions two and three, and for various types of domains.

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Learn how to design an experiment to test a causal relationship between variables. Follow five steps: define variables, write hypothesis, design treatments, assign subjects, and measure dependent variable.
(PDF) Design and Analysis of Experiments
This is an introductory textbook dealing with the design and analysis of experiments. It is based on college-level courses in design of experiments that I have taught for over 40 years at Arizona ...
A Comprehensive Guide to Design of Experiments: Concepts ...
Design of Experiments (DOE) is a powerful statistical methodology that enables researchers and practitioners to systematically plan, design, and analyze experiments in a controlled manner.
Design of Experiments Specialization [4 courses] (ASU)
Learn modern experimental design methods and software tools from Arizona State University. Earn a career certificate and apply your skills to various industries and problems.
Lesson 1: Introduction to Design of Experiments
Learn the basics of design and analysis of experiments, a method to investigate cause-and-effect relationships. Explore the history, principles, guidelines and examples of DOE with STAT 503 textbook and online course.
Design of Experiments
Projects: One ongoing group project. Exams: 2 midterm exams and 1 final. Textbooks: ... Tentative: Design and Analysis of Experiments by Douglas Montgomery, 8th edition (ISBN: 978-1-1181-4692-7). Computer Requirements: ProEd minimum computer requirements. Knowledge of a statistical software (e.g., SAS, JMP, R, MATLAB) that includes a linear ...
Design and Analysis of Experiments
A comprehensive guide to experimental design and analysis, covering topics such as factorial experiments, polynomial regression, analysis of covariance, and computer experiments. Download the PDF or EPUB version of the book, or access the supplementary material and reviews online.
Design and Analysis of Experiments
Learn how to design, conduct, and analyze experiments in various scientific fields using factorial and fractional factorial designs, analysis of variance, regression, and response surface modeling. This five-day course covers the basics of experimental design, Taguchi methods, and software applications with real examples.
Design and Analysis of Experiments, 10th Edition
A textbook on product and process design improvement through quality and performance optimization. Covers factorial and fractional factorial design, response surface techniques, regression analysis, and more, with examples and software tools.
Design and Analysis of Experiments
Learn how to design, conduct, and analyze experiments in various scientific fields using factorial and fractional factorial designs, analysis of variance, regression, and response surface modeling. This course covers the basics of experimental design, hypothesis testing, and software applications with real examples and exercises.
PDF Design of Experiments
Learn how to plan and perform experimental investigations using the methodology of Design of Experiments (DoE) to gain a better understanding of a process or system. The book covers system analysis, response variables, experimental factors, replication, blocking, randomization, interactions, and different experimental strategies.
A Deep Dive into Design of Experiments (DOE) Engineering
Learn how DOE Engineering is a systematic and statistical approach to optimize processes, improve product quality, and make informed decisions. Explore the key components, types, and real-world examples of DOE Engineering in various industries.
Design and Analysis of Experiments
A book edited by Klaus Hinkelmann that covers various topics in experimental design and analysis, such as genetic crosses, gene expression microarrays, and robustness. The book provides theoretical foundations, methods, and applications for different types of experiments.
Design and Analysis of Experiments, 10th Edition
Design and Analysis of Experiments provides a rigorous introduction to product and process design improvement through quality and performance optimization. Clear demonstration of widely practiced techniques and procedures allows readers to master fundamental concepts, develop design and analysis skills, and use experimental models and results in real-world applications.
Five Hands-on Experiments for a Design of Experiments Course
3.4.2 Experimental Design. To setup for this experiment, group leaders were given eight note cards. On four of the cards, they had been given a randomly selected word or phrase from a list of common words or phrases that were found on the internet. Additionally the cards were labeled A-1, A-2, A-3, A-4, B-1, B-2, etc.
Welcome
Welcome. This is the free website for Design and Analysis of Experiments and Observational Studies using R. A hardcopy of the book can be purchased from Routledge. This book grew out of course notes for a twelve-week course (one term) on the Design of Experiments and Observational Studies in the Department of Statistical Sciences at the ...
Design and Analysis of Experiments, 7th Edition
Design and Analysis of Experiments, 7th Edition. Welcome to the Web site for Design and Analysis of Experiments, Seventh Edition by Douglas C. Montgomery. This Web site gives you access to the rich tools and resources available for this text. You can access these resources in two ways: Using the menu at the top, select a chapter.
PDF Design and Analysis of Experiments
design experiments is still critical for being able to determine which factors e ect the observations. These notes were produced by consolidating two sources. One is the text of Wu and Hamada, Experiments: Planning, Analysis, and Optimization. The second is lecture notes and lecture slides from Dr. Doug Wiens and Dr. Linglong Kong, respectively.
Design and Analysis of Experiments
A chapter from a handbook of labor, human resources and population economics that reviews the econometric and statistical methods for causal inference from randomized experiments. It covers design and inferential issues in classical and nonclassical randomized experiments, as well as machine learning approaches and external and internal validity.
PDF STAT 158: Design and Analysis of Experiments
STAT 158: Design and Analysis of Experiments ... as to find an equitable solution with respect to finishing the project. Helicopter experiment A portion of the last homework will be based on an experiment run partially during the class during the last two weeks. The experiment will be started during the class, but must be finished outside of
Design and analysis of experiments : Das, M. N. (Manindra Nath), 1923
Concepts of experiments: design and analysis -- Complete block designs -- Factorial experiments -- Asymmetrical factorial and split-plot designs -- Incomplete block designs -- Orthogonal latin squares -- Designs for bio-assays and response surfaces -- Analysis of covariance and transformation -- Weighing designs
Design and analysis projects in mechanical engineering
Design and Analysis of Wheel Rim Using Finite Element Method. Simulation of Plume Spacecraft Interaction- Mechanical Project. Design and Analysis of Truck Chassis - Mechanical Project. Design, Modeling and Material Optimization of Engine Piston for 150cc Motor Cycle.
Regression Analysis Course 09: Logistic Regression
The class is geared toward engineers who need to understand relationships between inputs and response metrics in their experiments and data. The course covers simple and multiple-input linear regression; how to deal with qualitative inputs and pass-fail-type responses; how to check the adequacy of the analysis results; and tricks available to ...
The past and present of thought experiments' research at Glancy
In the development of physical theories, thought experiments play a crucial role. Research on this topic began in 1976 and has continued to the present. This study aims to provide a more complete picture of the progress of thought experiments over the past two decades. To achieve this, this study employs bibliometric mapping methods. A total of 679 published papers were analyzed, including ...
Experimental Structural Design of a Novel Variable-Sweep Wing Based on
Experimental Structural Design of a Novel Variable-Sweep Wing Based on a Four-Bar Planar Linkage. Authors: Gui Cheng ... Through parametric analysis, main parameters have been identified, and the structure is optimized: the longitudinal position (direction of the fuselage) of the wing's center of gravity is designed to maintain minimal change ...
Consultancy for Economic Analysis and M&E Plans for IFD/CTI Loan
What you'll need: Education: master's degree in economics (Post graduate courses in Economics or related fields with strong quantitative skills is encouraged). Experience: five-year experience in data analysis, statistics, econometrics, and research (3 years of relevant experience preferred). Previous experience conducting or assisting design and implementation of project economic analysis ...
Principal Scientist II, Emerging Technologies
Demonstrated ability to set up experiment design for in vivo experiments and advanced statistical analysis. Basic knowledge of artificial intelligence and machine learning models. Experience with digital home-cage monitoring solutions and/or other monitoring technologies. Strong leadership skills and experience managing multidisciplinary teams.
[2409.03686] Numerical spectral analysis of Cauchy-type inverse
View PDF HTML (experimental) Abstract: This work is devoted to inverse problems for elliptic partial differential equations in an Euclidean domain, in which the boundary and/or interior conditions are given merely on some accessible portion of the boundary and/or inside the domain, the goal being the efficient construction of an approximation for the unknown solution in the remaining part of ...

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Design and Analysis of Experiments

A Comprehensive Guide to Design of Experiments: Concepts, Techniques, and Case Study Analysis

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