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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Introduces the applications of repeated measures design processes with the popular IBM SPSS software Repeated Measures Design for Empirical Researchers presents comprehensive coverage of the formation of research questions and the analysis of repeated measures using IBM SPSS and also includes the solutions necessary for understanding situations where the designs can be used. In addition to explaining the computation involved in each design, the book presents a unique discussion on how to conceptualize research problems as well as identify appropriate repeated measures designs for research purposes. Featuring practical examples from a multitude of domains including psychology, the social sciences, management, and sports science, the book helps readers better understand the associated theories and methodologies of repeated measures design processes. The book covers various fundamental concepts involved in the design of experiments, basic statistical designs, computational details, differentiating independent and repeated measures designs, and testing assumptions. Along with an introduction to IBM SPSS software, Repeated Measures Design for Empirical Researchers includes: * A discussion of the popular repeated measures designs frequently used by researchers, such as one-way repeated measures ANOVA, two-way repeated measures design, two-way mixed design, and mixed design with two-way MANOVA * Coverage of sample size determination for the successful implementation of designing and analyzing a repeated measures study * A step-by-step guide to analyzing the data obtained with real-world examples throughout to illustrate the underlying advantages and assumptions * A companion website with supplementary IBM SPSS data sets and programming solutions as well as additional case studies Repeated Measures Design for Empirical Researchers is a useful textbook for graduate- and PhD-level students majoring in biostatistics, the social sciences, psychology, medicine, management, sports, physical education, and health. The book is also an excellent reference for professionals interested in experimental designs and statistical sciences as well as statistical consultants and practitioners from other fields including biological, medical, agricultural, and horticultural sciences. J. P. Verma, PhD, is Professor of Statistics and Director of the Center for Advanced Studies at Lakshmibai National Institute of Physical Education, India. Professor Verma is an active researcher in sports modeling and data analysis and has conducted many workshops on research methodology, research designs, multivariate analysis, statistical modeling, and data analysis for students of management, physical education, social science, and economics. He is the author of Statistics for Exercise Science and Health with Microsoft Office Excel, also published by Wiley.
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
Illustration Credits
Chapter 1: Foundations of Experimental Design
Introduction
What is Experimental Research?
Design of Experiment and its Principles
Statistical Designs
Factorial Experiment
Terminologies in Design of Experiment
Considerations in Designing an Experiment
Exercise
Assignment
Bibliography
Chapter 2: Analysis of Variance and Repeated Measures Design
Introduction
Understanding Variance and Sum of Squares
One Way Analysis of Variance for Independent Measures Design
Illustration I
Repeated Measures Design
When to Use Repeated Measures ANOVA
Solving Repeated Measures Design with One-Way ANOVA
Illustration II
Bonferroni Correction
Effect Size
Exercise
Assignment
Bibliography
Chapter 3: Testing Assumptions in Repeated Measures Design Using SPSS
Introduction
First Step in Using SPSS
Assumptions
Remedial Measures when Assumption Fails
Sample Size Determination
Exercise
Assignment
Bibliography
Chapter 4: One-Way Repeated Measures Design
Introduction to Design
Advantage of One-Way Repeated Measures Design
Weakness of Repeated Measures Design
Application
Layout Design
Steps in Solving One-Way Repeated Measures Design
Illustration
Exercise
Assignment
Bibliography
Chapter 5: Two-Way Repeated Measures Design
Introduction
Advantages of Using Two-Way Repeated Measures Design
Assumptions
Layout Design
Application
Steps in Solving Two-Way Repeated Measures Design
Illustration
Exercise
Assignment
Bibliography
Chapter 6: Two-Way Mixed Design
Introduction
Advantage of Two-Way Mixed Design
Assumptions
Application
Layout Design
Steps in Solving Mixed Design with Two-Way ANOVA
Illustration
Exercise
Assignment
Bibliography
Chapter 7: One-Way Repeated Measures Manova
Introduction
When to Use Repeated Measures MANOVA?
Why to Use Repeated Measures MANOVA?
Assumptions
Application
Layout Design
Steps in Solving One-Way Repeated Measures MANOVA
Illustration
Exercise
Assignment
Bibliography
Chapter 8: Mixed Design with Two-Way Manova
Introduction
What Happens in Manova Experiment
Assumptions
Layout Design
Application
Steps in Solving Mixed Design with Two-Way Manova
Illustration
Exercise
Assignment
Bibliography
Appendix
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Foundations of Experimental Design
Figure 1.1 Layout of the completely randomized design
Figure 1.2 Layout of the randomized block design
Figure 1.3 Layout of the matched pairs design
Figure 1.4 Layout of Latin square design
Figure 1.5 Layout of the 3×3 factorial design
Figure 1.6 Allocation of treatments by matching the subjects
Figure 1.7 Layout of the design after including extraneous variable in the design
Chapter 2: Analysis of Variance and Repeated Measures Design
Figure 2.1 Scheme of distributing sum of squares and degrees of freedom
Figure 2.2 Means plot of the pull-ups performance in three strength training groups
Figure 2.3 Layout of the one-way repeated measures design having levels of the factor as time point.
Figure 2.4 Layout of the one-way repeated measures design having three treatment conditions
Figure 2.5 Layout of the one-way repeated measures design having three treatment conditions
Figure 2.6 Scheme of distributing total sum of squares and degrees of freedom in one-way repeated measures design
Figure 2.7 Means plot of the mood scores during workout with different types of music
Chapter 3: Testing Assumptions in Repeated Measures Design Using SPSS
Figure 3.1 Screen showing option for creating/opening file
Figure 3.2 Screen showing option for defining variables and coding
Figure 3.3 Screen showing format of data feeding
Figure 3.4 Screen for initiating commands for testing normality and identifying outliers
Figure 3.5 Screen showing option for selecting variables and detecting outliers
Figure 3.6 Screen showing options for computing Shapiro–Wilk test and the Q–Q plot
Figure 3.7 Normal Q–Q Plot for the data on memory recall
Figure 3.8 Box plot for all three groups of data
Figure 3.9 Screen for initiating commands for testing sphericity
Figure 3.10 Screen showing options for defining variables
Figure 3.11 Screen showing options for adding independent and dependent variables for analysis
Figure 3.12 Screen showing option for selecting variables for testing sphericity
Figure 3.13 Confidence intervals for mean
μ
Figure 3.14 Showing IQ scores in a population
Chapter 4: One-Way Repeated Measures Design
Figure 4.1 Layout of the one-way repeated measures design having levels as different treatments
Figure 4.2 Layout of the one-way repeated measures design having levels as time durations
Figure 4.3 Layout of the design for the study shown in the illustration
Figure 4.4 Scheme of distributing total sum of squares and degrees of freedom
Figure 4.5 Screen for initiating commands for single factor repeated measures design
Figure 4.6 Screen showing options for defining dependent and independent variables
Figure 4.7 Screen showing options for adding independent and dependent variables for analysis
Figure 4.8 Screen showing option for selecting within-subjects variables and obtaining means plot
Figure 4.9 Screen showing option for computing descriptive statistics and pairwise comparison of means using the Bonferroni correction
Figure 4.10 Marginal means plot
Chapter 5: Two-Way Repeated Measures Design
Figure 5.1 Layout of the two-way repeated measures design.
Figure 5.2 Layout of the two-way repeated measures design when one of the factors is time.
Figure 5.3 Layout of the repeated measures design with two factors
Figure 5.4 Scheme of distributing total sum of squares and degrees of freedom in the two-way repeated measures design
Figure 5.5 Data format in the repeated measures design with two factors
Figure 5.6 Screen showing options for defining independent and dependent variables
Figure 5.7 Screen showing option for selecting variables defining all treatment combinations
Figure 5.8 Screen showing option for means plot
Figure 5.9 Screen showing option for computing various outputs in the repeated measures design with two factors
Figure 5.10 Marginal means plot of Music
Figure 5.11 Screen showing options for defining independent and dependent variables
Figure 5.12 Screen showing option for selecting three levels of environment in no music group
Figure 5.13 Screen showing option for means plot of Environment in no music group
Figure 5.14 Screen showing option for computing various outputs in one-way repeated measures ANOVA
Figure 5.15 Marginal means plot of Music × Environment
Figure 5.16 Marginal means plot of Environment × Music
Chapter 6: Two-Way Mixed Design
Figure 6.1 Layout of the mixed design with two-factors where levels of the within-subjects factor are the three treatments
Figure 6.2 Layout of the mixed design with two factors where levels of the within-subjects factor are the time durations
Figure 6.3 Layout of the mixed design in the illustration
Figure 6.4 Scheme of distributing total sum of squares and degrees of freedom in the mixed design
Figure 6.5 Screen for initiating commands for the mixed design
Figure 6.6 Screen showing options for defining dependent and independent variables and its levels
Figure 6.7 Screen showing options for adding independent and dependent variables for analysis
Figure 6.8 Screen showing option for selecting within-subjects (movie) and between-subjects variables (Age)
Figure 6.9 Screen showing options for comparing main effect for within-subjects factor (Movie) and other statistics
Figure 6.10 Screen showing option for post-hoc test for the between-subjects factor (Age)
Figure 6.11 Screen showing option for means plots
Figure 6.12 Marginal means plot of Movie
Figure 6.13 Marginal means plot of Age
Figure 6.14 Screen showing option for splitting the data file for one-way repeated measures ANOVA
Figure 6.15 Screen showing option for selecting within-subjects variables
Figure 6.16 Screen showing option for pair-wise comparison of group means using Bonferroni correction
Figure 6.17 Marginal means plot of Age × Movie
Figure 6.18 Screen showing option for selecting the variables for analyzing simple effect of between-subjects variable
Figure 6.19 Screen showing option for post-hoc test
Figure 6.20 Screen showing option for descriptive statistics and testing assumption
Figure 6.21 Marginal means plot of Movie × Age
Chapter 7: One-Way Repeated Measures Manova
Figure 7.1 Layout of the one-way repeated measures MANOVA design having three levels of independent factor as different treatments
Figure 7.2 Layout of the one-way repeated measures MANOVA design having three treatment levels as time durations
Figure 7.3 Layout of the one-way repeated measures MANOVA design in the illustration
Figure 7.4 Data format in one-way repeated measure MANOVA
Figure 7.5 Screen for initiating command for one-way repeated measure MANOVA
Figure 7.6 Screen showing options for defining independent and dependent variables
Figure 7.7 Screen showing option for selecting variables defining all treatment combinations
Figure 7.8 Screen showing option for means plot
Figure 7.9 Screen showing option for generating various outputs in one-way repeated measures MANOVA
Figure 7.10 Box plots of Maths scores
Figure 7.11 Box plots of English scores
Figure 7.12 Box plots of Reasoning scores
Figure 7.13 Marginal means plot of Maths
Figure 7.14 Marginal means plot of English
Figure 7.15 Marginal means plot of Reasoning
Chapter 8: Mixed Design with Two-Way Manova
Figure 8.1 Layout of the mixed design with two-way MANOVA where levels of the within-subject factor are different treatment conditions
Figure 8.2 Layout of the mixed design with two-way MANOVA where levels of the within-subjects factor are time durations
Figure 8.3 Layout of the mixed design with two factors in the illustration
Figure 8.4 Data format in mixed design with two-way MANOVA
Figure 8.5 Screen for initiating commands for mixed design with MANOVA
Figure 8.6 Screen showing options for defining independent and dependent variables
Figure 8.7 Screen showing option for selecting variables defining all treatment combinations
Figure 8.8 Screen showing option for various means plot for each dependent variable
Figure 8.9 Screen showing option for post hoc test for the between-subjects factor (Sex) for each dependent variable
Figure 8.10 Screen showing options for comparing the effect of within-subjects factor (Chocolate) and other statistics
Figure 8.11 Screen for initiating commands for splitting data file
Figure 8.12 Screen showing option for splitting the data file in different sex category
Figure 8.13 Box plots for the data in male category
Figure 8.14 Screen showing options for defining variables
Figure 8.15 Screen showing option for selecting within-subjects variables
Figure 8.16 Screen showing options for generating the output for simple effect of within-subjects factor (Chocolate) and other statistics
Figure 8.17 Marginal means plot of Sex × Chocolate for the data on Taste
Figure 8.18 Screen showing option for selecting the variables for analyzing simple effect of Sex
Figure 8.19 Screen showing option for post hoc test
Figure 8.20 Screen showing option for descriptive statistics and testing assumption
Figure 8.21 Marginal means plot of Chocolate×Sex for the data on Taste
Figure 8.22 Marginal means plot of Sex × Chocolate for the data on Crunchiness
Figure 8.23 Marginal means plot of Chocolate × Sex for the data on Crunchiness
Figure 8.24 Marginal means plot of Sex × Chocolate for the data on Flavor
Figure 8.25 Marginal means plot of Chocolate × Sex for the data on Flavor
List of Tables
Chapter 2: Analysis of Variance and Repeated Measures Design
Table 2.1 Computation of Sum of Squares and Mean Sum of Squares
Table 2.2 Pull-ups Scores in Different Strength Training Groups
Table 2.3 Computation in One-Way ANOVA
Table 2.4 ANOVA Table for the Data on Pull-ups
Table 2.5 Post-Hoc Comparison of Means Using Tukey Test
Table 2.6 Mean Pull-Ups in Different Strength Training Groups
Table 2.7 Mood Score of the Subjects After Each Dinner Session
Table 2.8 Computation in One-Way Repeated ANOVA
Table 2.9 ANOVA Table for the Repeated Measures on the Data on Mood
Table 2.10 Computation for Sphericity
Table 2.11 Mauchly's Test of Sphericity
Table 2.12 Tests of Within-Subjects Effect
Table 2.13 Pair-Wise Comparisons
Chapter 3: Testing Assumptions in Repeated Measures Design Using SPSS
Table 3.1 Profile Data
Table 3.2 Scores on Memory Recall at Different Time
Table 3.3 Tests of Normality for the Data On Memory Recall
Table 3.4 Mauchly's Test of Sphericity
Table 3.5 Different Transformation for the Data on Memory Recall in the Morning Group
Table 3.6 Tests of Normality for the Transformed Variable of Shooting Scores in Free Angle Group
Chapter 4: One-Way Repeated Measures Design
Table 4.1 Data on Reasoning Ability Measured at Different Time Points During Intervention Program With Meditation
Table 4.2 Tests of Normality for the Data on Reasoning Ability
Table 4.3 Descriptive Statistics
Table 4.4 Mauchly's Test of Sphericity
a
Table 4.5
F
Table for Testing Significance of Within-subjects Effects
Table 4.6 Pairwise Comparison of Marginal Means
Chapter 5: Two-Way Repeated Measures Design
Table 5.1 Number of Match Box Prepared Per Hour in a Day
Table 5.2 Mauchly's Test of Sphericity
Table 5.3 Descriptive Statistics
Table 5.4
F
-Table for Testing the Significance of Within-Subjects Effects
Table 5.5 Estimates of Marginal Means of Music
Table 5.6 Pairwise Comparison of Marginal Means of Music
Table 5.7 Mauchly's Test of Sphericity in Different Music Categories
Table 5.8
F
-Table for Testing Significance of Environment (Within-Subjects) Effect in Each Music Category
Table 5.9 Pairwise Comparisons of Means in Each Music Category
Table 5.10 Mauchly's Test of Sphericity
b
in Different Music
Table 5.11
F
-Table for Testing Significance of Music (within-subjects) Effects in Each Environment
Table 5.12 Pairwise Comparisons of Means in Each Environment
Table 5.13 Test of Normality
Table 5.14 Data on Weight (in kg) Obtained on the Housewives Under Different Treatment Conditions
Table 5.15 Data on reaction time (in msec) obtained on subjects under different treatment conditions
Chapter 6: Two-Way Mixed Design
Table 6.1 Score on Enjoyment Reported by the Subjects after Watching Movies
Table 6.2 Test of Normality
Table 6.3 Box's Test for Equality of Covariance Matrices
Table 6.4 Levene's Test for Equality of Error Variances
Table 6.5 Mauchly's Test of Sphericity
Table 6.6 Descriptive Statistics
Table 6.7
F
-Table for Testing Significance of Movie (Within-Subjects) Effects
Table 6.8 Pair-Wise Comparison of Marginal Means of Movie Irrespective of Age
Table 6.9
F
-Table for testing significance of Age (between-subjects) effects
Table 6.10 Pair-wise Comparison of Marginal Means of Age
Table 6.11 Mauchly's test of sphericity
a
in different age categories
Table 6.12
F
-Table for Testing Significance of Movie (Within-Subjects) Effects in Each Age Category
Table 6.13 Pair Wise Comparisons of Mean
s
in Each Age Category
Table 6.14 Test of Homogeneity of Variances
Table 6.15
F
-Table for Testing Significance of Age (between-Subjects) Effects in Each Movie Category
Table 6.16 Pair-Wise Comparisons of Mean
s
in Each Movie Categories
Table 6.17 Weights of the Subjects Measured at Different Duration During Exercise Intervention
Table 6.18 Sales Figure of Fruit Drink Units Sold in Different Treatment Conditions
Chapter 7: One-Way Repeated Measures Manova
Table 7.1 Marks Obtained by the Students in Different Subjects at Different Times of the Day
Table 7.2 Descriptive Statistics
Table 7.3 Correlations
Table 7.4 Test of Normality
Table 7.5 Multivariate
a,b
Tests of Within-Subjects Effects
Table 7.6 Mauchly's Test of Sphericity
a
Table 7.7 Univariate Tests: One-Way Repeated Measure ANOVA for Each Dependent Variable
Table 7.8 Estimates of Marginal Means in Different Groups
Table 7.9 Pair-Wise Comparison of Marginal Means in Each Dependent Variable
Table 7.10 Ratings of the Subjects on Different Characteristics of Mobiles
Table 7.11 Data on Performance Parameters of the Subjects at Different Duration
Chapter 8: Mixed Design with Two-Way Manova
Table 8.1 Response on the Characteristics of Chocolate
Table 8.2 Correlations Matrix for Male Response
Table 8.3 Correlations Matrix for Female Response
Table 8.4 Test of Normality
Table 8.5 Levene's Test of Equality of Error Variances
a
Table 8.6 Box's Test of Equality of Covariance Matrices
a
Table 8.7 Mauchly's Test of Sphericity
b
Table 8.8 Multivariate Tests
b
Table 8.9 Estimates of Marginal Means (All Chocolate Groups Combined)
Table 8.10 ANOVA Table for Testing Between-Subjects Effects in Each Dependent Variable
Table 8.11 Estimates of Marginal Means (Both Sexes Combined)
Table 8.12 Univariate Tests: Repeated Measures ANOVA Table for Each Dependent Variable
Table 8.13 Mauchly's Test of Sphericity in Different Sex
Table 8.14
F
-Table for Testing Significance of Chocolate (Within-Subjects) Effects in Each Sex Category
Table 8.15 Descriptive Statistics
Table 8.16 Pair-wise Comparisons of Marginal Means in Each Sex Category
Table 8.17 Test of Homogeneity of Variances
Table 8.18 ANOVA Table for Testing Significance of Sex (Between-Subjects) Effects in Each Chocolate Category
Table 8.19 Descriptive Statistics
Table 8.20 Mauchly's Test of Sphericity in Different Sex
Table 8.21
F
-Table for Testing Significance of Chocolate (Within-Subjects) Effects in Each Sex Category
Table 8.22 Descriptive Statistics
Table 8.23 Pair-wise Comparisons of Marginal Means in Each Sex Category
Table 8.24 Test of Homogeneity of Variances
Table 8.25
F
-Table for Testing Significance of Sex (Between-Subjects) Effect on Crunchiness in Each Chocolate Category
Table 8.26 Descriptive Statistics
Table 8.27 Mauchly's Test of Sphericity in Different Sex
Table 8.28
F
-Table for Testing Significance of Chocolate (Within-Subjects) Effects in Each Sex Category
Table 8.29 Descriptive statistics
Table 8.30 Pair-wise Comparisons of Marginal Means in Each Sex Category
Table 8.31 Test of Homogeneity of Variances
Table 8.32
F
-Table for Testing Significance of Sex (Between-Subjects) Effects in Each Chocolate Category
Table 8.33 Descriptive Statistics
Table 8.34 Response on the symptoms of depression
Appendix
Table A.1 The Normal Curve Area between the Mean and a Given
z
Value
Table A.2
F
-Table: Critical Values
α
= 0.05
Table A.3
F
-Table: Critical Values
α
= 0.01
Table A.4 Critical Values of Studentized Range Distribution (
q
) for Familywise ALPHA = 0.05
Repeated Measures Design for Empirical Researchers
J. P. Verma
Centre for Advanced StudiesLakshmibai National Institute of Physical EducationGwalior, India
Copyright © 2016 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Verma, J. P.
Repeated measures design for empirical researchers / J.P. Verma.
pages cm
Includes index.
ISBN 978-1-119-05271-5 (cloth)
1. Science–Methodology. 2. Experimental design. I. Title.
Q175.V4235 2015
001.4′2–dc23
2014048319
This book is Dedicated to
S G Deshmukh
For being my friend, philosopher and guide
Preface
I got inspired to write this book when I started teaching course work to the PhD scholars. During interaction with the participants while conducting many research workshops I used to get the feedback on conducted sessions of ‘research experiments’. Numerous requests for guidance came from research scholars on how to conduct research experiments that used various designs with repeated measures. Many researchers use Repeated Measures Design (RMD) in their studies due to non-availability of sufficient subjects. As a matter of fact, the curriculum of various master degree programs does not elaborate much on this technique. Hence, researchers' understanding is limited in this area. While conducting an experiment, many scholars stumble not because they have difficulty in learning a specific research design but instead they are not equipped to handle problem-solving approach in their experiments.
Although a lot of content is available on the independent measures design but very little of it deals with repeated measures design. It is the task of researchers to understand these designs and interpret their findings from such material because they do not provide in-depth explanation to the solutions. This book on RMD has been written to fill this gap. The intention of writing this book is to help the empirical researchers in any area to understand situations where such designs can be used, and provide a handy solution to analyze them with the popular IBM® SPSS® Statistics software (SPSS). Each design in the book has been discussed with solved illustrations and detailed interpretation of findings.
This book emphasizes the importance of this design in any experimental research and discusses the most widely used RMDs in empirical studies. It provides readers with basic understanding of statistical designs and facilitates them in solving and generating insights of repeated measures designs to address their research issues. The content of this book can be covered in two credit courses in the curriculum of Master's/M.Phil/PhD programs for most of the disciplines such as Psychology, Management, Social Sciences, Medicine, Physical Education, Sports Sciences, Nutrition, and so on. One of the important features of this book is that it follows a very simple approach to make the concept clear with solved illustrations.
After understanding the requirements of researchers in experimental studies it took me around five years to write this book. During the course of writing, the focus was on how to make the readers understand all the statistical designs discussed in the text. Even the most complex design like two-factor mixed MANOVA design has been discussed in a simple manner so that the researchers may be tempted to use in case of need. This book has been structured in such a manner so as to address the FAQs of the researchers as experienced by me. Each chapter has been deliberated with the finest details so as to satisfy the need of applied researchers and satisfy the theoretical statisticians as well.
The main USP of this book is that it provides comprehensive solutions along with interpretations and guidelines for using the SPSS software to the researchers. The book contains eight chapters, which are planned in increasing order of conceptual difficulty usually experienced by the researchers. The first three chapters are focused on understanding the mechanism in solving experimental designs. In chapter four to eight, various repeated measures designs have been discussed. These chapters start with the introduction of design, advantage and disadvantage of the design, application area and layout design. Finally, a solved example with the SPSS software has been illustrated in each chapter to understand the procedure and interpretation of outputs in the design.
Chapter 1 introduces fundamentals of experimental designs. It discusses various principles of design of experiments and explains all the basic statistical designs so as to build up the foundation of the readers in understanding various designs mentioned in different chapters. Various terms used in solving different designs have been discussed. A thorough discussion has been made on how to develop a good empirical study by controlling various errors in the experiment.
Chapter 2 focuses on understanding the basic mechanism in solving independent measures and repeated measures ANOVAs. Procedure involved in pair-wise comparison of means has been shown in both types of ANOVAs. An effort has been made to make the readers understand, how splitting of the total sum of squares is different in both the cases and how the repeated measures design enhances efficiency in experiments.
Chapter 3 discusses assumptions required for the repeated measures design in detail along with the methods to test them by using the SPSS software. Remedial measures in case of violating the assumptions have been deliberated in detail.
One-way repeated measures design has been discussed in Chapter 4. Different situations have been shown where this design can be used in order to help the readers to select this design for their studies. Besides this, layout of this design has been discussed in two different types of studies; firstly, in which the levels of within-subjects factor are different treatments and secondly, where they are different time durations. The steps involved in this design have been explained to provide a road map to the researchers in solving the design. Solved illustrations will help the readers to use them effectively in their studies.
Chapter 5deals with the two-way repeated measures design. It describes how to use this design in a situation where both the factors in a factorial experiment are within-subjects. Different applications have been discussed in the chapter, and a procedure for testing various assumptions in the design has been illustrated in order to facilitate the researchers to use them in their studies. A thorough treatment has been given to analyze the main and simple effects in the design by using the SPSS software.
Chapter 6 explains the two-way mixed design in which one of the factors is a between-subject and the other is a within-subject. Detailed treatments on testing assumptions and investigating the main and simple effects have been deliberated so as to draw meaningful conclusions in the study.
Chapter 7 is devoted to the one-way repeated measures MANOVA. A detailed discussion has been made about the situations where this design can be used. There is an elaborate description as to why this design should be used in experimental studies and how to develop hypotheses based on research questions to be investigated in the studies.
Finally, in Chapter 8 we have discussed mixed design with two-way MANOVA in detail. Often researchers face difficulty in using this design; hence, an intensive work has been done to make them comfortable by creating a road map. A solved example has been discussed in detail for clarifying the procedure involved in multivariate and univariate testing. Minute details have been provided to analyze the simple effects in the univariate analysis. A thorough guideline has been provided to deal with the family-wise error rate, which inflates due to multiple univariate analysis in this design.
I hope that this book would be helpful to the researchers for their course work and research studies.
I would like to express my sincere gratitude to my friend Prof. Jagdish Prasad who has reviewed few chapters and edited the text which has enhanced the quality of the book. I am thankful to my professional colleagues namely Prof. D. P. Singh, Prof. Y. P. Gupta and Prof. V. Sekhar for helping me to edit some of the chapters in this book. I am indebted to Dr. Indu Bora for timely help in providing her expert comments in correcting some portion of the manuscript.
I would like to place on records my gratitude to Susanne Steitz-Filler, Senior Editor, John Wiley & Sons and her team for providing me all the support and encouragement in presenting this book to the audience in its present form. I am thankful to Sari Friedman for providing me all the support and timely guidance in the publication of this text. She was very cooperative and supportive in dealing all my queries during the whole process of publication. At last I would like to thank Nomita Swaminathan, Production Editor, Kiruthika Balasubramanian, Project Manager and her team in producing this book by typesetting and editing the entire text.
Thanks to all my research scholars and numerous researchers who had posed a variety of questions on research designs, which helped me in identifying the contents of this book. Above all, I want to thank my wife, Haripriya, and children Prachi and Priyam and the rest of my family, who supported and encouraged me in spite of all the time it took me away from them. It was a long and difficult journey for them.
At last I beg forgiveness from all those who have been with me over the years and whose names I have failed to mention.
For Instructors and Students Supplementary material for the book is available on a companion website, which is accessible via “www.wiley.com” at some point. I request the readers to send in their suggestions and queries to me via e-mail at [email protected] and I shall respond to them at the earliest.
Prof. J. P. Verma, PhD
Director, Centre for Advanced StudiesLakshmibai National Institute of Physical Education,GwaliorE-mail: [email protected]
Illustration Credits
The IBM SPSS Statistics has been used solving various applications in different chapters of the book with the permission of the International Business Machines Corporation, © SPSS, Inc., an IBM Company. The following screen images of the software are Reprinted Courtesy of International Business Machines Corporation, © SPSS. “SPSS was acquired by IBM in October 2009.”
Figure 3.1
Screen showing option for creating/opening file.
Figure 3.2
Screen showing option for defining variables and coding.
Figure 3.3
Screen showing format of data feeding.
Figure 3.4
Screen for initiating commands for testing normality and identifying outliers.
Figure 3.5
Screen showing option for selecting variables and detecting outliers.
Figure 3.6
Screen showing options for computing Shapiro–Wilk test and the Q–Q plot.
Figure 3.9
Screen for initiating commands for testing sphericity.
Figure 3.10
Screen showing options for defining variables.
Figure 3.11
Screen showing options for adding independent and dependent variables for analysis.
Figure 3.12
Screen showing option for selecting variables for testing sphericity.
Figure 4.5
Screen for initiating commands for single factor repeated measures design.
Figure 4.6
Screen showing options for defining dependent and independent variables.
Figure 4.7
Screen showing options for adding independent and dependent variables for analysis.
Figure 4.8
Screen showing option for selecting within-subjects variables and obtaining means plot.
Figure 4.9
Screen showing option for computing descriptive statistics and pairwise comparison of means using the Bonferroni correction.
Figure 5.5
Data format in the repeated measures design with two factors.
Figure 5.6
Screen showing options for defining independent and dependent variables.
Figure 5.7
Screen showing option for selecting variables defining all treatment combinations.
Figure 5.8
Screen showing option for means plot.
Figure 5.9
Screen showing option for computing various outputs in the repeated measures design with two factors.
Figure 5.11
Screen showing options for defining independent and dependent variables.
Figure 5.12
Screen showing option for selecting three levels of environment in no music group.
Figure 5.13
Screen showing option for means plot of Environment in no music group.
Figure 5.14
Screen showing option for computing various outputs in one-way repeated measures ANOVA.
Figure 6.5
Screen for initiating commands for the mixed design.
Figure 6.6
Screen showing options for defining dependent and independent variables and its levels.
Figure 6.7
Screen showing options for adding independent and dependent variables for analysis.
Figure 6.8
Screen showing option for selecting within-subjects (movie) and between-subjects variables (Age).
Figure 6.9
Screen showing options for comparing main effect for within-subjects factor (Movie) and other statistics.
Figure 6.10
Screen showing option for post-hoc test for the between-subjects factor (Age).
Figure 6.11
Screen showing option for means plots.
Figure 6.14
Screen showing option for splitting the data file for one-way repeated measures ANOVA.
Figure 6.15
Screen showing option for selecting within-subjects variables.
Figure 6.16
Screen showing option for pair-wise comparison of group means using Bonferroni correction.
Figure 6.18
Screen showing option for selecting the variables for analyzing simple effect of between-subjects variable.
Figure 6.19
Screen showing option for post-hoc test.
Figure 6.20
Screen showing option for descriptive statistics and testing assumption.
Figure 7.4
Data format in one-way repeated measure MANOVA.
Figure 7.5
Screen for initiating command for one-way repeated measureMANOVA.
Figure 7.6
Screen showing options for defining independent and dependent variables.
Figure 7.7
Screen showing option for selecting variables defining all treatment combinations.
Figure 7.8
Screen showing option for means plot.
Figure 7.9
Screen showing option for generating various outputs in one-way repeated measures MANOVA.
Figure 8.4
Data format in mixed design with two-way MANOVA.
Figure 8.5
Screen for initiating commands for mixed design with MANOVA.
Figure 8.6
Screen showing options for defining independent and dependent variables.
Figure 8.7
Screen showing option for selecting variables defining all treatment combinations.
Figure 8.8
Screen showing option for various means plot for each dependent variable.
Figure 8.9
Screen showing option for post hoc test for the between-subjects factor (Sex) for each dependent variable.
Figure 8.10
Screen showing options for comparing the effect of within-subjects factor (Chocolate) and other statistics.
Figure 8.11
Screen for initiating commands for splitting data file.
Figure 8.12
Screen showing option for splitting the data file in different sex category.
Figure 8.14
Screen showing options for defining variables.
Figure 8.15
Screen showing option for selecting within-subjects variables.
Figure 8.16
Screen showing options for generating the output for simple effect of within-subjects factor (Chocolate) and other statistics.
Figure 8.18
Screen showing option for selecting the variables for analyzing simple effect of Sex.
Figure 8.19
Screen showing option for post hoc test.
Figure 8.20
Screen showing option for descriptive statistics and testing assumption.
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Chapter 1Foundations of Experimental Design
Introduction
Empirical research provides knowledge to the researchers through direct or indirect observations or experiences. Empirical research may either involve correlational or experimental approach. In correlational research one looks to establish relationship between two variables. In such studies a premise is made that two variables may be related in some way and then values of both the variables are obtained under different conditions to test a hypothesis if indeed there is a relationship between the two. The obtained correlation is tested for its significance. The drawback of the correlational study is that it does not establish the cause and effect relationship even if the correlation is found to be statistically significant. For instance, if the observed correlation between the caffeine intake and concentration of mind is significant and positive, it cannot be said that caffeine causes concentration. The increase in the concentration due to the increase in the caffeine intake may be due to age, motivation, gender, other lifestyle parameters.
On the other hand, experimental research provides cause and effect relationship because in such experiment a treatment is deliberately administered by a researcher on a group of individuals or objects to see its impact under a controlled environment. In other words, if changes are made in the variable A that leads to changes in variable B, one can conclude that A causes B. For example, to see the impact of exercise on muscular strength a researcher may administer different intensity of exercise to different groups of individuals to see its effect. If a particular intensity of exercise improves muscular strength more than others, one may conclude that exercise intensity causes muscular strength. On the other hand, if there is no difference in the average muscular strength among different exercise groups, it may be inferred that the exercise intensity has nothing to do with muscular strength.
Authenticity in an experimental research is ensured only when an appropriate experimental design is used. Experimental design is a blueprint of the procedures which enables a researcher to test his hypothesis under a controlled environment. It describes the procedure of allocating treatments to the individuals in a sample. There are many ways in which an experimental design can be classified. One such classification is based on the method of allocating treatments to the subjects. On the basis of this criterion, experimental design can be classified into three categories; independent measures design, repeated measures design, and mixed design. In independent measures design each subject gets one and only one treatment, whereas in repeated measures design each subject is tested under all treatments. In mixed design each subject receives one and only treatment of first factor, but gets tested in all the treatments of second factor. This book specifically deals with some of the important repeated measures designs and mixed designs. To understand these designs and its applications, it is important to understand different aspects of experimental research such as principles of experimental design, types of statistical designs, terminologies used, and other considerations in planning an experimental research.
What is Experimental Research?
An experimental research is a process of studying the effect of manipulating independent variable on some dependent variable(s) observed on subjects in a controlled environment. For instance, in studying the effect of progressive relaxation on concentration, the progressive relaxation is an independent variable whereas the concentration is a dependent one. While conducting an experimental research, a researcher always tries to maintain control in an experiment so that valid conclusion can be drawn on the basis of findings. In experimental research the experimenter is allowed to manipulate independent variable to see its impact on the dependent variable. For instance, in the above example the experimenter can decide the duration or the intensity of the progressive relaxation program. Since the experimenter manipulates an independent variable to see its impact on dependent variable, cause and effect relationship can be explained on the basis of findings.
On the other hand in observational study, a researcher collects and analyzes data without manipulating independent variable. Here also the relationship is investigated between independent and dependent variable observed on the subjects. Since researcher is not allowed to manipulate an independent variable, causal interpretations cannot be efficiently made. If relationship is investigated between height and vertical jump performance of sprinters, the observed correlation may not be the strong evidence for causal relationship between them because the independent variable, height, has not been manipulated to see its impact on the vertical jump performance. This is because the experimenter cannot observe the control on the study. The subjects might have different weight, skill, motivation, and fitness level which do not allow interpreting the strong cause and effect relationship between height and the vertical jump performance. The observational study is also known as correlational study or status study.
Since validity of findings in an experiment depends upon the control observed during the experimentation, it is important to design the experiment in such a way so as to minimize the error involved in it. Using appropriate design in an experiment ensures proper allocation of treatments to the subjects so that experimental error is minimized. This ensures internal validity in the experiment. Design of experiment along with its principles has been discussed in detail in the following section.
Design of Experiment and its Principles
Design of experiment can be defined as a roadmap for organizing an experimental study for testing a research hypothesis in an efficient manner. Design of experiment facilitates an experimenter to observe control in an experiment, thereby reducing the experimental error and ensuring internal validity in findings. More specifically it provides a plan according to which treatments are allocated to the subjects in order to reduce experimental error. While planning a study a researcher needs to design an experiment in such a manner that the similarity is ensured among the experiential groups. The experimental error is controlled by controlling the effect of extraneous variables. To design an experiment a researcher must have the knowledge about homogeneity of experimental material or the subjects on which the experiment is required to be conducted. Besides, one should be able to identify those extraneous variables which may affect findings if not controlled. Depending upon the homogeneous conditions of subjects, an experimental design is identified. There are ways and means in testing the efficiency of design used in a research study. The efficiency of two different designs in the same experiment may be compared by using the error variance. This has been shown in Chapter 2. To have the control in an experiment and ensuring maximum accuracy in findings, Ronald A. Fisher has suggested the three basic principles of design of experiment, namely, Randomization, Replication, and Blocking.
Randomization
One of the main principles of design of experiment is randomization. Randomization refers to randomly allocating treatments to the subjects. Randomization ensures similarity in the experimental groups. It controls bias and extraneous variables which might affect findings of the study. Readers must note that the random selection of subjects and random allocation of treatments are two different things. Consider a study in which three different types of beverages, tea, coffee, and soft drink, are compared for their effect on reaction time. If 30 subjects are selected in the study let us see how randomization is done. Firstly, the initial sample of 30 subjects is selected randomly from the population of interest. Out of these subjects three subjects are randomly selected and the treatments are allocated randomly to them. Then another three samples are selected randomly from the remaining lot and treatments are again randomly allocated to them. In this all 30 subjects are assigned to three different treatment groups. In this study selecting 30 sample subjects randomly from the population of interest does not ensure that the treatment groups are similar, but helps the researcher to generalize findings about the population from which the sample has been drawn.
In other words, random selection of subjects ensures external validity in findings. Complete randomization is only possible if subjects are uniform. On the other hand, perfect random allocation of treatments to the subjects ensures that treatment groups are homogenous and do not contain any bias. This random allocation of treatments to the subjects ensures internal validity in findings. If external and internal validity are ensured, one can be quite sure in the above experiment that whatever the effect of a particular beverage on the subject's reaction time is observed, it is due to the beverage only and not due to any other reason. Besides this, randomization also provides the validity of F-test. Further, assumption of independence of observations in F-test also gets satisfied due to randomization.
Replication
Replication refers to repeating the treatment a number of times on different subjects. It is a fact that a treatment applied on single subject does not provide sufficient evidence of the effect of that treatment, so replication is needed. Single observation also does not provide the valid estimate of the parameters in the study so replication of treatments is essential. It is also a fact that standard error of sample mean or difference of sample means (group means) is inversely proportionate to the replication of treatments. So if number of replication increases the error variance or standard error decreases. If the treatment is effective the average effect of replication will reflect its experimental worth. If it is not few subjects in the sample who may have reacted to the treatment will be negated by the majority of subjects who were unaffected by it. If the above mentioned experiment of beverages is administered on three subjects only, and if the soft drink is found to improve the reaction time, the result may not be acceptable until unless this result is observed on most of the subjects in the sample. Thus, replication reduces variability in experimental results and provides confidence to the researcher in drawing conclusion about the effect of treatment on dependent variable.
Blocking
Blocking is a technique of reducing experimental error by including an extraneous variable in the experiment. Blocking refers to dividing heterogeneous experimental units into homogenous blocks so that the units in the blocks are homogeneous. In other words whole experimental material is divided into homogeneous strata. Blocks are made if experimenter has some knowledge about the experimental material or subjects prior to conducting an experiment, through pilot study or uniformity trial or some prior studies. Blocking technique is used if an experimenter knows that the variability exists among the subjects. Generally, size of the block should be equal to the number of treatments. After dividing the experimental units into blocks, the treatments are randomly allocated in each block. Blocking enhances precision in the study by reducing the experimental error. In the above example of beverages if gender is considered as blocking variable, the blocks of male and female may be made in which treatments may be allocated randomly.
Statistical Designs
It is important for the researchers to know about various kinds of statistical designs so as to choose the appropriate one for their study to obtain reliable findings. Selection of design depends upon many parameters such as number of factors to be investigated, variability of the experimental units, and degrees of precision required. In empirical research, studies can be classified in two categories; single factor studies and multifactor studies. In single factor study the effect of only one factor on some dependent variable is investigated, whereas, in multifactor studies effect of two or more independent factors on some dependent variable is investigated. Multifactor studies are also known as factorial experiment. Factorial experiment may have two or more independent factors, each having two or more levels. All these studies can be conducted by using any of the three basic statistical designs namely; Completely Randomized Design, Randomized Block Design and Latin Square Design. Choice of using these designs depends upon the knowledge about variability of the experimental materials or subjects. We shall discuss these designs briefly later in this chapter.
In the example of the beverages discussed above the effect of only one factor is investigated, hence the design used for analysis would be one factor design. Here the treatment factor has three levels and therefore three treatment conditions are to be compared for their effectiveness. But if along with the beverage, the effect of duration is also required to be investigated, the experiment is said to be the two factor(or multifactor) study. Similarly, more than two factors can also be simultaneously investigated and the design in such situation would be known as multifactor design. If the effect of more than two factors is investigated simultaneously, the analysis becomes very complex and therefore researchers usually investigate the effect of either one or two factors only. Whatever design a researcher uses, it is analyzed by using the group of techniques known as analysis of variance (ANOVA). In any experimental design the three basic principles of randomization, replication and blocking are used. Selection of the design of experiment depends upon the fact as to how we wish to carry out these principles. All types of designs discussed above will be explained with the help of examples in the following sections.
