Repeated Measures Design for Empirical Researchers

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 two–way repeated measures design, two–way mixed design, one–way repeated measures ANOVA, 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 related 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 author of Statistics for Exercise Science and Health with Microsoft® Office Excel®, also published by Wiley.

Preface xv

1 Foundations of Experimental Design 1

Introduction, 1

What is Experimental Research? 2

Design of Experiment and its Principles, 3

Randomization, 3

Replication, 4

Blocking, 4

Statistical Designs, 4

Completely Randomized Design, 5

Randomized Block Design, 6

Matched Pairs Design, 7

Factorial Experiment, 8

Terminologies in Design of Experiment, 9

Subject, 10

Experimental Unit, 10

Treatment, 10

Criterion Variable, 10

Factors, 11

Variation and Variance, 11

Experimental Error, 11

External Validity, 11

Internal Validity, 12

Considerations in Designing an Experiment, 12

Systematic Variance, 13

Extraneous Variance, 13

Randomization Method, 13

Elimination Method, 14

Matching Group Method, 14

Adding Additional Independent Variable, 14

Statistical Control, 15

Error Variance, 16

Exercise, 16

Assignment, 17

References, 17

2 Analysis of Variance and Repeated Measures Design 19

Introduction, 19

Understanding Variance and Sum of Squares, 20

One Way Analysis of Variance for Independent Measures Design, 22

Assumptions, 22

Illustration I, 23

Partitioning of Variation in the Design, 23

Computation, 24

Explanation, 24

Partitioning of SS and Degrees of Freedom, 25

Computation, 25

Results, 27

Post–Hoc Analysis, 27

Repeated Measures Design, 28

When to Use Repeated Measures ANOVA, 29

Assumptions, 30

Solving Repeated Measures Design With One–Way ANOVA, 31

Illustration II, 32

Hypothesis Construction, 32

Layout Design, 33

One–Way Repeated Measures ANOVA Model, 33

Computation in Repeated Measures Design with One–Way ANOVA, 34

Explanation, 35

Computation, 35

Testing Sphericity Assumption, 37

Correcting for Degrees of Freedom, 39

Results, 41

Pair–Wise Comparison of Means, 41

Bonferroni Correction, 42

Effect Size, 43

Exercise, 44

Assignment, 45

References, 46

3 Testing Assumptions in Repeated Measures Design Using SPSS 49

Introduction, 49

First Step in Using SPSS, 50

Assumptions, 51

Testing Normality, 52

Test of Normality, 55

Q Q Plot for Normality, 55

Testing Outliers, 57

Testing Sphericity, 57

Remedial Measures when Assumption Fails, 60

Transforming Nonnormal Data into Normal, 60

Choice of Design and Sphericity, 61

Sample Size Determination, 62

Important Terms, 62

Confidence Interval, 62

Confidence Level, 63

Power of the Test, 64

Sample Size Determination on the Basis of Cost, 65

Sample Size Determination on the Basis of Accuracy Factor, 65

Sample Size in Estimating Mean, 65

Sample Size in Hypothesis Testing, 66

Exercise, 66

Assignment, 67

References, 68

4 One–Way Repeated Measures Design 71

Introduction to Design, 71

Advantages of One–Way Repeated Measures Design, 72

Weaknesses of Repeated Measures Design, 72

Application, 72

Layout Design, 73

Case I: When the Levels of Within–Subjects Variable are Different

Treatment Conditions, 73

Case II: When the Levels of Within–Subjects Variable are Different

Time Durations, 74

Steps in Solving One–Way Repeated Measures Design, 75

Illustration, 75

Testing Assumptions, 75

Layout Design, 76

Distribution of Variation and Degrees of Freedom, 77

Hypothesis Construction, 78

Level of Significance, 78

Solving One–Way Repeated Measures Design Using SPSS, 79

SPSS Output and Interpretation, 81

Descriptive Statistics, 81

Testing Sphericity, 82

Testing Significance of Within–Subjects Effect, 84

How to Report the Findings, 86

Inference, 86

Exercise, 86

Assignment, 87

References, 88

5 Two–Way Repeated Measures Design 89

Introduction, 89

Advantages of Using Two–Way Repeated Measures Design, 90

Assumptions, 90

Layout Design, 91

Case I: When Levels of Within–Subjects Variable are Different Treatment Conditions, 91

Case II: When the Levels of the Within–Subjects Variable are Different Time Periods, 92

Application, 92

Steps in Solving Two–Way Repeated Measures Design, 93

Illustration, 95

Layout Design, 95

Distribution of Variation and Degrees of Freedom, 95

Research Questions, 98

Hypotheses Construction, 98

Level of Significance, 99

Solving Repeated Measures Design with Two–Way ANOVA Using SPSS, 99

SPSS Output and Interpretation, 103

Testing Assumptions, 106

Data Type, 106

Independence of Measurement, 106

Normality, 106

Sphericity, 113

Descriptive Statistics, 113

Testing Main Effect of Music (Within–Subjects), 113

Pairwise Comparison of Marginal Means of Music Groups, 114

Means Plot of Music, 114

Testing Main Effect of Environment (Within–Subjects), 114

Testing Significance of Interaction (Environment × Music), 114

Type I Error for Simple Effect, 114

Simple Effect of Environment (Within–Subjects), 115

Simple Effect of Music (Within–Subjects), 117

How to Report the Findings, 118

Assumptions, 118

Testing Main Effects, 119

Testing Simple Effects, 119

Inference, 120

Exercise, 120

Assignment, 121

References, 122

6 Two–Way Mixed Design 125

Introduction, 125

Advantages of Two–Way Mixed Design, 127

Assumptions, 127

Application, 128

Layout Design, 129

Case I: When Levels of the Within–Subjects Variable are Different Treatment Conditions, 129

Case II: When Levels of the Within–Subjects Variable are Different Time Period, 130

Steps in Solving Mixed Design with Two–Way ANOVA, 131

Illustration, 132

Layout Design, 132

Distribution of Variation and Degrees of Freedom, 134

Research Questions, 135

Hypothesis Construction, 136

Level of Significance, 136

Solving Mixed Design with Two–Way ANOVA using SPSS, 137

SPSS Outputs and Interpretation, 140

Testing Assumptions, 141

Assumption of Normality, 141

Homogeneity of Variance Covariance Matrices, 142

Homogeneity of Variance, 142

Sphericity Assumption, 143

Descriptive Statistics, 143

Testing Main Effect of Movie (within–Subjects), 143

Pair–Wise Comparison of Marginal Means of Movie Groups, 144

Means Plot of Movie, 146

Testing Main Effect of Age (Between–Subjects), 146

Pair–Wise Comparison of Marginal Means of Age Groups, 146

Means Plot of Age, 146

Testing Significance of Interaction (Movie × Age), 146

Simple Effect of Movie (within–Subjects), 147

Simple Effect of Age (between–subjects), 152

How to Report the Findings, 155

Assumptions, 156

Testing Main Effects, 156

Testing Simple Effects, 156

Inference, 158

Exercise, 158

Assignment, 158

References, 159

7 One–Way Repeated Measures MANOVA 161

Introduction, 161

When to Use Repeated Measures MANOVA? 162

Why to Use Repeated Measures MANOVA? 162

Assumptions, 163

Application, 164

Layout Design, 165

Case I: When Levels of Within–Subjects Variable are Different Treatment Conditions, 165

Case II: When Levels of Within–Subjects Variable are Different Time Period, 166

Steps in Solving One–Way Repeated Measures MANOVA, 166

Illustration, 167

Layout Design, 167

Research Questions, 168

Hypotheses Construction, 168

Level of Significance, 170

Solving One–Way Repeated Measures MANOVA Design with SPSS, 170

SPSS Output and Interpretation, 173

Descriptive Statistics, 174

Testing Assumptions, 174

Testing Correlation, 174

Testing Normality, 176

Testing Outliers, 176

Multivariate Testing, 178

Univariate Testing, 181

Testing Sphericity, 181

Pair–Wise Comparison of Marginal Means, 181

Means Plot of Maths, 181

Means Plot of English, 181

Means Plot of Reasoning, 182

How to Report the Findings, 183

Assumptions, 183

Testing Multivariate Effect, 183

Testing Univariate Effect, 183

Inference, 184

Exercise, 184

Assignment, 186

References, 186

8 Mixed Design with Two–Way MANOVA 189

Introduction, 189

What Happens in Manova Experiment, 190

Assumptions, 191

Multivariate Analysis, 191

Univariate Analysis, 192

Layout Design, 192

Case I: When the Levels of Within–Subjects Variable are Different Treatment Conditions, 192

Case II: When the Levels of the Within–Subjects Variable are Different Time Periods, 193

Application, 193

Steps in Solving Mixed Design with Two–Way Manova, 194

Illustration, 196

Layout Design, 196

Research Questions, 198

Hypotheses Construction, 198

Level of Significance, 200

Solving Mixed Design with Two–Way MANOVA Using SPSS, 200

SPSS Output and Interpretation, 204

Multivariate Outcome, 204

Main effect of each dependent variable, 204

Simple effect of each dependent variable, 205

Testing Assumptions, 206

Data Type, 206

Testing Correlations, 206

Testing Normality, 210

Testing Outliers, 210

Homogeneity of Variances, 211

Homogeneity of Variance Covariance Matrices, 211

Sphericity Assumption for Within–Subjects Conditions, 211

Multivariate Testing, 213

Univariate Testing, 215

Main Effect of Between–Subjects Factor (Sex), 215

Main Effect of Within–Subjects Factor (Chocolate), 215

Level of Significance for Simple Effect, 219

Simple Effect on Taste, 219

Simple Effect on Crunchiness, 227

Simple Effect on Flavor, 231

Means Plots (Sex × Chocolate), 233

How to Report Findings, 235

Assumptions, 236

Multivariate Effects, 237

Univariate Main Effects, 237

Univariate Simple Effects, 237

Inference, 238

Exercise, 238

Assignment, 240

References, 240

Appendix A Appendix 243

Index 253

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 author of Statistics for Exercise Science and Health with Microsoft® Office Excel®, also published by Wiley.