# Repeated Measures Design for Empirical Researchers

# Repeated Measures Design for Empirical Researchers

ISBN: 978-1-119-05250-0 August 2015 288 Pages

**E-Book**

$100.99

## Description

**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.

## Related Resources

### Student

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 5

Completely Randomized Design 5

Randomized Block Design 6

Matched Pairs Design 8

Latin Square designs 8

Factorial Experiment 9

Terminologies in Design of Experiment 10

Subject 11

Experimental Unit 11

Factor and Treatment 11

Criterion Variable 12

Variation and Variance 12

Experimental Error 12

External Validity 13

Internal Validity 13

Considerations in Designing an Experiment 13

Systematic Variance 14

Extraneous Variance 14

Randomization Method 15

Elimination Method 15

Matching Group Method 15

Adding Additional Independent Variable 16

Statistical Control 16

Error Variance 17

Exercise 17

Assignment 18

Bibliography 18

**2 Analysis of Variance and Repeated Measures Design 21**

Introduction 21

Understanding Variance and Sum of Squares 22

One Way Analysis of Variance for Independent Measures Design 24

Assumptions 24

Illustration I 25

Partitioning of Total Variation in the Design 26

Computation 26

Explanation 27

Partitioning of SS and Degrees of Freedom 27

Computation 27

Results 29

Post-Hoc Analysis 29

Means Plot 31

Repeated Measures Design 31

When to Use Repeated Measures ANOVA 32

Assumptions 32

Solving Repeated Measures Design With One-Way ANOVA 33

Illustration II 34

Hypothesis Construction 34

Layout Design 35

One-Way Repeated Measures ANOVA Model 36

Computation in Repeated Measures Design with One-Way ANOVA 36

Explanation 37

Computation 37

Testing Sphericity Assumption 39

Correcting for Degrees of Freedom 41

Results 43

Pair-Wise Comparison of Means 43

Bonferroni Correction 44

Effect Size 45

Exercise 46

Assignment 47

Bibliography 48

**3 Testing Assumptions in Repeated Measures Design Using SPSS 51**

Introduction 51

First Step in Using SPSS 52

Assumptions 53

Testing Normality 54

Test of Normality 57

Q–Q Plot for Normality 57

Box-plot for Identifying Outliers 59

Testing Sphericity 60

Remedial Measures when Assumption Fails 62

Transforming Nonnormal Data into Normal 62

Choice of Design and Sphericity 63

Sample Size Determination 64

Important Terms 64

Confidence Interval 64

Confidence Level 65

Power of the Test 66

Sample Size Determination on the Basis of Cost 67

Sample Size Determination on the Basis of Accuracy Factor 67

Sample Size in Estimating Mean 67

Sample Size in Hypothesis Testing 68

Exercise 68

Assignment 69

Bibliography 70

**4 One-Way Repeated Measures Design 73**

Introduction to Design 73

Advantage of One-Way Repeated Measures Design 74

Weakness of Repeated Measures Design 74

Application 74

Layout Design 75

Case I: When the Levels of Within-Subjects Variable are Different Treatments 75

Case II: When the Levels of Within-Subjects Variable are Different Time Durations 76

Steps in Solving One-Way Repeated Measures Design 77

Illustration 77

Testing Assumptions 77

Layout Design 78

Distribution of Variation and Degrees of Freedom 79

Hypothesis Construction 80

Level of Significance 80

Solving One-Way Repeated Measures Design Using SPSS 81

SPSS Output and Interpretation 83

Descriptive Statistics 83

Testing Sphericity 84

Testing Significance of Within-Subjects Effect 86

How to Report the Findings 88

Inference 88

Exercise 88

Assignment 89

Bibliography 90

**5 Two-Way Repeated Measures Design 91**

Introduction 91

Advantages of Using Two-Way Repeated Measures Design 92

Assumptions 92

Layout Design 93

Case I: When Levels of Within-Subjects Variable are Different Treatment Conditions 93

Case II: When the Levels of the Within-Subjects Variable are Different Time Durations 94

Application 94

Steps in Solving Two-Way Repeated Measures Design 95

Illustration 97

Layout Design 97

Distribution of Variation and Degrees of Freedom 98

Research Questions 100

Hypotheses Construction 100

Level of Significance 101

Solving Repeated Measures Design with Two-Way ANOVA Using SPSS 101

SPSS Output and Interpretation 104

Testing Assumptions 105

Data Type 106

Independence of Measurement 106

Normality 106

Sphericity 106

Descriptive Statistics 106

Testing Main Effect of Music (Within-Subjects) 106

Pairwise Comparison of Marginal Means of Music Groups 108

Means Plot of Music 108

Testing Main Effect of Environment (Within-Subjects) 108

Testing Significance of Interaction (Environment × Music) 108

Type I Error for Simple Effect 110

Simple Effect of Environment (Within-Subjects) 110

Simple Effect of Music (Within-Subjects) 116

How to Report the Findings 120

Assumptions 120

Testing Main Effects 120

Testing Simple Effects 121

Inference 121

Exercise 121

Assignment 122

Bibliography 124

**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 Factor are Different Treatment Conditions 129

Case II: When Levels of the Within-Subjects Factor 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) 144

Pair-Wise Comparison of Marginal Means of Movie Groups 144

Means Plot of Movie 145

Testing Main Effect of Age (Between-Subjects) 145

Pair-Wise Comparison of Marginal Means of Age Groups 146

Means Plot of Age 146

Testing Significance of Interaction (Movie × Age) 147

Simple Effect of Movie (Within-Subjects) 147

Simple Effect of Age (Between-Subjects) 151

How to Report the Findings 155

Assumptions 155

Testing Main Effects 156

Testing Simple Effects 156

Inference 157

Exercise 157

Assignment 158

Bibliography 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 Factor are Different Treatment Conditions 165

Case II: When Levels of Within-Subjects Factor 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

Bibliography 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 Factor are Different Treatment Conditions 192

Case II: When the Levels of the Within-Subjects Factor 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

Bibliography 240

Appendix 243

Index 255