# Testing Statistical Assumptions in Research

1. Edition June 2019

224 Pages, Hardcover*Textbook*

**978-1-119-52841-8**

Comprehensively teaches the basics of testing statistical assumptions in research and the importance in doing so

This book facilitates researchers in checking the assumptions of statistical tests used in their research by focusing on the importance of checking assumptions in using statistical methods, showing them how to check assumptions, and explaining what to do if assumptions are not met.

Testing Statistical Assumptions in Research discusses the concepts of hypothesis testing and statistical errors in detail, as well as the concepts of power, sample size, and effect size. It introduces SPSS functionality and shows how to segregate data, draw random samples, file split, and create variables automatically. It then goes on to cover different assumptions required in survey studies, and the importance of designing surveys in reporting the efficient findings. The book provides various parametric tests and the related assumptions and shows the procedures for testing these assumptions using SPSS software. To motivate readers to use assumptions, it includes many situations where violation of assumptions affects the findings. Assumptions required for different non-parametric tests such as Chi-square, Mann-Whitney, Kruskal Wallis, and Wilcoxon signed-rank test are also discussed. Finally, it looks at assumptions in non-parametric correlations, such as bi-serial correlation, tetrachoric correlation, and phi coefficient.

* An excellent reference for graduate students and research scholars of any discipline in testing assumptions of statistical tests before using them in their research study

* Shows readers the adverse effect of violating the assumptions on findings by means of various illustrations

* Describes different assumptions associated with different statistical tests commonly used by research scholars

* Contains examples using SPSS, which helps facilitate readers to understand the procedure involved in testing assumptions

* Looks at commonly used assumptions in statistical tests, such as z, t and F tests, ANOVA, correlation, and regression analysis

Testing Statistical Assumptions in Research is a valuable resource for graduate students of any discipline who write thesis or dissertation for empirical studies in their course works, as well as for data analysts.

Acknowledgments xi

About the Companion Website xii

1 Importance of Assumptions in Using Statistical Techniques 1

1.1 Introduction 1

1.2 Data Types 2

1.2.1 Nonmetric Data 2

1.2.2 Metric Data 2

1.3 Assumptions About Type of Data 3

1.4 Statistical Decisions in Hypothesis Testing Experiments 4

1.4.1 Type I and Type II Errors 5

1.4.2 Understanding Power of Test 6

1.4.3 Relationship Between Type I and Type II Errors 7

1.4.4 One-Tailed and Two-Tailed Tests 8

1.5 Sample Size in Research Studies 8

1.6 Effect of Violating Assumptions 11

Exercises 12

Answers 16

2 Introduction of SPSS and Segregation of Data 17

2.1 Introduction 17

2.2 Introduction to SPSS 17

2.2.1 Data File Preparation 19

2.2.2 Importing the Data Set from Excel 21

2.3 Data Cleaning 23

2.3.1 Interpreting Descriptive Statistics Output 26

2.3.2 Interpreting Frequency Statistic Output 27

2.4 Data Management 27

2.4.1 Sorting Data 28

2.4.1.1 Sort Cases 28

2.4.1.2 Sort Variables 29

2.4.2 Selecting Cases Using Condition 31

2.4.2.1 Selecting Data of Males with Agree Response 32

2.4.3 Drawing Random Sample of Cases 34

2.4.4 Splitting File 36

2.4.5 Computing Variable 36

Exercises 40

Answers 42

3 Assumptions in Survey Studies 45

3.1 Introduction 45

3.2 Assumptions in Survey Research 46

3.2.1 Data Cleaning 46

3.2.2 About Instructions in Questionnaire 46

3.2.3 Respondent's Willingness to Answer 47

3.2.4 Receiving Correct Information 47

3.2.5 Seriousness of the Respondents 47

3.2.6 Prior Knowledge of the Respondents 48

3.2.7 Clarity About Items in the Questionnaire 48

3.2.8 Ensuring Survey Feedback 48

3.2.9 Nonresponse Error 48

3.3 Questionnaire's Reliability 49

3.3.1 Temporal Stability 49

3.3.1.1 Test-Retest Method 49

3.3.2 Internal Consistency 50

3.3.2.1 Split-Half Test 50

3.3.2.2 Kuder-Richardson Test 52

3.3.2.3 Cronbach's Alpha 55

Exercise 60

Answers 63

4 Assumptions in Parametric Tests 65

4.1 Introduction 65

4.2 Common Assumptions in Parametric Tests 66

4.2.1 Normality 66

4.2.1.1 Testing Normality with SPSS 67

4.2.1.2 What if the Normality Assumption Is Violated? 71

4.2.1.3 Using Transformations for Normality 72

4.2.2 Randomness 74

4.2.2.1 Runs Test for Testing Randomness 75

4.2.3 Outliers 76

4.2.3.1 Identifying Outliers with SPSS 77

4.2.4 Homogeneity of Variances 79

4.2.4.1 Testing Homogeneity with Levene's Test 79

4.2.5 Independence of Observations 82

4.2.6 Linearity 82

4.3 Assumptions in Hypothesis Testing Experiments 82

4.3.1 Comparing Means with t-Test 83

4.3.2 One Sample t-Test 83

4.3.2.1 Testing Assumption of Randomness 84

4.3.2.2 Testing Normality Assumption in t-Test 85

4.3.2.3 What if the Normality Assumption Is Violated? 88

4.3.3 Sign Test 88

4.3.4 Paired t-Test 88

4.3.4.1 Effect of Violating Normality Assumption in Paired t-Test 91

4.3.5 Rank Test 91

4.3.6 Independent Two-Sample t-Test 92

4.3.6.1 Two-Sample t-Test with SPSS and Testing Assumptions 92

4.3.6.2 Effect of Violating Assumption of Homogeneity 96

4.4 F-test For Comparing Variability 97

4.4.1 Analysis of Variance (ANOVA) 98

4.4.2 ANOVA Assumptions 99

4.4.2.1 Checking Assumptions Using SPSS 99

4.4.3 One-Way ANOVA Using SPSS 105

4.4.4 What to Do if Assumption Violates? 109

4.4.5 What if the Assumptions in ANOVA Are Violated? 109

4.5 Correlation Analysis 118

4.5.1 Karl Pearson's Coefficient of Correlation 118

4.5.2 Testing Assumptions with SPSS 119

4.5.2.1 Testing for Linearity 119

4.5.3 Coefficient of Determination 122

4.6 Regression Analysis 125

4.6.1 Simple Linear Regression 126

4.6.2 Assumptions in Linear Regression Analysis 128

4.6.2.1 Testing Assumptions with SPSS 128

Exercises 136

Answers 139

5 Assumptions in Nonparametric Tests 141

5.1 Introduction 141

5.2 Common Assumptions in Nonparametric Tests 141

5.2.1 Randomness 142

5.2.2 Independence 142

5.2.2.1 Testing Assumptions Using SPSS 142

5.2.2.2 Runs Test for Randomness Using SPSS 143

5.3 Chi-square Tests 144

5.3.1 Goodness-of-Fit Test 145

5.3.1.1 Assumptions About Data 145

5.3.1.2 Performing Chi-square Goodness-of-Fit Test Using SPSS 146

5.3.2 Testing for Independence 148

5.3.2.1 Assumptions About Data 148

5.3.2.2 Performing Chi-square Test of Independence Using SPSS 148

5.3.3 Testing for Homogeneity 152

5.3.3.1 Assumptions About Data 153

5.3.3.2 Performing Chi-square Test of Homogeneity Using SPSS 153

5.3.4 What to Do if Assumption Violates? 155

5.4 Mann-Whitney U Test 156

5.4.1 Assumption About Data 157

5.4.2 Mann-Whitney Test Using SPSS 157

5.4.3 What to Do if Assumption Violates? 159

5.5 Kruskal-Wallis Test 161

5.5.1 Assumptions About Data 162

5.5.2 Kruskal-Wallis H Test Using SPSS 162

5.5.3 Dealing with Data When Assumption Is Violated 166

5.6 Wilcoxon Signed-Rank Test 168

5.6.1 Assumptions About Data 168

5.6.2 Wilcoxon Signed-Rank Test Using SPSS 168

5.6.3 Remedy if Assumption Violates 172

Exercises 172

Answers 174

6 Assumptions in Nonparametric Correlations 175

6.1 Introduction 175

6.2 Spearman Rank-Order Correlation 175

6.3 Biserial Correlation 178

6.4 Tetrachoric Correlation 182

6.4.1 Assumptions for Tetrachoric Correlation Coefficient 182

6.4.1.1 Testing Significance 183

6.5 Phi Coefficient (Phi) 184

6.6 Assumptions About Data 188

6.7 What if the Assumptions Are Violated? 188

Exercises 188

Answers 190

Appendix Statistical Tables 193

Bibliography 203

Index 209

ABDEL-SALAM G. ABDEL-SALAM, PHD, is Assistant Professor of Statistics and Head of Student Data Management Section and Coordinator for the Statistical Consulting Unit at Qatar University, Qatar. He is a PStat(r) by the American Statistical Association and CStat by the Royal Statistical Society. He taught at different international universities such as; Virginia Polytechnic Institute and State University (Virginia Tech), Oklahoma State University and Cairo University.