Basic Statistics for Life Scientists

List of Boxes ix

Preface xi

About the Companion Site xv

1 A Primer on Data Summarization and Visualization 1

1.1 Numerical Summary of Data 1

1.2 Data Visualization 5

2 The p-Value and Concept of Statistical Significance 13

2.1 Beware of Misconceptions 17

3 Statistical Tests: How to Get the p-Value 25

3.1 t-Tests 29

3.1.1 Unpaired t-Test 29

3.1.2 Welch’s Unpaired t-Test 37

3.1.3 Paired t-Test 38

3.1.4 Equivalence Testing 40

3.2 Non-parametric Alternatives to t-Tests for Comparison of Two Groups 42

3.2.1 Mann–Whitney U Test (Wilcoxon Rank-Sum) 42

3.2.2 Brunner–Munzel Test 48

3.2.3 Other Non-parametric Unpaired Tests 48

3.2.4 Wilcoxon Signed-Rank Test 49

3.2.5 Sign Test 49

3.3 Tests for Frequency of Occurrence 50

3.3.1 Fisher’s Exact Test and Some of Its Alternatives 50

3.3.2 Chi-Square Test 52

3.4 Correlation and Regression Analyses 52

3.4.1 Correlation 52

3.4.1.1 Pearson Correlation 54

3.4.1.2 Spearman Correlation 56

3.4.1.3 Kendall Correlation 56

3.4.1.4 Final Comments on Correlation 58

3.4.2 Linear Regression 60

3.4.3 Non-linear Regression and Comparing Curve Data 67

3.5 ANOVA Methods for Comparison of Multiple Groups 70

3.5.1 One-Way ANOVA 70

3.5.2 Repeated Measures ANOVA 75

3.5.3 Two-Way ANOVA 76

3.6 Permutation Tests 77

4 Common Pitfalls Associated with the Use of p-Values and Statistical Significance 83

4.1 Multiple Testing Problem (and How to Correct for It) 83

4.1.1 Multiple Hypothesis Testing Corrections 85

4.2 Underpowered Study Design (and Power Calculations) 88

4.2.1 Power Calculations 89

4.3 Pseudoreplication (and Hierarchical Statistics) 94

4.4 N-Hacking (and Interim and Sequential Analysis) 99

5 Problems of the Concept of Statistical Significance; Alternative Approaches 105

6 Experimental Design 111

6.1 Starting the Project 111

6.1.1 Pre-registration 111

6.2 Stopping the Project 112

6.3 Control Experiments 113

6.4 Discarding Data 113

6.5 Blinding 114

6.6 Randomization and Blocking 115

6.7 Uncontrolled Factors 117

6.8 Which Experimental Model Should Be Used? 118

7 Concluding Remarks 121

Further Reading 123

Appendix A A Brief Overview of Tools for Statistical Analysis 125

Appendix B Additional Points on Tests for Contingency Tables 129

B.1 Fisher’s Test Conservatism 129

B.2 Additional Details on Useful Alternatives to Fisher’s Test 131

Appendix C On the p-Value as a Measure of Evidence 133

Code Samples 135

Samples for Section 1.1 136

Samples for Section 1.2 136

Samples for Section 3.1 143

Samples for Section 3.2 147

Samples for Section 3.3 150

Samples for Section 3.4 151

Samples for Section 3.5 159

Samples for Section 3.6 161

Samples for Section 4.1 165

Samples for Section 4.2 166

Samples for Section 4.3 170

Bibliography 173

Index 181