Practical Statistics for Environmental and Biological Scientists

Preface ix

Part I Statistics Basics 1

1 Introduction 3

1.1 Do you need statistics? 3

1.2 What is statistics? 4

1.3 Some important lessons I have learnt 5

1.4 Statistics is getting easier 6

1.5 Integrity in statistics 7

1.6 About this book 8

2 A Brief Tutorial on Statistics 9

2.1 Introduction 9

2.2 Variability 9

2.3 Samples and populations 10

2.4 Summary statistics 11

2.5 The basis of statistical tests 19

2.6 Limitations of statistical tests 24

3 Before You Start 27

3.1 Introduction 27

3.2 What statistical methods are available? 28

3.3 Surveys and experiments 33

3.4 Designing experiments and surveys — preliminaries 35

3.5 Summary 43

4 Designing an Experiment or Survey 45

4.1 Introduction 45

4.2 Sample size 45

4.3 Sampling 50

4.4 Experimental design 56

4.5 Further reading 60

5 Exploratory Data Analysis and Data Presentation 63

5.1 Introduction 63

5.2 Column graphs 65

5.3 Line graphs 67

5.4 Scatter graphs 69

5.5 General points about graphs 71

5.6 Tables 73

5.7 Standard errors and error bars 74

6 Common Assumptions or Requirements of Data for Statistical Tests 77

6.1 Introduction 77

6.2 Common assumptions 81

6.3 Transforming data 84

Part II Statistical Methods 91

7 t-tests and F-tests 93

7.1 Introduction 93

7.2 Limitations and assumptions 94

7.3 t-tests 95

7.4 F-test 103

7.5 Further reading 105

8 Analysis of Variance 107

8.1 Introduction 107

8.2 Limitations and assumptions 109

8.3 One-way ANOVA 111

8.4 Multiway ANOVA 119

8.5 Further reading 127

9 Correlation and Regression 129

9.1 Introduction 129

9.2 Limitations and assumptions 130

9.3 Pearson’s product moment correlation 131

9.4 Simple linear regression 135

9.5 Correlation or regression? 142

9.6 Multiple linear regression 143

9.7 Comparing two lines 146

9.8 Fitting curves 148

9.9 Further reading 151

10 Multivariate ANOVA 153

10.1 Introduction 153

10.2 Limitations and assumptions 154

10.3 Null hypothesis 156

10.4 Description of the test 156

10.5 Interpreting the results 158

10.6 Further reading 161

11 Repeated Measures 163

11.1 Introduction 163

11.2 Methods for analysing repeated measures data 166

11.3 Designing repeated measures experiments 170

11.4 Further reading 170

12 Chi-square Tests 173

12.1 Introduction 173

12.2 Limitations and assumptions 174

12.3 Goodness of fit test 175

12.4 Test for association between two factors 178

12.5 Comparing proportions 181

12.6 Further reading 184

13 Non-parametric Tests 185

13.1 Introduction 185

13.2 Limitations and assumptions 188

13.3 Mann—Whitney U-test 189

13.4 Two-sample Kolmogorov—Smirnov test 191

13.5 Two-sample sign test 193

13.6 Kruskal—Wallis test 195

13.7 Friedman’s test 198

13.8 Spearman’s rank correlation 200

13.9 Further reading 203

14 Principal Component Analysis 205

14.1 Introduction 205

14.2 Limitations and assumptions 207

14.3 Description of the method 207

14.4 Interpreting the results 209

14.5 Further reading 218

15 Cluster Analysis 221

15.1 Introduction 221

15.2 Limitations and assumptions 222

15.3 Clustering observations 223

15.4 Clustering variables 226

15.5 Further reading 228

Appendices 229

A Calculations for statistical tests 231

B Concentration data for Chapters 14 and 15 247

C Using computer packages 249

D Choosing a test: decision table 261

E List of worked examples 265

Bibliography 271

Index 273