Statistics

Michael J. Crawley, FRS, Department of Biological Sciences, Imperial College of Science, Technology and Medicine. Author of three bestselling Wiley statistics titles and five life science books.

Preface xi Chapter 1 Fundamentals 1 Everything Varies 2 Significance 3 Good and Bad Hypotheses 3 Null Hypotheses 3 p Values 3 Interpretation 4 Model Choice 4 Statistical Modelling 5 Maximum Likelihood 6 Experimental Design 7 The Principle of Parsimony (Occams Razor) 8 Observation, Theory and Experiment 8 Controls 8 Replication: Its the ns that Justify the Means 8 How Many Replicates? 9 Power 9 Randomization 10 Strong Inference 14 Weak Inference 14 How Long to Go On? 14 Pseudoreplication 15 Initial Conditions 16 Orthogonal Designs and Non-Orthogonal Observational Data 16 Aliasing 16 Multiple Comparisons 17 Summary of Statistical Models in R 18 Organizing Your Work 19 Housekeeping within R 20 References 22 Further Reading 22 Chapter 2 Dataframes 23 Selecting Parts of a Dataframe: Subscripts 26 Sorting 27 Summarizing the Content of Dataframes 29 Summarizing by Explanatory Variables 30 First Things First: Get to Know Your Data 31 Relationships 34 Looking for Interactions between Continuous Variables 36 Graphics to Help with Multiple Regression 39 Interactions Involving Categorical Variables 39 Further Reading 41 Chapter 3 Central Tendency 42 Further Reading 49 Chapter 4 Variance 50 Degrees of Freedom 53 Variance 53 Variance: A Worked Example 55 Variance and Sample Size 58 Using Variance 59 A Measure of Unreliability 60 Confidence Intervals 61 Bootstrap 62 Non-constant Variance: Heteroscedasticity 65 Further Reading 65 Chapter 5 Single Samples 66 Data Summary in the One-Sample Case 66 The Normal Distribution 70 Calculations Using z of the Normal Distribution 76 Plots for Testing Normality of Single Samples 79 Inference in the One-Sample Case 81 Bootstrap in Hypothesis Testing with Single Samples 81 Students t Distribution 82 Higher-Order Moments of a Distribution 83 Skew 84 Kurtosis 86 Reference 87 Further Reading 87 Chapter 6 Two Samples 88 Comparing Two Variances 88 Comparing Two Means 90 Students t Test 91 Wilcoxon Rank-Sum Test 95 Tests on Paired Samples 97 The Binomial Test 98 Binomial Tests to Compare Two Proportions 100 Chi-Squared Contingency Tables 100 Fishers Exact Test 105 Correlation and Covariance 108 Correlation and the Variance of Differences between Variables 110 Scale-Dependent Correlations 112 Reference 113 Further Reading 113 Chapter 7 Regression 114 Linear Regression 116 Linear Regression in R 117 Calculations Involved in Linear Regression 122 Partitioning Sums of Squares in Regression: SSY = SSR + SSE 125 Measuring the Degree of Fit, r 2 133 Model Checking 134 Transformation 135 Polynomial Regression 140 Non-Linear Regression 142 Generalized Additive Models 146 Influence 148 Further Reading 149 Chapter 8 Analysis of Variance 150 One-Way ANOVA 150 Shortcut Formulas 157 Effect Sizes 159 Plots for Interpreting One-Way ANOVA 162 Factorial Experiments 168 Pseudoreplication: Nested Designs and Split Plots 173 Split-Plot Experiments 174 Random Effects and Nested Designs 176 Fixed or Random Effects? 177 Removing the Pseudoreplication 178 Analysis of Longitudinal Data 178 Derived Variable Analysis 179 Dealing with Pseudoreplication 179 Variance Components Analysis (VCA) 183 References 184 Further Reading 184 Chapter 9 Analysis of Covariance 185 Further Reading 192 Chapter 10 Multiple Regression 193 The Steps Involved in Model Simplification 195 Caveats 196 Order of Deletion 196 Carrying Out a Multiple Regression 197 A Trickier Example 203 Further Reading 211 Chapter 11 Contrasts 212 Contrast Coefficients 213 An Example of Contrasts in R 214 A Priori Contrasts 215 Treatment Contrasts 216 Model Simplification by Stepwise Deletion 218 Contrast Sums of Squares by Hand 222 The Three Kinds of Contrasts Compared 224 Reference 225 Further Reading 225 C