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Chapter 1 Models, tests and data 1 1.1 Basics 1 1.2 Models 2 1.3 Types of data 3 1.4 Significance tests 5 1.5 Confidence intervals 6 1.6 Statistical tests using models 7 1.7 Model fitting and analysis: exploratory and confirmatory analyses 7 1.8 Computer-intensive methods 8 1.9 Bayesian methods 8 1.10 Reporting statistical results in the literature 9 1.11 Reading statistics in the literature 10 Multiple choice questions 10 Chapter 2 Multiple linear regression 12 2.1 The model 12 2.2 Uses of multiple regression 13 2.3 Two independent variables 14 2.4 Interpreting a computer output 19 2.5 Multiple regression in action 25 2.6 Assumptions underlying the models 26 2.7 Model sensitivity 28

2.8 Stepwise regression 31 2.9 Reporting the results of a multiple regression 32 2.10 Reading the results of a multiple regression 32 Frequently asked questions 33 Multiple choice questions 35 Chapter 3 Logistic regression 37 3.1 The model 37 3.2 Uses of logistic regression 40 3.3 Interpreting a computer output: grouped analysis 40 3.4 Logistic regression in action 44 3.5 Model checking 45 3.6 Interpreting a computer output: ungrouped analysis 47 3.7 Case–control studies 49 3.8 Interpreting a computer output: unmatched case–control study 50 3.9 Matched case–control studies 51 3.10 Interpreting a computer output: matched case–control study 52 3.11 Conditional logistic regression in action 55 3.12 Reporting the results of logistic regression 55 3.13 Reading about logistic regression 56 Frequently asked questions 56 Multiple choice questions 57 Chapter 4 Survival analysis 59 4.1 Introduction 59 4.2 The model 60 4.3 Uses of Cox regression 62 4.4 Interpreting a computer output 62 4.5 Survival analysis in action 65

4.6 Interpretation of the model 65 4.7 Generalisations of the model 66 4.8 Model checking 67 4.9 Reporting the results of a survival analysis 69 4.10 Reading about the results of a survival analysis 70 Frequently asked question 70 Exercise 70 Chapter 5 Random effects models 74 5.1 Introduction 74 5.2 Models for random effects 75 5.3 Random vs fixed effects 76 5.4 Use of random effects models 77 5.5 Random effects models in action 78 5.6 Ordinary least squares at the group level 79 5.7 Computer analysis 80 5.8 Model checking 84 5.9 Reporting the results of a random effects analysis 85 5.10 Reading about the results of a random effects analysis 85 Frequently asked question 86 Chapter 6 Other models 88 6.1 Poisson regression 88 6.2 Ordinal regression 92 6.3 Time-series regression 97 6.4 Reporting Poisson, ordinal or time-series regression in the literature 100 6.5 Reading about the results of Poisson, ordinal or time-series regression in the literature 101 CONTENTS vii Appendix 1 Exponentials and logarithms 103 Appendix 2 Maximum likelihood and significance tests 105 Appendix 3 Bootstrapping 115 Appendix 4 Bayesian Methods 121 Answers to exercises 125 Index 127

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