| Preface |
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v | |
| About the authors |
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vi | |
| Acknowledgements |
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vii | |
| Introduction: Why should you read this book? |
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1 | (4) |
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Part 1 Why you should want to do power analysis |
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1 | (1) |
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Part 2 Why you should want to do power analyses our way |
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2 | (1) |
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Why have we based the book on R and how much R will we assume you know? |
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3 | (1) |
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3 | (1) |
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3 | (2) |
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1 What is statistical power? |
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5 | (18) |
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1.1 An important preliminary: sampling and statistical testing |
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6 | (2) |
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1.2 Null hypothesis statistical testing |
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8 | (9) |
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1.3 Type I and Type II errors |
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17 | (3) |
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1.4 How do we define statistical power? |
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20 | (3) |
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2 Why low power is undesirable |
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23 | (16) |
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2.1 With a low-powered study you risk missing interesting effects that are really there |
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24 | (1) |
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2.2 You cannot read much into lack of statistical significance in a low-powered study |
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25 | (1) |
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2.3 You cannot read much into statistical significance in a low-powered study |
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25 | (5) |
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2.4 Your estimation of the size of an apparent effect can be unreliable in low-powered studies |
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30 | (5) |
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2.5 Should you ever knowingly carry out a low-powered study? |
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35 | (4) |
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3 Improving the power of an experiment |
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39 | (20) |
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3.1 The challenge posed by inherent variation |
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40 | (2) |
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3.2 Are you measuring the right variables? |
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42 | (2) |
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3.3 Can you measure variables more precisely? |
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44 | (1) |
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3.4 Repeated measurement and subsampling to reduce inherent variation |
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45 | (1) |
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3.5 Can you select experimental material so as to reduce inherent variation? |
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46 | (1) |
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3.6 Can you strengthen the effect that you are interested in? |
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47 | (4) |
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3.7 Can you change the design of your experiment to boost power? |
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51 | (1) |
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3.8 Would you be willing to accept a higher rate of Type I error? |
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52 | (1) |
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3.9 Can you increase sample size? |
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53 | (1) |
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3.10 Practical and ethical reasons why you should not always seek to further increase power |
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54 | (1) |
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3.11 Case study: thinking a bit more about how much power is enough |
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55 | (4) |
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4 How to quantify power by simulation |
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59 | (30) |
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4.1 What you need to know to estimate power, and ways to produce plausible estimates of these |
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60 | (3) |
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4.2 The concept of estimating power by repeated evaluation of synthetic data |
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63 | (4) |
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4.3 The nuts and bolts of generating synthetic data and estimating power in a single one-factor design |
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67 | (7) |
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4.4 Using simulation to compare alternative ways of doing the same experiment |
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74 | (1) |
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4.5 Selecting between different alternative experiments to decide which experiment you are actually going to do, and reporting its power |
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75 | (2) |
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4.6 Case study: presenting and interpreting your power analysis |
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77 | (12) |
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5 Simple factorial designs |
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89 | (850) |
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5.1 Introducing our focal example |
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80 | (1) |
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5.2 Think about your data frame as a way to envisage your experiment |
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80 | (2) |
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5.3 Generating a simulated data set for our focal experiment |
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82 | (8) |
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5.4 Comparing different designs |
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90 | (4) |
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5.5 Drop-outs: using power analysis to explore the possible impact of adverse events |
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94 | (3) |
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5.6 Factors with more than two levels |
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97 | (2) |
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6 Extensions to other designs |
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99 | (1) |
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6.1 A simple linear regression |
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100 | (1) |
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6.2 Beyond the straight and narrow |
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106 | (4) |
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6.3 When we don't control the values of our predictors |
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110 | (2) |
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6.4 When things are not normal |
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112 | (3) |
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115 | (4) |
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7 Dealing with multiple hypotheses |
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119 | (12) |
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7.1 Several research questions in a single study |
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120 | (1) |
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7.2 Designs that implicitly test multiple hypotheses |
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120 | (5) |
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125 | (6) |
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8 Applying our simulation approach beyond null hypothesis testing: parameter estimation, Bayesian, and model-selection contexts |
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131 | (14) |
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8.1 Likelihood of obtaining a specified precision of parameter estimation |
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132 | (7) |
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8.2 Translating the concept of power across to Bayesian analysis |
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139 | (2) |
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8.3 Using simulations to help with model-selection approaches |
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141 | (1) |
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8.4 Exploiting your freedom in how you define study effectiveness |
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142 | (3) |
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Appendix: Some handy hints on simulating data in R |
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145 | (8) |
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145 | (1) |
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145 | (1) |
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146 | (1) |
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Drawing samples of categorical data |
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146 | (1) |
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Permutations and indexing |
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147 | (1) |
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148 | (1) |
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Generating samples of continuous variables |
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149 | (1) |
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Generating correlated data |
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150 | (3) |
| Glossary |
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153 | (4) |
| Index |
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157 | |
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