Preface

Part I The Methods

1 What can the reader expect from this book?

1.1 A calibration scale for evidence

1.2 The efficacy of glass ionomer versus resin sealants for prevention of caries

1.3 Measures of effect size for two populations

1.4 Summary

2 Independent measurements with known precision

2.1 Evidence for one-sided alternatives

2.2 Evidence for two-sided alternatives

2.3 Examples

3 Independent measurements with unknown precision

3.1 Effects and standardized effects

3.2 Paired comparisons

3.3 Examples

4 Comparing treatment to control

4.1 Equal unknown precision

4.2 Differing unknown precision

4.3 Examples

5 Comparing K treatments

5.1 Methodology

5.2 Examples

6 Evaluating risks

6.1 Methodology

6.2 Examples

7 Comparing risks

7.1 Methodology

7.2 Examples

8 Evaluating Poisson rates

8.1 Methodology

8.2 Example

9 Comparing Poisson rates

9.1 Methodology

9.2 Example

10 Goodness-of-fit testing

10.1 Methodology

10.2 Example

11 Evidence for heterogeneity of effects and transformed effects

11.1 Methodology

11.2 Examples

12 Combining evidence: fixed standardized effects model

12.1 Methodology

12.2 Examples

13 Combining evidence: random standardized effects mode

13.1 Methodology

13.2 Example

14 Meta-regression

14.1 Methodology

14.2 Commonly encountered situations

14.3 Examples

15 Accounting for publication bias

15.1 The downside of publishing

15.2 Examples

Part II The Theory

16 Calibrating evidence in a test

16.1 Evidence for one-sided alternatives

16.2 Random p-value behavior

16.3 Publication bias

16.4 Comparison with a Bayesian calibration

16.5 Summary

17 The basics of variance stabilizing transformations

17.1 Standardizing the sample mean

17.2 Variance stabilizing transformations

17.3 Poisson model example

17.4 Two-sided evidence from one-sided evidence

17.5 Summary

18 One-sample binomial tests

18.1 Variance stabilizing the risk estimator

18.2 Confidence intervals for p

18.3 Relative risk and odds ratio

18.4 Confidence intervals for small risks p

18.5 Summary

19 Two-sample binomial tests

19.1 Evidence for a positive effect

19.2 Confidence intervals for effect sizes

19.3 Estimating the risk difference

19.4 Relative risk and odds ratio

19.5 Recurrent urinary tract infections

19.6 Summary

20 Defining evidence in t-statistics

20.1 Example

20.2 Evidence in the Student t-statistic

20.3 The Key Inferential Function for Student’s model

20.4 Corrected evidence

20.5 A confidence interval for the standardized effect

20.6 Comparing evidence in t- and z-tests

20.7 Summary

21 Two-sample comparisons

21.1 Drop in systolic blood pressure

21.2 Defining the standardized effect

21.3 Evidence in the Welch statistic

21.4 Confidence intervals for d

21.5 Summary

22 Evidence in the chi-squared statistic

22.1 The noncentral chi-squared distribution

22.2 A vst for the noncentral chi-squared statistic

22.3 Simulation studies

22.4 Choosing the sample size

22.5 Evidence for l *>* l0

22.6 Summary

23 Evidence in F-tests

23.1 Variance stabilizing transformations for the noncentral F

23.2 The evidence distribution

23.3 The Key Inferential Function

23.4 The random effects model

23.5 Summary

24 Evidence in Cochran’s Q for heterogeneity of effects

24.1 Cochran’s Q: the fixed effects model

24.2 Simulation studies

24.3 Cochran’s Q: the random effects model

24.4 Summary

25 Combining evidence from K studies

25.1 Background and preliminary steps

25.2 Fixed standardized effects

25.3 Random transformed effects

25.4 Example: drop in systolic blood pressure

25.5 Summary

26 Correcting for publication bias

26.1 Publication bias

26.2 The truncated normal distribution

26.3 Bias correction based on censoring

26.4 Summary

27 Large-sample properties of variance stabilizing transformations

27.1 Existence of the variance stabilizing transformation

27.2 Tests and effect sizes

27.3 Power and efficiency

27.4 Summary

References

Index