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