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Meta Analysis: A Guide to Calibrating and Combining Statistical Evidence acts as a source of basic methods for scientists wanting to combine evidence from different experiments. The authors aim to promote a deeper understanding of the notion of statistical evidence. The book is comprised of two parts - The Handbook, and The Theory. The Handbook is a guide for combining and interpreting experimental evidence to solve standard statistical problems. This section allows someone with a rudimentary knowledge in general statistics to apply the methods. The Theory provides the motivation, theory and…mehr
Meta Analysis: A Guide to Calibrating and Combining Statistical Evidence acts as a source of basic methods for scientists wanting to combine evidence from different experiments. The authors aim to promote a deeper understanding of the notion of statistical evidence. The book is comprised of two parts - The Handbook, and The Theory. The Handbook is a guide for combining and interpreting experimental evidence to solve standard statistical problems. This section allows someone with a rudimentary knowledge in general statistics to apply the methods. The Theory provides the motivation, theory and results of simulation experiments to justify the methodology. This is a coherent introduction to the statistical concepts required to understand the authors' thesis that evidence in a test statistic can often be calibrated when transformed to the right scale.
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Autorenporträt
Dr. E. Kulinskaya - Director, Statistical Advisory Service, Imperial College, London. Professor S. Morgenthaler - Chair of Applied Statistics, Ecole Polytechnique Fédérale de Lausanne, Switzerland. Professor Morgenthaler was Assistant Professor at Yale University prior to moving to EPFL and has chaired various ISI committees. Professor R. G. Staudte - Department of Statistical Science, La Trobe University, Melbourne. During his career at La Trobe he has served as Head of the Department of Statistical Science for five years and Head of the School of Mathematical and Statistical Sciences for two years. He was an Associate Editor for the Journal of Statistical Planning & Inference for 4 years, and is a member of the American Statistical Association, the Sigma Xi Scientific Research Society and the Statistical Society of Australia.
Inhaltsangabe
1. What can the reader expect? 1.1 A calibration scale for evidence 1.2 Glass ionomer versus resin sealants 1.3 Measures of effect size for two studies 1.4 Summary I. THE METHODS 23
2. Measurements with known precision 2.1 Evidence for one-sided alternatives 2.2 Evidence for two-sided alternatives 2.3 Examples
3. 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 59 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
15. Accounting for publication bias 15.1 The downside of publishing 15.2 Examples 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. Variance stabilizing transformations 17.1 Standardizing the sample mean 17.2 Variance stabilizing transformations 17.3 Poisson model example 17.4 2-sided evidence from 1-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
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 ± 21.5 Summary
22. Evidence in the Â2-statistic 22.1 The non-central Â2 distribution 22.2 A vst for the non-central Â2 statistic 22.3 Simulation studies 22.4 Choosing the sample size 22.5 Evidence for > 0 22.6 Summary 22.7 Summary
23. Evidence in F-tests 23.1 vst 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 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 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. Publication Bias 26.1 Publication Bias 26.2 The Truncated Normal Distribution 26.3 Bias Correction Based on Censoring 26.4 Summary
27. Asymptotics 27.1 Existence of the variance stabilizing transformation 27.2 Tests and Effect sizes 27.3 Power and efficiency 27.4 Summary
1. What can the reader expect? 1.1 A calibration scale for evidence 1.2 Glass ionomer versus resin sealants 1.3 Measures of effect size for two studies 1.4 Summary I. THE METHODS 23
2. Measurements with known precision 2.1 Evidence for one-sided alternatives 2.2 Evidence for two-sided alternatives 2.3 Examples
3. 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 59 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
15. Accounting for publication bias 15.1 The downside of publishing 15.2 Examples 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. Variance stabilizing transformations 17.1 Standardizing the sample mean 17.2 Variance stabilizing transformations 17.3 Poisson model example 17.4 2-sided evidence from 1-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
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 ± 21.5 Summary
22. Evidence in the Â2-statistic 22.1 The non-central Â2 distribution 22.2 A vst for the non-central Â2 statistic 22.3 Simulation studies 22.4 Choosing the sample size 22.5 Evidence for > 0 22.6 Summary 22.7 Summary
23. Evidence in F-tests 23.1 vst 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 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 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. Publication Bias 26.1 Publication Bias 26.2 The Truncated Normal Distribution 26.3 Bias Correction Based on Censoring 26.4 Summary
27. Asymptotics 27.1 Existence of the variance stabilizing transformation 27.2 Tests and Effect sizes 27.3 Power and efficiency 27.4 Summary
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