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# Meta-Analytic Statistical Inferences for Continuous Measure Outcomes as a Function of Effect Size Metric and Other Assumptions [Internet].

### Editors

### Source

Rockville (MD): Agency for Healthcare Research and Quality (US); 2013 Apr. Report No.: 13-EHC075-EF.

AHRQ Methods for Effective Health Care.

### Excerpt

#### INTRODUCTION:

_{E}-M_{C}) rather than representing effects in the standardized mean difference (SMD). A fundamental difference between the two strategies is that the UMD incorporates the observed variance of the measures as a component of the analytical weights (viz., sampling error or inverse variance) in statistically modeling the results for each study. In contrast, the SMD incorporates the measure’s variance directly in the effect size itself (i.e., SMD=[M_{E}−M_{C}]/SD) and not directly in the analytical weights. The UMD approach has been conventional even though its bias and efficiency are unknown; these have also not been compared with the SMD. Also unresolved is which of many possible available equations best optimize statistical modeling for the SMD in use with repeated measures designs (one or two groups).

#### METHODS:

*k* = 10, 20, 50, and 100); (2) mean study sample sizes (5 values of *N* ranging from small to very large); (3) the ratio of the within-study observed measure variances for experimental and control groups and at pretest and post-test (ratios: 1:1, 2:1, and 4:1); (4) the post-test mean of each pseudo experimental group to achieve 3 parametric effect sizes (δ= 0.25, 0.50, and 0.80); (5) normal versus nonnormal distributions (4 levels); and (6) the between-studies variance (τ^{2}= 0, 0.04, 0.08, 0.16, and 0.32). For the second issue, (7) the correlation between the two conditions was manipulated (ρ_{pre-post} = 0, 0.25, 0.50, and 0.75).

#### RESULTS AND CONCLUSIONS:

### Sections

- Preface
- Acknowledgments
- Peer Reviewers
- Introduction
- Methods
- Results
- Discussion
- References
- Glossary of Terms
- Appendix A Bias and Efficiency Results for Standardized and Raw Mean Differences (Specific Aim 1)
- Appendix B Bias, Efficiency, and Theoretical Variance for All Effect Size Indexes and Their Variances (Specific Aim 2)

## PubMed Commons