1. Why Meta-Analysis? Mata Hari, not Meta-Analysis Slide 15.1 1. When Narrative Literature Reviewers Have Drawn Conflicting Conclusions 2.When There are Many Studies 3.When It Is Desired to Synthesize Study Results Across Different Samples and Materials.

2. Meta-Analysis Purposes Slide 15.2 1.Summarizing available data. 2.Explaining the variability among different studies.

3. Steps in Completing a Meta-Analysis Slide 15.3A Sampling Quantitative Studies

4. Steps in Completing a Meta-Analysis Code Essential Study Differences in Studies and Compute Effect Sizes from Studies Slide 15.3B Sampling Quantitative Studies

5. Steps in Completing a Meta-Analysis Code Essential Study Differences in Studies and Compute Effect Sizes from Studies If fail-safe number < 5N L + 10, collect additional studies Slide 15.3C Compute Fail-Safe Number Sampling Quantitative Studies

6. Steps in Completing a Meta-Analysis Code Essential Study Differences in Studies and Compute Effect Sizes from Studies If fail-safe number < 5N L + 10, collect additional studies Compute Mean Effect Size Slide 15.3D Compute Fail-Safe Number Sampling Quantitative Studies

7. Steps in Completing a Meta-Analysis Code Essential Study Differences in Studies and Compute Effect Sizes from Studies If fail-safe number < 5N L + 10, collect additional studies Compute Mean Effect Size Compute Diffuse Comparison Slide 15.3E Compute Fail-Safe Number Sampling Quantitative Studies

8. Steps in Completing a Meta-Analysis Code Essential Study Differences in Studies and Compute Effect Sizes from Studies If fail-safe number < 5N L + 10, collect additional studies Compute Mean Effect Size Compute Diffuse Comparison Slide 15.3F Compute (additional) Focused Comparisons Compute Fail-Safe Number Sampling Quantitative Studies If diffuse comparison statistically significant

9. Steps in Completing a Meta-Analysis Code Essential Study Differences in Studies and Compute Effect Sizes from Studies If fail-safe number < 5N L + 10, collect additional studies Compute Mean Effect Size Compute Diffuse Comparison If diffuse comparison statistically significant Conclude If diffuse comparison not statistically significant Slide 15.3 Compute (additional) Focused Comparisons Compute Fail-Safe Number Sampling Quantitative Studies

10. Criteria for Including Studies Make sure the studies meet the assumptions underlying the use of meta-analysis: –E–Empirical studies only –S–Studies must include clear information about: »f»final sample sizes »a»actual effect sizes—or there must be access to all the coefficients necessary to compute the effect sizes »r»reliability for measured variables. The number of studies drawn from a single article or research report should not be too great. Usually no more than two or three studies from the same research article or report. Studies should be excluded if they are radically different from others. Slide 15.4

11. Transforming a Fisher’s Z Back into a Correlations To transform a Z Fisher back to an untransformed correlation, the following formula is used: Slide 15.6A

12. The Diffuse Test Slide 15.7A is the is the Fisher Z for the effect from study j, is the mean Fisher Z score, and k is the number of effects analyzed. Applying the data from the study, the following computation is revealed:, where n is the number of events in study j,

13. Focused Comparison 1: The Number of Variables in the Study Slide 15.10A

14. Computing a “Fail-Safe” Number Slide 15.14A

15. Computing a “Fail-Safe” Number Slide 15.14B, where Z j is (Z rj * ) [the Fisher’s Z transformation of correlations (r) for each (j) study included in the meta-analysis multiplied by, where N j is the sample size of each (j) study];

16. Computing a “Fail-Safe” Number Slide 15.14C, where Z j is (Z rj * ) [the Fisher’s Z transformation of correlations (r) for each (j) study included in the meta-analysis multiplied by, where N j is the sample size of each (j) study]; is the square of the z value the corresponds to the one- tailed probability level of the significance tests. Since p is commonly.05, the one-tailed z score including all but the last 5% of the area under the standard normal curve is 1.645

17. Computing a “Fail-Safe” Number Slide 15.14, where Z j is (Z rj * ) [the Fisher’s Z transformation of correlations (r) for each (j) study included in the meta-analysis multiplied by, where N j is the sample size of each (j) study]; is the square of the z value the corresponds to the one- tailed probability level of the significance tests. Since p is commonly.05, the one-tailed z score including all but the last 5% of the area under the standard normal curve is 1.645 N L is the number of studies located for use in the meta- analysis.