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Exploring Hedges’ Approaches in Meta-Analysis: Weights, Data Transformation, and Comparisons

This text delves into the methodologies employed by Hedges and others in meta-analysis, focusing on the two primary camps in the field. It contrasts Hedges' use of inverse variance weights with other approaches, such as those by Schmidt & Hunter and Rosenthal. The significance of confidence intervals, homogeneity tests, and the estimation of random effects variance components (REVC) are illustrated numerically. The document helps clarify how different methods impact study weight and data transformation, supporting researchers in choosing appropriate analysis techniques.

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Exploring Hedges’ Approaches in Meta-Analysis: Weights, Data Transformation, and Comparisons

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Presentation Transcript

  1. Hedges’ Approach

  2. Two main camps in MA • Schmidt & Hunter • Hedges et al. • Rosenthal • Hedges & Olkin • DerSimonian & Laird • Hedges & Vevea • Differ in Weights and Data Transformation

  3. Weights Defined • SH use N, NA2 • Hedges uses inverse variance weights. • Sampling variances and inverses:

  4. InV Weights Pros & Cons

  5. Data Transformation r .10 .20 .30 .40 .50 .60 .70 .80 .90 z .10 .20 .31 .42 .55 .69 .87 1.10 1.47

  6. Confidence Interval Because w=N-3, this basically means that the confidence interval is the mean plus or minus 2 times the root of 1/(Total N).

  7. Homogeneity Test When the null (homogeneous rho) is true, Q is distributed as chi-square with (k-1) df, where k is the number of studies. This is a test of whether Random Effects Variance Component is zero.

  8. Estimating the REVC If REVC estimate is less than zero, set to zero. REVC is SH Var(rho), but in the metric of z, not r.

  9. Random-Effects Weights Inverse variance weights give weight to each study depending on the uncertainty for the true value of that study. For fixed-effects, there is only sampling error. For random-effects, there is also uncertainty about where in the distribution the study came from, so 2 sources of error. The InV weight is, therefore:

  10. Numerical Illustration (1)

  11. Numerical Illustration (2)

  12. Numerical Illustration (3) Fixed-effects mean and CI: Retranslate to r: Now pretend Q was significant, so REVC>0.

  13. Numerical Illustration (4)

  14. Numerical Illustration (5) Comparison of Results

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