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Hedges ’ Approach

Hedges ’ Approach. Two main camps in MA. Schmidt & Hunter Hedges et al. Hedges & Olkin Hedges & Vevea Differ in Weights and Data Transformation Others – HLM, Rosenthal, Bayesian, not as common. Weights Defined. SH use N, NA 2 for weights Hedges uses inverse variance weights.

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Hedges ’ Approach

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  1. Hedges’ Approach

  2. Two main camps in MA • Schmidt & Hunter • Hedges et al. • Hedges & Olkin • Hedges & Vevea • Differ in Weights and Data Transformation • Others – HLM, Rosenthal, Bayesian, not as common

  3. Weights Defined • SH use N, NA2 for weights • Hedges uses inverse variance weights. • Sampling variances and inverses: To analyze correlations, Hedges will use z and (N-3).

  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. Method due to DerSimonian & Laird. This method works well, even though the estimator gives an approximation. In metafor, this estimator is applied if method= “DL”. Iterative numerical analysis is needed for an exact solution. In metafor, this estimator is the default, method=“REML”, for restricted maximum likelihood.

  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: *we will go into this in greater detail next week. Try to accept this for now and to understand it next week.

  10. Numerical Illustration (1)

  11. Numerical Illustration (2)

  12. Numerical Illustration (3) Fixed-effects mean and CI: But, generally best to use RE, even if Q is n.s.

  13. Numerical Illustration (4) Not prediction interval.

  14. Numerical Illustration (5) Comparison of Results (not a prediction interval)

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