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Effective Methods of Combining Effect Sizes: A Comprehensive Overview

Learn how to combine effect sizes using simple means, weighted averages, and different weight choices to achieve unbiased and efficient estimates. Understand the selection of unit weights, inverse variance method, and other specialized weights for accurate effect size estimation.

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Effective Methods of Combining Effect Sizes: A Comprehensive Overview

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  1. Combining Effect Sizes Taking the Average

  2. How to Combine (1) • Take the simple mean (add all ES, divide by number of ES) M=(1+.5+.3)/3 M = 1.8/3 M=.6 Unbiased, consistent, but not efficient estimator. But see Bonnet for an argument for using unit wts

  3. How to Combine (2) • Take a weighted average M=(1+1+.9)/(1+2+3) M=(2.9)/6 M=.48 (cf .6 w/ unit wt) (Unit weights are special case where w=1.)

  4. How to Combine (3) • Choice of Weights (all are consistent, will give good estimates as the number of studies and sample size of studies increases) • Unit • Unbiased, inefficient • Sample size • Unbiased (maybe), efficient relative to unit • Inverse variance – endorsed by PMA, IMA • Reciprocal of sampling variance • Biased (if parameter figures in sampling variance), most efficient • Other – special weights depend on model, e.g., adjust for reliability (Schmidt & Hunter)

  5. How to Combine (4) • Inverse Variance Weights are a function of the sample size, and sometimes also a parameter. • For the mean: • For r: • For r transformed to z: Note that for two of three of these, the parameter is not part of the weight. For r, however, larger observed values will get more weight. Mean can be biased.

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