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Combining Effect Sizes

Combining Effect Sizes. Taking the Average. 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. How to Combine (2).

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Combining Effect Sizes

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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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