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Combining Effect Sizes. What to Combine? How to do it?. What to Combine? (1). Whether effect sizes can/should be combined is controversial Safe if studies are replications (identical IV, DV, design, only difference is observations)

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combining effect sizes

Combining Effect Sizes

What to Combine?

How to do it?

what to combine 1
What to Combine? (1)
  • Whether effect sizes can/should be combined is controversial
  • Safe if studies are replications
    • (identical IV, DV, design, only difference is observations)
    • Random samples from same population – results in a sampling distribution
what to combine 2
What to Combine (2)
  • Not safe or reasonable to combine if
    • IV or DV measures different constructs across studies (e.g., DV in study 1 is taxes paid, and DV in study 2 is subjective well being)
    • Different study designs ( study 1 has random assignment to condition; study 2 allows participants to choose conditions)
what to combine 3
What to Combine (3)
  • OK to combine if
    • Measures are same across studies (e.g., all studies use GRE) (can use unstandardized ES in analysis)
    • Measures across all studies are parallel (can use unstandardized ES)
    • Measures are essentially tau equivalent (same reliability, different mean and SD); use Standardized ES
    • Measures are congeneric (diff reliability, different M and SD) use Standardized ES, may adjust model for reliability.
what to combine 4
What to Combine (4)
  • Most social science studies are hard to justify as proper for a meta-analysis
  • Glass (any and all therapy, any and all outcomes)
  • Gaugler (assessment centers)
  • When is a study a replication?
  • Compare to medicine (e.g., aspirin and heart attack)
how to combine 1
How to Combine (1)
  • Take the simple mean (add all ES, divide by number of ES)


M = 1.8/3


Unbiased, consistent, but not efficient estimator.

how to combine 2
How to Combine (2)
  • Take a weighted average




(cf .6 w/ unit wt)

(Unit weights are special case where w=1.)

how to combine 3
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
      • 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)
how to combine 4
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.