Statistics How To

Hedges’ g: Definition, Formula

Effect Size > Hedges’ g

What is Hedges’ g?

Hedges’ g is a measure of effect size. Effect size tells you how much one group differs from another — usually a difference between an experimental group and control group.

Hedges’ g and Cohen’s d are extremely similar. Both have an upwards bias (an inflation) in results of up to about 4%. The two statistics are very similar except when sample sizes are below 20, when Hedges’ g outperforms Cohen’s d. Hedges’ g is therefore sometimes called the corrected effect size.

  • For very small sample sizes (<20) choose Hedges’ g over Cohen’s d.
  • For sample sizes >20, the results for both statistics are roughly equivalent.
  • If standard deviations are significantly different between groups, choose Glass’s delta instead. Glass’s delta uses only the control group’s standard deviation (SDC).

Formula

The Hedge’s g formula is:



Where:

The main difference between Hedge’s g and Cohen’s D is that Hedge’s g uses pooled weighted standard deviations (instead of pooled standard deviations).

A note on small sample sizes:
Hedges’ g (like Cohen’s d) is biased upwards for small samples (under 50). To correct for this, use the following formula:


Interpreting Results

A g of 1 indicates the two groups differ by 1 standard deviation, a g of 2 indicates they differ by 2 standard deviations, and so on. Standard deviations are equivalent to z-scores (1 standard deviation = 1 z-score).

Rule of Thumb Interpretation

Cohen’s d and Hedges’ g are interpreted in a similar way. Cohen suggested using the following rule of thumb for interpreting results:

  • Small effect (cannot be discerned by the naked eye) = 0.2
  • Medium Effect = 0.5
  • Large Effect (can be seen by the naked eye) = 0.8

Cohen did suggest caution when using this rule of thumb. The terms “small” and “large” effects can mean different things in different areas. For example, a “small” reduction in suicide rates is invaluable, where a “small” weight loss may be meaningless. Durlak (2009) suggests referring to prior studies to see of where your results fit into the bigger picture.

References:
Cohen, J. (1977). Statistical power analysis for the behavioral sciences. Routledge.
Durlak, J. (2009) How to Select, Calculate, and Interpret Effect Sizes. Journal of Pediatric Psychology. March: 34(9):917-28.
Ellis, P. (2010). The Essential Guide to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research Results. Available here.
Hedges, L. (1981). Distribution Theory for Glass’s Estimator of Effect Size and Related Estimators. Journal of Educational Statistics. Vol. 6, No. 2 (Summer, 1981), pp. 107-128. Entire PDF available for free from JSTOR.
Hedges L. V., Olkin I. (1985). Statistical methods for meta-analysis. San Diego, CA: Academic Press

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Hedges’ g: Definition, Formula was last modified: October 12th, 2017 by Andale

2 thoughts on “Hedges’ g: Definition, Formula

  1. Andale Post author

    Hi, Dirk,
    Thanks for your comments. I did a little further digging and re-read the original Hedge’s article on Jstor. The Stata blog post was interesting. It says “Hedges’s g incorporates an adjustment which removes the bias of Cohen’s d” but doesn’t actually state what that adjustment is. It looks to me that the major difference between the two is that Hedge’s g uses a pooled and weighted SD instead of a pooled SD (without weights). Would you agree?