An effect size measure that has really, or should have, replaced Cohen’s d as it corrects for the fact that Cohen’s d for any sample overestimates the population effect size particularly with small n. It is “Hedges’s” with two “s”s as the name of the man who first described and explained it was “Hedges” not “Hedge”!
Details #
I’ve spent a silly amount of time getting my head around Hedges’s g in the last few weeks including understanding how it is computed and simulating the impacts of various things on its value. That’s all in my Rblog post about it but the summary points are:
- g was developed in relation to the comparison of the means of two independent samples but, as a correction to d it can be applied just as well the values of d from repeated measures change effect sizes (of which there are two, but that’s another story!)
- there is an accurate method to compute g for the equal sized sample, equal variance (homoscedastic), Gaussian distribution scenario but it’s computationally expensive so it’s usually computed using a very accurate approximation not using that method
- there was a typo in Hedges’s original paper when he presented the approximation! (see the Rblog post if you care what it is!)
- though it’s true that d does overestimate the population value the overestimation becomes tiny even with sample sizes we see in our field, e.g. over 100 and, given all the other issues we have about non-random samples, insisting on g is a bit of a fetish, shibboleth or virtue signalling!
- compounding that, like d, g, is affected by unequal sample sizes, heteroscedasticity and non-Gaussian distributions, markedly so with heavy kurtosis and opposite skew in the two populations for which the effect size is sought: all common situations in our field …
- that makes is almost certainly better to estimate g and its confidence interval by bootstrapping (though you probably need each dataset to have more than 30 observations for that to be robust) … but I confess I am going on one paper that looked at this, I haven’t explored it myself.
Try also #
Chapters #
We didn’t put it in the book but Chapter 8 and service comparisons would probably be where you might encounter effect sizes.
Online resources #
My Rblog post about Hedges’s g and Cohen’s d
My shiny app that will give you the correct value of g given values of d and n
Dates #
First created 21.i.24, updated 27.viii.25 to reflect work I’ve done exploring the index: see the Rblog post.
