Interpreting size of the mean difference in multipleGroup

[dirkp...@gmail.com]

Hi Phil,

I have a pretty straightforward question; when I find a mean difference in a multiple group analysis, how do I interpret this difference, in terms of the effect size?

Since it is compared with the reference group, for which the mean and variances are fixed, can I just interpreted it like a Cohen's d value?

Best, 

Dirk

[Phil Chalmers]

Hi Dirk,

I assume you mean the mean difference in the latent trait distributions? These distribution parameters do have a Cohen's d type feel to them, but they aren't exactly the same as the variances are not pooled. If you really  wanted to obtain a Cohen's d representation of this difference you could compute it manually. Assume that the variances were 1 and 1.5, and the means were 0 and -0.3 for the reference and focal group, respectively. Further, assume that the control group had 1000 observations while the reference group had only 500

ns <- c(1000, 500)
ps <- prop.table(ns)
vars <- c(1, 1.5)
means <- c(0, - 0.3)

# pooled variance
sp <- sum(ps * vars)
md <- diff(means)

d <- md / sp
d

# -0.2571429

So the focal group would be about -0.25 standard deviations less than the reference group according to this standardized metric. HTH.

Phil

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