# Effect size for interaction effect in pre-post treatment-control design

If you choose to analyse a pre-post treatment-control design with a continuous dependent variable using a mixed ANOVA, there are various ways of quantifying the effect of being in the treatment group. The interaction effect is one main option.

In general, I particularly like Cohen's d type measures (i.e., ${\frac{\mu_1 - \mu_2}{\sigma}}$). I don't like variance explained measures because results vary based on irrelevant factors such as relative sample sizes of groups.

Thus, I was thinking I could quantify the effect as follows

• $\Delta\mu_c = \mu_{c2} - \mu_{c1}$
• $\Delta\mu_t = \mu_{t2} - \mu_{t1}$
• Thus, the effect size could be defined as $\frac{\Delta\mu_t - \Delta\mu_c}{\sigma}$

where $c$ refers to control, $t$ to treatment, and 1 and 2 to pre and post respectively. $\sigma$ could be the pooled standard deviation at time 1.

Questions:

• Is it appropriate to label this effect size measure d?
• Does this approach seem reasonable?
• What is standard practice for effect size measures for such designs?

• Thanks. the Scott B. Morris' article is just what I was looking for. And yes, I agree that I should provide an explanation of the calculation (perhaps I call it something like $\hat{d}$). – Jeromy Anglim Nov 26 '10 at 3:01