# Repeated Measures Design & Effect Sizes, Normality

##### New Member
My question is about calculating effect sizes for a repeated measures design with a small sample size. I want to calculate Cohen's d.av (as recommended by Lakens, 2013 and others) instead of d.z (which you can compute using just your t-value and N), since the latter tends to overestimate your effect size. The statistics that go into d.av include Mean 1, Mean 2, SD1, SD2, r12, and N. This is fine, except that some of my pre/post variables are not normally distributed, making me question the use of means as part of my calculations for that statistic. The difference scores, however, are normally distributed, meaning paired t-tests are a valid approach with the data. I could simple use d.z but from my reading is sounds like the less desirable and less commonly used ES for repeated measure designs. I hope I am explaining the question well enough, it's making my head spin a little!

Any help would be greatly appreciated!!

#### Karabiner

##### TS Contributor
My question is about calculating effect sizes for a repeated measures design with a small sample size.
You cannot calculate effect sizes from sample data,
just effect size measures. And the problem that sample
effect size measures deviate from the true effect size
(in the population) is even bigger in small samples (large
samlping error). So why do you want to calculate
effect size measures here?
some of my pre/post variables are not normally distributed, making me question the use of means as part of my calculations for that statistic.
Is normality required for using means? I guess not.
The difference scores, however, are normally distributed,
Is this based on a statistical test? With a small sample size, non-significant
results of normality tests are nearly meaningless due to small power.
I hope I am explaining the question well enough
Well, you did not explicitly ask one.

With kind regards

K.