Is 'r' an effect size for the size of the difference in a repeated measures t-test?
I've gotten into a debate about whether r is an effect size for the difference between two within-subjects means. I'm certain it isn't, but the person I'm discussing this with (perfectly pleasantly, I might add), is adamant that it is. They've provided three 'supporting' citations, but to me none of them actually are supporting.
My opinion is that r is an effect size, but of the correlation between the two variables, rather than the size of the difference between the two variables. Thus r could be 1.0, but the size of the difference could be zero.
The correlation coefficient r is directly related to the coefficient of determination r2. r2 is used to determine if a distribution shows a correlation. Perhaps a statistics person could address more efficiently.
@Andrew This link could possibly be helpful to you cause.
https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/td
Several formulas have been given for converting t statistic into an effect size. A formula for converting t statistic into correlation has also been given.
"Is 'r' an effect size for the size of the difference in a repeated measures t-test?"
No. Although r may be considerd an effect size measure, it is not about the mean difference. It's easy to see if you take a variable with a unit. Let's take the blood pressure of subjects being treated with betablockers. The pressure is measured in mmHg before and after the treatment. The unit of the mean difference is "mmHg", a difference in pressure. The correlation coefficient r, in contrast, is unitless.
The value of r tells us how useful the paired design is to estimate the mean difference. If the values where not correlated (low r), one might get more information from independent measurements using twices the sample size, in which case one would possibly not need an extra control group (the paired analysis needs a control group in any case because the first measurement as well as anything that can happen between the two measurements may impact the second measurement [e.g. the patient is less nervous because she then knows the procedure already and has lower blood pressure just because of this]).
Thanks all for your replies. I began doubting myself as the other person seems fixed on the idea r is an effect size For differences.
regards, Andrew
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