For Mann Whitney U results I have computed the pearson's r (cohen) as an effect size as advised by (Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). " Effect size estimates: Current use, calculations, and interpretation"
Since the sampling distribution of Pearson's r is not normally distributed, Pearson's r is converted to Fisher's z' and the confidence interval is computed using Fisher's z'.
as shown here: http://davidmlane.com/hyperstat/B27932.html
However, for my first result examining group differences on social cognition
Group 1 (Mdn=12; IQR=3.5) & Group 2 (Mdn=12, 1QR=0).
The mann whitney result was U=75, P=0.017, r=0.28 (medium effect size).
When I use the Fishers z conversion method I get r 95% confidence intervals of lower limit -0.082 to upper limit 0.203.
1. As I understand it if your confidence interval crosses 0 your p value should be not significant?
2. Does anyone know what I am doing wrong here or why an incongruent result like this may arise?
3. Is there any other options that would give similar info to confidence intervals for cohens r that are more straightforward to calculate?
( I am only trained in SPSS)
Thanks very much in advance for any help,
Best wishes,
Iona
I am not sure that I totally have your problem, but is it the case that you have a significant p from MW, but the CI (calculated correctly with Fisher z transformation and back transformation) for the PPM r contains zero, and that is the problem? If so, these are two different tests with different distributions, and indeed are not even testing precisely the same hypothesis, so would not necessarily render the same inferential result.
Hello Iona,
1. SPSS computes p-value for the Mann-Whitney U via the "large-sample" (z) approximation, so the result you get might not match with the exact p-value.
2. As well, the estimate of the effect size, r (via z / sqrt(N)) is also an approximation, not an exact value.
So, the two results, statistical significance vs. CI for effect size, might not agree with one another.
You didn't indicate your sample size (or whether the data set had any tied rank cases), so it's not possible to derive exact values.
Good luck with your work.
It's not possible to get negative limits for r² from Fisher's approach. So I assume the CI limits (-0.082, 0.203) refer to z. But the z-transform of r²=0.28 is 0.288. This value is not in the CI ! So there is something wrong. It would have been possible to check if you had given the sample size (and more clearly described how you calculated the CI) ...
Apart from that - after Cohen, r² < 0.3 is considered a weak effect, not a medium effect. But ist's anyway more than questionable if these criteria have any relevance.
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