1. Can effect size be negative? In my analysis, some z score values are negative. If I compute only r, effect size could be negative. In such case how to interpret negative effect size. I am confused whether I need to compute r or r square to report effect size.
2. Is it necessary to compute effect size for Mann Whitney result that is insignificant?
It is more usual to report r than r2 (see e.g. http://yatani.jp/teaching/doku.php?id=hcistats:mannwhitney)
Theoretically the effect coefficients can be negative (except if you are calculating R2), however in your case this depends on which group do you consider as first, and which as second. Therefore, to interpret the effect size you should use the absolute value.
As far as insignificant results are concerned, you should report the effect sizes, this is especially important if you have small sample size because significance is dependent on the sample size. Even if you do have large sample, the effect size provides a basis for power analysis for future studies and it provides the data for meta-analyses.
I hope this helps
There is no reason that prevent effect size to be negative.
There is no relationship between computing effect size and the test being significant or not. You need them, you compute them. The test will say if they are significantly different from 0 (typically), which is another question. And probably in that case, confidence intervals on the "effect size" will give more informative answers.
Thanks Miroslav and Emmanuel for your useful posts. Some online calculators are also reporting only absolute value of r. Will you please help me out on how to report and interpret effect sizes for insignificant Mann Whitney result? If possible, please provide me an illustration.
I don't think effect size reporting depends on the fact that test result is significant or not. So use exactly the same reporting scheme. Same thing for the interpretation.
By the way, if you already give test's p-value and sample sizes, then r is easy to compute, hence adds very few information. For a MW test, « median difference » (and its confidence interval) should be both more informative and much easier to interpret, since it is directly in the scale of the original data — technically, "hodge-lehman's estimator of the shift parameter ".
It's a good suggestion. Now, I'll look into the aspect of hodge-lehman's estimator of the shift parameter. Thank you.
Here is an APA guideline for reporting Mann-Whitney test in your results section and information on effect sizes. http://evc-cit.info/psych018/Reporting_Statistics.pdf
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