I calculated 2 different effect size types for my analysis results, r and d. Of these, r gave mostly low effect sizes while d values gave high effect sizes. I hesitated to use d because I was working on ranking averages.
Analysis: Mann Whitney U
Distribution: Nonparametric
Number of groups: unequal
standard deviations of groups: not equal to each other
Thank you in advance
Cohen's d doesn't make much sense with the Mann-Whitney test.
For r, it depends what you mean by r. There's an effect size statistic, r, based on the z statistic from the Mann-Whitney test. This is common, and is a reasonable effect size statistic.
The effect size statistics for the Mann-Whitney test should simply reflect the probability of an observation in one group being larger than an observation in the other group. Effect size statistics that directly reflect this are Vargha and Delaney’s A, Cliff’s delta, and the Glass rank biserial coefficient.
The most appropriate effect size type for Mann-Whitney U analysis is commonly the odds ratio or the median difference.
These effect size measures are suitable for interpreting the results of a Mann-Whitney U analysis and can provide insights into the practical significance of the observed differences between groups. However, it's worth noting that effect size interpretation may vary depending on the context and specific research question being investigated.
Ma'Mon Abu Hammad , there is a form of odds ratio that can be used as an effect size statistic for a Mann-Whitney test, but you'd have to explain how that would work.
Ma'Mon Abu Hammad , can you say more why you think a median difference is appropriate. Here are some example data:
y
The most appropriate effect size measure for Mann-Whitney U analysis is the rank-biserial correlation coefficient (r). It provides an estimate of the strength and direction of the relationship between the independent groups and the outcome variable. The rank-biserial correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative relationship, 0 signifies no relationship, and 1 denotes a perfect positive relationship. It is calculated based on the U statistic from the Mann-Whitney U test and specific formulas depending on the test version and sample sizes. Other effect size measures like odds ratio or Cohen's d can also be utilized, but the rank-biserial correlation coefficient is commonly used and suitable for this type of analysis. For relevant insights, you could check out section 5.12 in the following book.
Berry, K. J., Johnston, J. E., & Mielke, P. W. (2018). The measurement of association: A permutation statistical approach. Springer. https://doi.org/10.1007/978-3-319-98926-6
Good luck,
The most appropriate effect size type for Mann-Whitney U analysis, also known as the Wilcoxon rank-sum test, is typically the probability of superiority (PS) or the probability of one randomly chosen observation from one group being greater than a randomly chosen observation from the other group.
The Mann-Whitney U test is a nonparametric test used to compare two independent groups' distributions and determine if they come from the same population or if one group tends to have higher or lower values than the other. It does not assume that the data follow a specific distribution.
While there are different effect size measures that can be used with the Mann-Whitney U test, such as the common language effect size (CLES) or the Mann-Whitney effect size (r), the probability of superiority (PS) is often considered the most appropriate for this test.
The probability of superiority (PS) is calculated as the proportion of pairs of observations where an observation from one group is greater than an observation from the other group. It provides a measure of the probability that a randomly selected observation from one group will have a higher value than a randomly selected observation from the other group.
The advantage of using the probability of superiority as the effect size measure is that it is intuitive and easy to interpret. It directly reflects the probability of one group being superior to the other. However, it's important to note that effect size interpretation can vary depending on the specific context and field of study.
When reporting the results of the Mann-Whitney U analysis, it is recommended to include the effect size measure, such as the probability of superiority, along with the statistical significance to provide a comprehensive understanding of the findings
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