Bayesian Mann-Whitney U Test Showing Means of Groups in Table and Median Difference in Plots

Comments

• andersony3k

  October 19 edited October 19

  I believe that the Mann-Whitney U test tells us, given a randomly sampled Value A (from Population A), and a randomly sampled Value B (from Population B), what's the probability that Value A is greater than Value B. So it's neither about means nor medians.

  https://pmc.ncbi.nlm.nih.gov/articles/PMC1120984/

  This 'probability of superiority' isn't usually included in the generated output, but the 'rank biserial correlation' effect size is -- and apparently, one can compute the probability of superiority from the rank biserial correlation:

  https://en.wikipedia.org/wiki/Probability_of_superiority

  R
• drravikch

  October 19

  Thank you for the educative input.

  So, can one report mean and standard deviation of the two groups instead of medians and IQR of the two groups, with the results of Mann-Whitney U test, in a paper for a publication?
• andersony3k

  October 19

  I think you can report any or all of those descriptive statistics, despite their disconnect from the Mann-Whitney U. Some people may not like it, though, because they think the Mann-Whitney U is about medians. Whatever you do, you should include an effect size for the Mann-Whitney U result (the rank biserial correlation and/or the probability of superiority).

  R
• drravikch

  October 19

  Thank you for the clarification.
• andersony3k

  October 20

  No problem. Also, I find the following example to be a helpful illustration that the Mann-Whitney U test isn't a test of difference between medians. The two groups have the same median (100), but the Mann-Whitney U test shows that the ranks (of all of the values together) tend to be significantly higher for one group than for the other. (My understanding is that the test functions as a test of medians only of the two groups happen to have identical pre-rank distributional shapes.)

  

  
  

  R
• drravikch

  October 22

  Thank you for demonstrating the concept of Mann-Whitney U test by an example.

  Using JASP can one know the distribution patterns of the two groups and get the relevant inferences?

  Will JASP facilitate the right way of identification of the distributions of data and select appropriate statistical test for a researcher without statistical background?
• EJ

  October 22

  This is currently a task that the researcher must do. The general rule is that when these tests give you very different outcomes, (a) you are in trouble; (b) you are probably better off with the Mann-Whitney

  EJ
• drravikch

  October 22

  Thank you.
• Dmartin427

  November 4

  drravikch,

  You can use the JASP Distribution module to check the fit of a given variable to all kinds of distributions. However, the utility of this may depend heavily on your familiarity with the topic of distributions. In any regard, unless JASP suddenly starts integrating the Gamlss package for distribution fitting (which would bring tears to my eyes), it is a process you will have to do manually.

  If you are deeply concerned about distribution and it's impact on your analysis, however, and you aren't familiar enough with statistics to dive into something like Generalized Linear Modeling, then may I recommend bootstrapping your Independent Samples T-Test's Confidence Intervals as a nice place to start?
• EJ

  November 4

  Dmartin427: maybe a good feature request?

  EJ
• drravikch

  November 4

  Thanks for the new points.

  For a researcher like a Clinician doctor with the following limitations:

  1. Who does not know anything about statistical distributions and how to check the fit of distribution of a variable, in order to select an appropriate statistical analysis, is it adequate if one knows about: the data type of a variable and the relevant statistical test to be used for the data type (eg: for comparing means of two groups the test is independent samples t-test with certain assumptions; for testing the difference or association between proportions of two groups, Fischer Exact test etc.). Is there such a path for Bayesian analysis?
  2. What is the best way of undertaking Bayesian statistical analysis using JASP with the goal of avoiding inappropriate use of Bayesiaan statistical analysis and interpretation?
  3. As suggested as an option, how to do bootstrapping Independent Samples T-Test's Confidence Intervals in JASP? is there some help module for that in JASP?

  Thank you all for trying to guide a novice to Bayesian path.