Statistical significance btw two medians

Question

We are preparing statistical analysis of cross-sectional study; and have the following question:

We want to check whether difference btw two age medians grouped by categorical variable (died vs alive) is statistically significant. We used Mann-Whitney U test. Did we choose the right test?

At least partial duplicates include https://stats.stackexchange.com/questions/470012/mann-whitney-test-clearing-up-confusion and https://stats.stackexchange.com/questions/136636/reporting-results-of-mann-whitney-u-test-means-vs-medians (and several others besides) — Glen_b, Jul 10 '22 at 23:28

score 4 · Accepted Answer · answered Jul 09 '22 at 05:58

4

No, the Mann-Whitney is not a test for differences in median. It's possible for two samples to have exactly the same median and for the Mann-Whitney test to be significant.

It's quite common, however, to report medians together with a Mann-Whitney test if you have to report a test. That's basically ok as long as you don't claim it's a test for difference in medians.

There is a test for medians, sometimes called "Mood's test", but it's not used very much. More usefully, you could get a bootstrap confidence interval for the difference or ratio of the medians

answered Jul 09 '22 at 05:58

Thomas Lumley

38,062

Thanks for your rapid answer – Abo7aneen Jul 09 '22 at 06:05
So, for means (t-test) for medians (Mood's test), Am I right? – Abo7aneen Jul 09 '22 at 06:05
Yes, basically. – Thomas Lumley Jul 09 '22 at 06:54
Thanks sir fir your help – Abo7aneen Jul 09 '22 at 06:56
Mood's test is considered to be obsolete by many because of its poor efficiency (power). Efficient tests for differences in medians come from model-based estimates, e.g. (1) if you have a log-normal distribution the efficient estimate of the median is the antilog of the mean of the logs, or (2) using a semiparametric model to estimate differences in medians. – Frank Harrell Jul 09 '22 at 11:52
Agree with you, Mood's test is not efficient – Abo7aneen Jul 09 '22 at 23:22

Statistical significance btw two medians

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