Hello Martina,

I presume you're considering the outcome/dependent variable as having at least ordinal strength. Given that, you might consider using the aligned rank transform procedure for what appears to be a 2 (sex) by 2 (diagnosis) factorial design.

Here are two links you may find helpful for learning about this nonparametric option:

1. https://faculty.washington.edu/wobbrock/pubs/chi-11.06.pdf

2. https://rcompanion.org/handbook/F_16.html

As for your primary concern about using a chi-squared approximation after a Mann-Whitney U test (comparing two batches of scores), I'm not sure I understand whether you're considering the chi-squared as: (a) the mechanism for a p-value approximation (there is a well-known z-approximation to the estimation of p-values from the U test, and z-squared may be treated as a single df chi-squared statistic); or (b) as a replacement for the U test itself.

If it is p-values you seek, the ideal solution is an exact test (which can be computationally quite simple with small group n values); is this what you have?

As well, exact critical values for small n values are frequently given in introductory statistics and nonparametric statistics texts (though that's not the same as a p-value computation). With group n >= 20, the large-sample z-approximation works very well; regardless of n, many statistical packages report p-values for the U test based on the z-approximation.

Good luck with your work.

It sounds like you have an unpaired test. Something analogous to a factorial design. You might consider the Scheirer–Ray–Hare test, or as David Morse suggested, the aligned ranks anova. In R, the latter procedure has good options for post-hoc testing.