I am carrying out a study in which I have $3$ groups $n= 2$, $n= 5$, $n=17$. Each group has a different inner ear abnormality, following the fitting of an ear implant I have measured their speech (ordinal data) and hearing scores (continuous data) at 1 and 2 years.
The group with only $2$ patients in must be excluded from stats I believe. For the two remaining groups, most of the data are normally distributed and most variances are similar for speech (ordinal data), but not for the hearing scores (continuous data).
I wonder if a Mann-Whitney $U$-test should be used for the following reasons:
- Ordinal data DV: although the data are normally distributed and most variances are similar, ordinal means that only a M-W can be done.
- Scale Data DV: the data are only normally distributed with homogeneity of variance in 2/3 of the measures, therefore again M-W? Or should a $t$-test be used (but doesn't a $t$-test assume homogeneity of variance)?