# Mann-Whitney test

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:

1. Ordinal data DV: although the data are normally distributed and most variances are similar, ordinal means that only a M-W can be done.
2. 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)?
• Welcome to the site, @Hannah. I took the liberty of editing your question to try to make it clearer. Please make sure it still says what you want it to. Apr 12, 2014 at 15:38
• I think we will need more information. Do you have measures at baseline (before implants)? What do you mean that the ordinal data are normally distributed? What do you mean that "most of the data are normally distributed"? Can you post a sample of your data, or a plot of them? Apr 12, 2014 at 15:39
• Hello Jung and Gaetan, Thank-you very much for your replies. I have measured scores for speech and language using two scales known as CAP and SIR, which are rating scales from 1-7 and 1-5. These have been measured pre-implant and post implant at 12 and 24 months for both measures (CAP & SIR). I have also measured the change in scores for both CAP and SIR from pre-implant to post implant at 12 months, and then post implant at 12 months compared to 24 months. In addition, hearing was tested before implant and at 12 and 24 months post implant. Apr 12, 2014 at 16:04
• I used Shapiro-Wilks to test normality by group, 1, 2 and 3- (IV) groups are based on their inner ear abnormality. This showed normal distribution for most of the variables, most results were > 0.05 (DV/dependant measures). I also ran Levine's test to check for homogeneity of variance and again for most of the variables, the result was > 0.05 showing variances were similar. However for hearing thresholds only 1 variable out of 3 had homogeneity of variance. Apr 12, 2014 at 16:05
• As Gaetan agreed and confirmed the Mann-Whitney seems appropriate for the CAP/SIR outcomes as these are ordinal. However hearing thresholds are scale continuous scale (dB HL), they are normally distributed but homogeneity of variance is violated in 2/3 variables (DV's) measured. Therefore I wondered if again Mann-Witney would help address this issue? I wonder if a t-test could be used with a cautionary approach that not all assumptions are met. Apr 12, 2014 at 16:06