I'd like to compare people's perception of safety at a certain location [which is a categorical variable on a scale of 1-10, with 1=feel very unsafe & 10=feel very safe] before and after being aware of some initiatives. Would a paired-sample t-test be appropriate or do I need to use non-parametric tests (e.g. Wilcoxon-Mann-Whitney test)?
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If your data are ordinal ratings, then they cannot be normally distributed. The Mann-Whitney (WMW) test is more appropriate. If you have a true likert scale (that is, many likert items that measure the same thing and which are summed or averaged to give a single number for each person), and if the scores do not lie up against the limits of the scale, then the $t$-test may be used, but the WMW is likely to have greater power.
answered Dec 5, 2014 at 17:14