T-Test or U-Test

Question

I have a number of items that are based on a Likert scale, with values ranging from 1 = not at all to 5 = very much so. I would like to compare answers to these questions between two groups. I would like to analyze each question separately. To my understanding, I need to use the Mann–Whitney U test, because I have ordinal data. Is that correct?

Answer 1

In short, yes. Though defaulting to a Mann–Whitney $U$ test is not a requirement. In general, you correctly note that you should treat Likert-type item responses as ordinal data (review this post for more information). Ordinal data often do not meet the assumptions of the standard $t$-test. The issue is the central tendency (i.e., mean) of your ordinal measure. We can't assume values center around a particular value, or even the item's midpoint. Likert-type measures discriminate based upon the item's ranking of values. Numerical quantities map to ordered responses; the "order" is often arbitrarily chosen by the designer of the survey instrument. For instance, values from 1–5 represent arbitrary codes (i.e., labels). A Mann-Whitney $U$ test, or any other "rank-based" test, does not depend on the numeric labels used to order the categories (review this post for more information). In fact, the test is invariant to the arbitrary labels assigned to the categories, so long as the ranking of responses is preserved.