Since this type of data is ordinal and not continuous

I agree, but I'll just pedantically note that it's also possible for a variable to be continuous

*and* ordinal (e.g., a visual analogue scale). Whether a variable is ordinal vs interval vs ratio is a measurement theory issue; whether it's continuous or discrete is more of a distributional issue. You may need to clarify what you're most worried about here:

1) Are you concerned that the

*distributional*/statistical assumptions of the t-test won't be satisfied? (i.e. because Likert data will by definition result in non-normal errors). If so, a large-ish sample deals with this (how large I don't know - simulations do sound good. It will depend on the number of items for the DV, the number of response options for each item, and the observed distribution of responses).

2) Are you concerned with the old

*measurement* argument that parametric tests are only admissible with interval or ratio data, but not ordinal data? (I.e. the

S.S. Stevens argument). This is a measurement theory issue, not a statistical or distributional one, and sample size isn't really relevant to this at all. (Note: Most people ignore this argument nowadays, but the fact that you mention ordinality makes me bring it up)

it would seem to lend itself to using a Mann-Whitney U-test to compare the medians.

The Mann-Whitney U can only be interpreted as testing a null hypothesis of equal medians under

quite restrictive conditions (i.e. identical distributions in each group bar a possible location shift). The more general null hypothesis it tests is "that P ( X < Y )= 0.5, where X and Y are random samples from the two populations at interest" (Fagerland 2009, see linked paper).