Using means on ordinal data is a long running debate, but IMO it makes no mathematical sense. Because there is no spacing information, only order, you cannot assume the variance is finite on an ordinal measure, and you cannot assume that the spacing is “on average” equal via the CLT either.
Some links to older discussions I know of:
After much personal study, I ended up asking myself that very question, and coming to the conclusion that nonparametrics are to be preferred, if you don’t want to go the Bayesian route.
There have been Monte Carlo studies going back to the 60’s documenting the sometimes large power advantages of rank tests to parametric counterparts in all cases except for a small (5%) loss of efficiency under strict normality, and about a 14% loss with tails thinner than a normal distribution.
Shlomo Sawilow…
Would this be the appropriate thread to add references on the issues related to using parametric assumptions on ordinal data? This has always bothered my mathematical conscience.
Prof. Harrell had posted a great link to a recent paper in another thread:
A draft copy an be found here (I assume it is OK to post a link to the draft):
Analyzing Ordinal Data with Metric Models: What Could Possibly Go Wrong?
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2692323
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