I just thought of a new justification doing the usual parametric analyses
on the numbered levels of a Likert-scale variable. Numbering the levels
is formally the same as ranking them, and a parametric analysis of a
rank-transformed variable is a non-parametric analysis. If non-parametric
analyses are OK, then so are parametric analyses of Likert-scale variables.
But... an important condition is that the sampling distribution of your
outcome statistic must be normal. This topic came up on this list a few
weeks ago. In summary, if the majority of your responses are stacked up on
one or other extreme value of the Likert scale for one or more groups in
the analysis, and if you have less than 10 observations in one or more of
those groups, your confidence intervals or p values are untrustworthy. See
http://newstats.org/modelsdetail.html#normal for more.
Will
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