>Suppose I have two variables where one is a dichotomous outcome
>and the other is ordinal (mild, uncomfortable, annoying, &
>debilitating). My question is this: is it possible to change
>the "interval" between strata of the ordinal variable, that is,
>if the clinician can justify asserting that, for example,
>"annoying" is 'five times worse' than "mild" and "debilitating"
>is 'eight times worse' than "mild", is there a way to
>incorporate that assessment into a non-parametric test, e.g.
>Wilcoxon rank sum test? In short, I suppose I am addressing
>two issues: interval length of the ordinal variable and
>"importance" of the severe responses (annoying & debilitating)
>relative to mild. Would something like this even be acceptable
>statistically & justifiable mathematically (assuming it is
>clinically justifiable), not to mention, possible in STATA?
I take this to mean that 5 people each with a "mild" symptom are
as bad (for the purpose of the analysis as 1 person with an
"annoying" symptom.
Clint here crosses the boundary between ordinal & interval
scales (strictly he also needs a value "uncomfortable", say 3 * mild).
It is now appropriate to work out means, totals, even standard
deviations; everything being in units of "mild". To legitimately
carry out out a t-test or regression, he needs only to declare that
his sample is large enough for the Normal approximation to work
(n>50, say). Otherwise, he can use bootstrapping for his
confidence intervals & p-values.
