47
More Accurate Guidelines
In
general, the t test and the Wilcoxon are not testing the same summary
measure
•Wilcoxon test statistic based on
Pr(X > Y)
•Null distribution is a
permutation test
–Wrong size as a test
of Pr(X > Y) = ½
•(unless a
semi-parametric model holds on some scale)
•(this can be fixed by
modifying the null variance)
–Inconsistent test of F(t)
= G(t)
•An infinite sample
size may not detect the alternative
•(And the Wilcoxon is
not transitive)