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Example: Wilcoxon Rank Sum Test
More accurate
guidelines:
–In the general case,
the t test and the Wilcoxon are not testing the same summary
measure
•Wrong size as a test
of Pr(X > Y) unless you assume a semi-parametric model on
some scale
•Inconsistent test of F(t)
= G(t)
•(And the Wilcoxon is
not transitive)
–Efficiency results
when a shift model holds for some monotonic transformation of the
data
•If propensity to
outliers is different between groups, the t test may be better even with
heavy tails
–(The variance can be
modified to achieve consistency)