Example: the Wilcoxon rank sum test
Common teaching:
·Not too
bad against normal data
·Better
than t test when data have heavy tails
More accurate guidelines:
·Above
holds when a shift model holds for some monotonic transformation
of the data
·If
propensity to outliers (mixture distributions) is different between
groups, the t test may be better even in presence of heavy
tails
·In the
general case, the t test and the Wilcoxon are not testing the
same summary measure