Frank E Harrell Jr wrote:
> > > Alex Yu wrote:
> > > >
> > > > Disadvantages of non-parametric tests:
> > > >
> > > > Losing precision: Edgington (1995) asserted that when more precise
> > > > measurements are available, it is unwise to degrade the precision by
> > > > transforming the measurements into ranked data.
> Edgington's comment is off the mark in most cases.  The efficiency of the
> Wilcoxon-Mann-Whitney test is 3/pi (0.96) with respect to the t-test
> IF THE DATA ARE NORMAL.  If they are non-normal, the relative
> efficiency of the Wilcoxon test can be arbitrarily better than the t-test.
> Likewise, Spearman's correlation test is quite efficient (I think the
> efficiency is 9/pi^2) relative to the Pearson r test if the data are
> bivariate normal.
> Where you lose efficiency with nonparametric methods is with estimation
> of absolute quantities, not with comparing groups or testing correlations.
> The sample median has efficiency of only 2/pi against the sample mean
> if the data are from a normal distribution.

Yes, the median is inefficient at the normal. This is the
location estimator corresponding to the sign test in the one-sample
case. But if you use the location estimator corresponding to the 
signed-rank test (say) instead, the efficiency improves substantially.


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