randomization, etc.

[Dave Krantz]

Jerry Dallal suggests that failure to sample randomly from well-defined
populations can be dealt with, in some cases by use of randomization
tests. I am not convinced by the argument that he quotes from his
paper. He needs to spell out in more detail rationale for choosing a
particular rejection region for the randomization test.

At any rate, the example Dallal cites, comparing retinyl ester
concentrations in normal versus HLP subjects, is amusing. But I would
not have analyzed such data in any of the ways he illustrates. Rather,
my thought would be that products of chemical reactions are often
determined roughly by equilibrium equations that tend to be
multiplicative, so that a log-additive model might be in order. And
though the separation between the two groups is relatively small
compared to the large standard deviation of the normal group, on an
arithmetic scale, (leading to a t statistic of only about 2.2) the
separation between the two groups is ENORMOUS on a logarithmic scale,
compared to the standard deviations. Admittedly, the two observations
of 0.0 in the HLP group are inconvenient for logarithms. Something
more might be done with them--presumably the values could not really
have been 0, but must have been so close to 0 that the difference could
not be measured accurately. With some knowledge of the resolution of
the measurement procedure near 0, one could substitute a reasonable
upper bound for those two values. But even if those two values are
just dropped temporarily, the resulting t statistic for the logarithmic
scale is over 8.0; and so I find the evidence for difference in
location (with standard deviation perhaps proportional to location)
overwhelmingly strong.

Dave Krantz (d...@stat.columbia.edu)