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Re: st: ttest and log transformation

From   Nick Cox <[email protected]>
To   [email protected]
Subject   Re: st: ttest and log transformation
Date   Mon, 29 Sep 2008 15:07:00 -0500


The arsinh (preferably not arcsinh for reasons discussed in SJ 8(3) 2008) is qualitatively similar to the neglog. As earlier flagged, see -transint- from SSC for more discussion and references.

Verkuilen, Jay wrote:

Nick already mentioned doing something like a qq- or pp-plot, both of
which may provide much more direct analysis of your problem.

With positive definite distributions, logging often helps but the
lognormal is at the edge of stability for moments to exist. (The log-t,
of which the lognormal is a boundary case, has no moments at all).
Chances are good you really want to compare the medians of your
distributions, not the means.
For parametric models, I highly suggest using one of the survival
analysis programs, e.g., -streg- for parametric or -stcox- for
non-parametric. You'll have to make a fake "censoring" indicator
variable that simply shows none of your values are censored.
Negative values are trouble. For that case, an alternative to the log
that works for negative values is the arcsinh, which turns the problem
into an estimation for the massively underutilized Johnson SU
distribution (the lognormal is Johnson SL, the normal is the SI and the
logistic normal is the SB).
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