Newsgroups: bit.listserv.stat-l
Date:         Mon, 6 Apr 1992 21:17:00 EST
From:         "Philip Gallagher,(919)966-7275" <UPHILG@UNC.BITNET>
Subject:      When are transformations reasonable/respectable?

April Milliken-Janne <BIOM030@UNLVM> asks an interesting question,
namely,
> So, now to my question, since the world is not in log units, why would I ever
> be able to argue the use of a transformation?  My conclusions will be based o
> original data...shouldn't my analysis also be?  Other disciplines say "You ca
> prove ANYTHING with statistics"...by transforming our data to make it fit eve
> BETTER, aren't we guilty as charged?

    April, here is an outsider's firmly held feeling on the matter
    (although it will probably be different tomorrow!).  Statisticians
    often introduce transformations to satisfy reasonably objective
    mathematical criteria, such as the distributions of residuals, etc.
    No one I both know and respect introduces transformations simply
    in order to get better p-values - rather the transformations
    are selected in order to create variables which better satisfy
    the (objective) requirements of the statistical procedure(s)
    being used.  As a one-time bench scientist, I prefer to use
    these transformations only when I can find a theoretical reason
    why the process under study should follow the distribution that
    the transformation implies, say, exponential.  I cringe when
    I feel forced to introduce a transformation for which I cannot
    postulate a thoroughly reasonable physical mechanism.

    Understand, now, I can't summon a really good criticism of
    an analyst who transforms variables solely to meet distribu-
    tional requirements, and I certainly can't put up with either
    the idea of using statistical procedures without meeting the
    distributional requirements or transforming data just to get better
    p-values.  At the same time, I can't be happy with transformations
    that aren't in any way theoretically justifiable (on
    non-statistical grounds).  But, please remember that many
    times mathematical transformations that are mystifying to
    mathematically unsophisticated folks are in fact
    reasonable.  I have in mind a close personal friend who
    thought that introducing a term of time-squared was unreasonable
    because "... there is no such thing as time-squared in real life."
    Eventually I was able to make him understand nonlinear
    processes, but that particular transformation certainly didn't
    seem reasonable to my friend at first (he hadn't spent a
    bunch of years as a mathematically devious physicist!).
    So, some transformations may require a whole lot of
    sophisticated thinking before one can justify them, but,
    hopefully, the justifications will be supported by good
    scientific thinking rather than sophistry.

                                         Phil Gallagher


    On re-reading this I'm not sure I made the point that
    really worries me.  Here it is:  I often feel that some
    really good statisticians are seduced into making transformations
    based totally on (valid!) statistical grounds without
    adequately considering the implications that those
    transformations have for the theory of the discipline from
    which the data arise.
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