On 13 Feb 2000 05:37:36 -0800, [EMAIL PROTECTED]
(Graham D Smith) wrote:
> Surely for a given dataset there is an optimal transformation of the form
> f(x) = (x + a)^b for reducing heterogeneity of variance (or skew or both),
> where a is an offset equal to the minimum score. Does anyone know how the
> optimal value of b can be found? This transformation would encompass the
> reciprocal, square root and square transformations. Perhaps a more general
> form could incorporate the log transformation. Should the degrees of freedom
> be reduced when using such a method? If such a method exists why do people
> use the "suck it and see" approach?
>
- There is a response to a related question, in sci.stat.consult as
of Feb. 12, see
Dolby, J.L. 1963. "A quick method for choosing a transformation,"
TECHNOMETRICS 5, 317-325 describes a method for selecting a
transformation from the family of curves:
y = a + b(c + x)^p
Why do you say you want to reduce something? - and What? - and Which
of the 5 varieties of skewness? and How is it that you dare to, when
it distorts the original metric?
How do you justify an add-on? There are (often) simple arguments that
the power transformation (no add-on) might be *appropriate* to revise
the metric, to improve the sensibility of the prediction or fitting.
That will hardly ever extend to using an add-on to x, in the data I
have considered.
You have to be talking about *testing* rather than *model-building*
since the add-on destroys the last variety of linearity. IF there
were a manner known to us of doing what you propose -- an automatic
transformation, that provided a robust variety of testing -- I
imagine we would be doing it.
I think the problem comes down to this: in a small sample (or one
with an extreme outlier), such a strategy fails because it
over-capitalizes on chance. (Dealing with an outlier is not a trivial
matter.) In a large, healthy sample, the ANOVA is robust, or a
simpler, intentional transformation can be defended. Also, the Ideal
transformation may fall outside of that family.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
===========================================================================
This list is open to everyone. Occasionally, people lacking respect
for other members of the list send messages that are inappropriate
or unrelated to the list's discussion topics. Please just delete the
offensive email.
For information concerning the list, please see the following web page:
http://jse.stat.ncsu.edu/
===========================================================================
