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Re: st: van der Waerden transformation

From   Maarten Buis <>
Subject   Re: st: van der Waerden transformation
Date   Fri, 13 Apr 2012 09:33:05 +0200

On Thu, Apr 12, 2012 at 7:01 PM, Austin Nichols <> wrote:
> Maarten--
> how about test scores?

Why would you want to make up distances between ranks in test scores?
I can see why many of these do not have a natural unit, so some form
of standardization is called for, but that does not mean that they
should be forced into a normal/Gaussian distribution. If you find
considerable skewness in your raw scores, would the forced to be
normal variable really be a better represenation of what you found?

-- Maarten

> On Thu, Apr 12, 2012 at 12:42 PM, Maarten Buis <> wrote:
>> On Thu, Apr 12, 2012 at 6:11 PM, Scott Merryman wrote:
>>> Isn't the van der Waerden transformation just inverse_normal(rank/(N +1)) ?
>> That sounds like an awful idea. That way you are just "inventing"
>> distances between ranks that have nothing to do with what you
>> observed. If you (generally speaking, not Scott specifically) really
>> want to get rid of the skewness that badly, than just use the
>> percentile rank and be honest about the fact that you have thrown away
>> the information on the distances between the ranks rather than making
>> those distances up. In general, I would _not_ try to get rid of the
>> skewness, but rather use it. If it is a dependent variable that might
>> suggest a -glm- with maybe a log link function. If it is an
>> independent variable it might suggest a non-linear effect possibly to
>> be modeled with splines (see: -mkspline-).
>> I would be interested to hear if someone knows of an application where
>> this transformation would make some sense. I cannot imagine one, but
>> that may just be due to my lack of imagination.
>> -- Maarten
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Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen

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