Date:         Fri, 17 Apr 1998 16:50:53 GMT
Reply-To:     Richard F Ulrich <wpilib+@PITT.EDU>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         Richard F Ulrich <wpilib+@PITT.EDU>
Organization: University of Pittsburgh
Subject:      Re: L shaped distributions

      michelei@msn.com   : ms5079@cnsibm.albany.edu
Michele Scherneck (michelei@EMAIL.MSN.COM) wrote:
: We're trying to look at relationships among variables that have L-shaped
: distributions (severely positively skewed and kurtotic). Does anyone
: know of transformations that would be appropriate, or statistical tests
: that would be most appropriate in dealing with these types of variables?
: The shape appears not to be an aberration; in other words, this seems to
: be the natural shape of the type of variables we're dealing with.
 
: Suggestions or references would be much appreciated. Many thanks.
 
 
Tests appropriate  with  "these type of variables"?
 
All you have given is the gross shape of the distributions.
 
If it is appropriate to do a power transformation because of the
way the numbers arise (among other things, here, the
larger scores must have the larger errors)  then you would consider
powers less than 1.0 :  1/2 (square root); "0" (log);  -1 (reciprocal);
etc.
 
If you are interested in the actual Sums or Means, then doing
any  transformation is not reasonable, and you are stuck with
adjusting the tests you use, to emphasize robustness at the
expense of power.  (Reduced D.F.  or use of randomization or
bootstrap.)
 
Mosteller & Tukey is one text with a bit of discussion on when
to "re-express"  measures. I think my stat FAQ has other references
(get there from my home page).
 
--
Rich Ulrich, biostatistician                wpilib+@pitt.edu
http://www.pitt.edu/~wpilib/index.html   Univ. of Pittsburgh