st: Quintiles (?) distribution parameters with binary independent

["John Doe" <heteroskedastic@hotmail.com>]

Hello All,

I am looking for some guidance with how to think about a quintile/binary 
problem.

I have a binary variable (More, Less) which determines the distribution of 
an outcome variables (Window). The binary variable is actually continuous, 
but has been forced into a More/Less format by another researcher, and for 
good reason. The distribution of Window is important as there is a 
therapeutic Window within which it is effective, or not. From Window, I can 
estimate risks of various things. The best way to do this is by defining 
percentages in each range (again done by another researcher):

                     More1 (%)    Less1  (%)
Very Supra |        4.1                 4.1
Supra        |      13.8                17.6
Thera        |      56.7                46.2
Sub          |      16.4                8.6
Very Sub   |       9.0                13.5

As can be seen from this, More is associated with a higher percentage of 
"Thera" cases, and less "Sub". It also seems that Less is associated with 
more skew/kurtosis. Inuitively, it would make sense if More reduced the sd, 
moved the mean closer to Thera, and reduced S/K.

Is there any more valid way to go about analyzing this? What was listed 
above is my "data" currently, but I should be able to get the originals 
later. My basic problem is that the parameters of the distribution (mean, 
sd, S/K) are all outcomes of the binary, and I am a little weirded out by 
estimating three outcomes from this data.

Any thoughts would be much appreciated.

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