orthogonal coding with unequal n

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orthogonal coding with unequal n

Larry Lutsky
I know that contrast coding on nominal variables in regression involves
creating orthogonal codes so that the dummy variables are uncorrelated.
So for a variable with 3 categories one could use the following dummy
codes:

 

                        Dummy1           dummy2

Group1                   1                       1    

Group2                   0                      -2

Group3                  -1                       1

 

The first dummy variable tests for a linear effect and the second for a
quadratic effect.  The problem is I know this only works with equal n's
in each group.  When there are unequal n's, one must weight them by the
n size.  I'm not sure if I should just multiple each code by the sample
size or is there some other way to do it.  Thanks for any help you can
give me.

 

Larry Lutsky

Research Analyst

Metropolitan College of New York

75 Varick Street

New York, NY 10013

(212) 343-1234 Ext. 2445

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