🚀 go-pugleaf

Please assist me with the following problem (I will summarize solutions to the
list):

I would like to use the output from SAS's PROC FREQ to test for
non-linear associations in a r by c contingency table. I want to
take the difference between the chi square tests for general association
and for correlation, and use that as a chi square test for non-linear
associations.  Is this proper?  Does anyone have a reference?

Details (12 lines of text follow)
------------------------------------------------------------------------------
Factor R is ordinal with r levels.
Factor C is ordinal with c levels.

 2
X (Assoc) = A test for association between R and C with (r-1)(c-1) df.
            (Pearson chi-square)
 2
X (Corr) =  A test for correlation between R and C with 1 df.
            (Mantel-Haezel correlation statistic)

    2         2           2
Is X (Fit) = X (Assoc) - X (Corr) = A test for lack of fit due to non-linear
                                    associations between R and C with
                                    (r-1)(c-1)-1 df?
                     2                                               2
If r=2 or c=2, then X (Corr) is the Cochran-Armitage Trend test and X (Fit)
is an appropriate test for lack of fit due to non-linear trends.  I would
like to know if the lack of fit test is generalizable to r x c tables.

--------------------------------------------------------------------------
Allan Rosen                              Internet: ALZADR@vms.cis.pitt.edu
Epidemiology Data Center                 Bitnet:   ALZADR@pittvax.bitnet
127 Parran Hall, 130 DeSoto Street       Fax:   (412) 624-3775
Pittsburgh, PA  15261                    Phone: (412) 624-0418
--------------------------------------------------------------------------