topic Re: Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations in Statistical Procedures

Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations

PGStats — Thu, 28 May 2015 16:21:25 GMT

Hello,

The CMH statistic calculated on RIDIT scores (proc FREQ) takes the value (n-1)*Rs**2 where Rs is the Spearman rank correlation. This is of interest with multi-level tables, because it is the only way in SAS to get a stratum-adjusted Spearman correlation. How can I get the sign of Rs?

Re: Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations

Rick_SAS — Thu, 28 May 2015 18:54:33 GMT

You can get Spearmen coefficients from PROC CORR with the SPEARMAN option. For example, the Spearman coefficient for the following data is 0.36332 and n=21. The CMH statistic is (21-1)*(0.36332)**2 = 2.6400

data test;
call streaminit(1);
do i = 1 to 21;
   x = rand("table", 0.5, 0.3, 0.2);
   y = rand("table", 0.5-x/10, 0.3, 0.2+x/10);
   output;
end;
run;

proc corr data=test spearman noprob;
var x y;
run;

proc freq data=test;
tables x*y / scores=ridit cmh norow nopercent nocol;
run;

Re: Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations

PGStats — Thu, 28 May 2015 20:29:38 GMT

Thanks. But my question is about stratum-adjusted correlations. As with TABLES A*x*y / ...

Re: Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations

ballardw — Thu, 28 May 2015 20:57:28 GMT

Proc corr;

by A;

I would think would do it.

Re: Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations

PGStats — Thu, 28 May 2015 21:19:30 GMT

In proc freq, strata play a distinct role from BY analysis. A stratum-adjusted correlation is not the same as correlations by stratum. The former is a single coefficient of within strata relationship, the later are multiple coefficients, one for each stratum. - PG

Re: Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations

gergely_batho — Fri, 29 May 2015 23:26:52 GMT

What about dummy coding the strata variable, then using proc corr and putting all the dummy variables in the partial statement? (I haven't checked the validity of this approach.)

Re: Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations

SteveDenham — Mon, 01 Jun 2015 13:25:12 GMT

Hmm, that sounds logical to me--partialling out the strata effect ought to at least get the sign correct.

Steve Denham

Re: Proc FREQ : How to get the sign of stratum-adjusted Spearman correlations

PGStats — Thu, 04 Jun 2015 21:51:01 GMT

Back at this, at last. The partial correlation sounded indeed like an intuitively appealing idea, thanks . So I ran a simulation. Correlated random pairs were generated with proc simnormal. Data was divided into 5 groups with means 1, 2, 3, 5, 7 and Std devs 1, 2, 3, 5, 7, each group represented by 100 pairs. The exercise was repeated for correlations of 0.5 and -0.1. Partial and stratum-adjusted correlation estimates were compared for 1000 sets of 500 observations. Stratum-adjusted estimates were given the sign of the corresponding partial correlation as suggested by . Here are the results:

It is obvious to me that the two estimates are somewhat related and sligntly biassed toward zero, but certainly not equivalent. In the small negative correlation simulation, about 1% of the stratum-adjusted correlations were given the wrong sign.