How to understand the great difference value of Gamma in PROC FREQ?

[Jack2012]

Dear ALl,

I have question regard to the difference of Gamma in Figure 1 and Figure 2. How to interpret them  and what is the difference?

The other question is why Figure 1 code produce the Odds ratio and Relative risk estimates but not the Figure 2 code?

Thanks

/*Figure 1*/
proc freq data=dar_grp5;
   tables Treatment*SWAEVL2C/measures alpha=0.1 CL;
run;
/*Figure 2*/
proc freq data=compare;
   tables SWAEVL2C_gra*SWAEVL2C_syr/measures alpha=0.1 CL;/*SWAEVL2C_gra is the results for granules and SWAEVL2C_Syr is for Syrup*/
run;

[Rick_SAS · Accepted solution]

The formulas for these statistics are shown in the "Measures of Association" section of the PROC FREQ doc.

For the first TABLES statement:

C = number concordant = 10;

D = number discordant = 10;

Therefore Gamma = (C-D)/(C+D) = 0.

For the second TABLES statement:

C = 10;

D = 0;

Gamma = (C-D)/(C+D) = 1.

The odds ratio formula is also in the doc.

OR = n11 * n22 / (n12 * n21)

In the second run, the off diagonal counts are zero. therefore the odds ratio is undefined.

The RR computation is similar, and also undefined in the second situation.

[Doc_Duke]

In addition to Rick's comments, the Gamma, OR, and RR, and confidence limits are all based on asymptotic theory, so they should not be used with sample sizes this small.  PROC FREQ has a number of EXACT tests that are more appropriate.

[Jack2012]

Thanks for your comment. I fully agree.