When a binary response is measured several times or under different conditions, Cochran’s Q tests that the marginal probability of a positive response is unchanged across the times or conditions. When there are more than two response categories, you can use the CATMOD procedure to fit a repeatedmeasures model.
The data set Drugs
contains data for a study of three drugs to treat a chronic disease (Agresti, 2002). Fortysix subjects receive drugs A, B, and C. The response to each drug is either favorable ('F') or unfavorable ('U').
proc format; value $ResponseFmt 'F'='Favorable' 'U'='Unfavorable'; run;
data drugs; input Drug_A $ Drug_B $ Drug_C $ Count @@; datalines; F F F 6 U F F 2 F F U 16 U F U 4 F U F 2 U U F 6 F U U 4 U U U 6 ;
The following statements create oneway frequency tables of the responses to each drug. The AGREE option produces Cochran’s Q and other measures of agreement for the threeway table. These statements produce Output 40.10.1 through Output 40.10.5.
proc freq data=Drugs; tables Drug_A Drug_B Drug_C / nocum; tables Drug_A*Drug_B*Drug_C / agree noprint; format Drug_A Drug_B Drug_C $ResponseFmt.; weight Count; title 'Study of Three Drug Treatments for a Chronic Disease'; run;
The oneway frequency tables in Output 40.10.1 provide the marginal response for each drug. For drugs A and B, 61% of the subjects reported a favorable response while 35% of the subjects reported a favorable response to drug C. Output 40.10.2 and Output 40.10.3 display measures of agreement for the 'Favorable' and 'Unfavorable' levels of drug A, respectively. McNemar’s test shows a strong discordance between drugs B and C when the response to drug A is favorable.
Output 40.10.1: OneWay Frequency Tables
Study of Three Drug Treatments for a Chronic Disease 
Drug_A  Frequency  Percent 

Favorable  28  60.87 
Unfavorable  18  39.13 
Drug_B  Frequency  Percent 

Favorable  28  60.87 
Unfavorable  18  39.13 
Drug_C  Frequency  Percent 

Favorable  16  34.78 
Unfavorable  30  65.22 
Output 40.10.2: Measures of Agreement for Drug A Favorable
McNemar's Test  

Statistic (S)  10.8889 
DF  1 
Pr > S  0.0010 
Simple Kappa Coefficient  

Kappa  0.0328 
ASE  0.1167 
95% Lower Conf Limit  0.2615 
95% Upper Conf Limit  0.1960 
Output 40.10.3: Measures of Agreement for Drug A Unfavorable
McNemar's Test  

Statistic (S)  0.4000 
DF  1 
Pr > S  0.5271 
Simple Kappa Coefficient  

Kappa  0.1538 
ASE  0.2230 
95% Lower Conf Limit  0.5909 
95% Upper Conf Limit  0.2832 
Output 40.10.4 displays the overall kappa coefficient. The small negative value of kappa indicates no agreement between drug B response and drug C response.
Output 40.10.4: Overall Measures of Agreement
Overall Kappa Coefficient  

Kappa  0.0588 
ASE  0.1034 
95% Lower Conf Limit  0.2615 
95% Upper Conf Limit  0.1439 
Test for Equal Kappa Coefficients  

ChiSquare  0.2314 
DF  1 
Pr > ChiSq  0.6305 
Cochran’s Q is statistically significant (p=0.0145 in Output 40.10.5), which leads to rejection of the hypothesis that the probability of favorable response is the same for the three drugs.
Output 40.10.5: Cochran’s Q Test
Cochran's Q, for Drug_A by Drug_B by Drug_C 


Statistic (Q)  8.4706 
DF  2 
Pr > Q  0.0145 