Cochran's Q Test

Cochran's Q test is used to verify if k treatments have the same effect between three or more related groups. In essence, the Cochran’s Q test is an extension of the McNemar test [SDN]. While the results of Cochran’s Q test are informative, one should also measure the degree of agreement among the tests.


How To

Run: Statistics→Nonparametric Statistics → Cochran’s Q Test.

Select variables with a two-way randomized block design (rows are subjects, columns are treatments).

Listwise deletion is used for missing values removal.



The report includes Cochran’s Q test results and the table with proportions statistics for each variable.

The Cochran's Q test statistic is defined as following:

where k is the number of treatments,  is the column total for the jth treatment,  is the row total for the ith block, b is the number of blocks, N is the total number of observations. The null hypothesis is accepted if Q is less than critical X2, and rejected if Q > X2.

If p-level is less than  (default value – 0.05) then the H0 (the treatments are equally effective) is rejected and it is concluded that the significant difference among treatments exists.




The Cochran’s Q test is based on the following assumptions:

a) The sample of n subjects has been randomly selected from the population it represents;

b) The scores of subjects are in the form of a  dichotomous categorical variable (i.e., a "0" or "1").



 [SDN] Sheksin, David (2000) Handbook of Parametric and Nonparametric Statistical Procedures. SECOND EDITION Chapman & Hall/CRC