Cochran's Q test

Cochran's Q test is used to compare several paired samples of binary data. Run it in Excel using the XLSTAT add-on statistical software.

What is Cochran’s Q test

The Cochran’s Q test is presented as a particular case of the Friedman’s test (comparison a k paired samples) when the variable is binary.

As a consequence, the null H0 and alternative Ha hypotheses for the Cochran’s Q test are:

  • H0: the k treatments are not significantly different.
  • Ha: the k treatments are significantly different.

Asymptotic p-value computation is available. Furthermore, XLSTAT recently developed an algorithm that allows to fastly compute exact or Monte-Carlo approximated p-values.

Input data for the Cochran’s Q test

Two possible formats are available for the input data:

  • You can select data in a "raw" format. In this case, each column corresponds to a treatment and each row to a subject (or individual, or bloc).
  • You can also select the data in a "grouped" format. Here, each column corresponds to a treatment, and each row corresponds to a unique combine of the k treatments. You then need to select the frequencies corresponding to each combine.

Multiple pairwise comparison tests are available to compare the treatments if the null hypothesis is rejected, so that the treatments that are responsible for a difference can be identified.