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.

# Results

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 *j*^{th} treatment, is
the row total for the *i*^{th} 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 *X ^{2}*, and rejected if

*Q*>

*X*.

^{2}If p-level is less than (default value – 0.05) then the H_{0} (the treatments
are equally effective) is rejected and it is concluded that the
significant difference among treatments exists.

# Assumptions

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").

# References

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