McNemar introduced what is known today as a test for symmetry in a two by two contingency tables. The logic of the test is based on a sample of matched pairs with a dichotomous response. In our example, the sample consists of the scores before and after an education program and the responses before and after the program. Each pair of scores is from only one person. The pretest divides the group of responders according to their answers to a dichotomous question. The posttest divides the two groups into two groups of like labels. The result is a two by two table. We construct a test of homogeneity, where the proportion of initially partitioned subjects will be equally distributed over the same partition after the program is completed, conditioned on the initial distribution.
Drane, J. Wanzer and Thatcher, W. Gregory
"A Test-Retest Transition Matrix: A Modification of McNemar’s Test,"
Journal of Modern Applied Statistical Methods:
1, Article 21.
Available at: http://digitalcommons.wayne.edu/jmasm/vol3/iss1/21