Statistics in Crosstabulations - McNemar Chi-square

This test is applicable in situations where the frequencies in the 2x2 table represent dependent samples. For example, in a before-after design study, we may count the number of students who fail a test of minimal math skills at the beginning of the semester and at the end of the semester. Two chi-square values are reported: A/D and B/C. The chi-square A/D tests the hypothesis that the frequencies in cells A and D (upper left, lower right) are identical. The chi-square B/C tests the hypothesis that the frequencies in cells B and C (upper right, lower left) are identical.

As suggested by Siegel and Castellan (1988), a continuity correction is used to remove the imprecision of approximating a discrete distribution by a continuous distribution. For the A/D hypothesis, the chi-square statistic is computed as:

The B/C hypothesis is computed in the same manner with the B and C replacing A and D in the above formula.