McNemar Change Test

The McNemar change test is a statistical test that can be used for paired nominal data. It can test differences on a dichotomous-dependent variable between two related groups. For dichotomous dependent variables, some like to think of it as similar to a paired t test. Typically, the test is used when researchers want to look at changes in participants’ scores by comparing the proportion of people who changed in one direction (e.g., an increase in test scores) to the proportion changing in the opposite direction (e.g., a decrease in test scores). It is a distribution-free (nonparametric) test. It can be used for pretest and posttest designs, matched pairs, and case-control studies. This entry further describes the McNemar change test and considers assumptions, characteristics, and applications of the test, concluding with examples.

The McNemar change test was first published in 1947 in the journal Psychometrika by Quinn Michael McNemar. The McNemar test is applied to 2 × 2 contingency tables, with a dichotomous variable and matched pairs of subjects. The test then determines whether row and column marginal frequencies are equal. This can be referred to as marginal homogeneity. Table 1 provides an example of such a 2 × 2 contingency table.

The null hypothesis of marginal homogeneity states that the marginal probabilities for each outcome are the same (i.e., there is no difference)—the total rows are equal to the sum of columns. The mean of paired samples are equal and no (significant) change has occurred. The alternative hypothesis would state there is a significant difference—the total number of rows is not equal to the total number of columns, or that the paired sample means are not equal. Under the null hypothesis, if the frequencies in the cells B and C (discordants) are sufficiently large, $\frac{{(B-C)}^2}{B+C}$ has a chi-square distribution with one degree of freedom. Like other statistical tests, if the chi-square result is significant, the null hypothesis would be rejected. Most popular statistics programs like SPSS and R cater for the McNemar change test.