McNemar’s test is applied to a 2×2 contingency table x with a dichotomous trait, with matched pairs of subjects, of data cross-classified on the row and column variables to testing the null hypothesis of symmetry of the classification probabilities. More formally, the null hypothesis of marginal homogeneity states that the two marginal probabilities for each outcome are the same. The test rests on the two discordant counts, b = x(1,2) and c = x(2,1).

Under the null, with a sufficiently large number of discordants (b + c >= 25), the test statistic follows a chi-squared distribution with 1 degree of freedom. When the number of discordants is less than 25, then the mid-P exact McNemar test is used.

testtype will force mcnemar_test to apply a particular method for testing the null hypothesis independently of the number of discordants. Valid options for testtype:

• 'asymptotic' Original McNemar test statistic
• 'corrected' Edwards’ version with continuity correction
• 'exact' An exact binomial test
• 'mid-p' The mid-P McNemar test (mid-p binomial test)

The test decision is returned in h, which is 1 when the null hypothesis is rejected at the significance level alpha and 0 otherwise, and the p-value in p. 'Alpha' sets alpha, 0.05 by default, and the level 100 (1 - alpha)% of the confidence intervals. stats is a structure with the following fields:

Both intervals come from the exact Clopper-Pearson interval of the proportion b / (b + c), as does the exact test. With no discordant pairs both effect sizes and their intervals are NaN.

Further information about the McNemar’s test can be found at https://en.wikipedia.org/wiki/McNemar%27s_test

See also: crosstab, chi2test, fishertest

Source Code: mcnemar_test