How to perform a McNemar's test?

To perform a McNemar's test, compare the number of discordant pairs in a matched-pair experiment.

A McNemar's test is used to determine if there is a significant difference between two related proportions. It is commonly used in medical research to compare the effectiveness of two treatments on the same group of patients. The test is performed on a contingency table that shows the number of discordant pairs, or pairs where one treatment was effective and the other was not.

To perform the test, first, identify the number of discordant pairs in the contingency table. Then, calculate the test statistic using the formula:

χ² = (b-c)² / (b+c)

where b is the number of discordant pairs and c is the number of pairs where both treatments were effective or ineffective.

Next, determine the degrees of freedom for the test, which is one less than the number of discordant pairs. Use a chi-squared distribution table to find the critical value for the test at the desired level of significance.

Finally, compare the test statistic to the critical value. If the test statistic is greater than the critical value, reject the null hypothesis that there is no significant difference between the two treatments. If the test statistic is less than or equal to the critical value, fail to reject the null hypothesis.

It is important to note that McNemar's test assumes that the data is paired and that the two treatments are independent of each other. If these assumptions are not met, the test may not be appropriate.