13.21 : McNemar's Test

McNemar's Test is a nonparametric statistical test used to determine if there is a significant difference in proportions between two related groups when the outcome is binary (e.g., yes/no, success/failure). It is beneficial when we have paired data, such as pre-test/post-test designs, where the same subjects are measured under two different conditions. The test is named after the statistician Quinn McNemar, who introduced it in 1947. It is commonly used in situations where subjects are measured before and after a treatment or in matched-pair study designs.

Assumptions of McNemar's Test

For McNemar's test to produce valid results, the following assumptions must be met:

1. Paired Samples: The data must come from matched pairs, where each subject in one group corresponds to a subject in the other group (e.g., pre-post data or matched-pair design).
2. Dichotomous Outcome: The test is designed for binary outcomes, such as yes/no, success/failure, or presence/absence.
3. Independence of Pairs: Each pair should be independent of other pairs in the study. This means that the pairs (not individual observations) should be unrelated to each other.
4. Sufficient Sample Size: McNemar's test is robust for small sample sizes, but reliability decreases with very small samples. Generally, a minimum of 10 discordant pairs—where the outcomes differ between conditions—is recommended for meaningful results. With a small number of discordant pairs, the test may lack the power needed to detect a true difference between the paired conditions.

Applicability and Conditions

McNemar's test is particularly suited for the following situations:

1. Pre-Post Study Designs: Used to assess the effect of an intervention by comparing the responses of the same subjects before and after treatment.
2. Matched-Pair Studies: Applied when subjects are matched based on certain characteristics and then exposed to different treatments or conditions.
3. Clinical Trials: Here, the test is used to compare the effectiveness of treatments by analyzing the same group of patients at two different points in time.

McNemar's test is a valuable tool for analyzing paired nominal data, particularly in medical and psychological research, where pre-post designs and matched-pair studies are commonly used. By understanding and meeting the assumptions of the test, researchers can apply McNemar's test to draw reliable conclusions about differences in proportions between two related groups.