McNemar's Test Calculator

McNemar's test is a non-parametric statistical method used on paired nominal data, typically from 2x2 contingency tables with matched pairs. The test focuses exclusively on the discordant pairs (cells b and c), where the outcome changed between the two measurements. The test statistic follows a chi-square distribution with 1 degree of freedom and is calculated using the formula: Chi-square = ((|b - c| - 1)^2) / (b + c) when applying continuity correction, or without the minus-one term for standard asymptotic calculations. The resulting chi-square value is then converted into a p-value based on your chosen tail distribution to test your null hypothesis.

Imagine a clinical trial testing a new therapeutic cream for skin rashes on 100 patients. Each patient is evaluated before treatment and after treatment, categorized as either 'Rash Present' (Positive) or 'Rash Absent' (Negative). Suppose our 2x2 table yields the following discordant pairs: b = 24 patients had a rash before treatment but cleared up after (Positive to Negative), and c = 8 patients developed a rash after treatment despite being clear before (Negative to Positive). To calculate McNemar's test, we take the absolute difference between b and c (|24 - 8| = 16), square it (256), and divide by the sum of discordant pairs (24 + 8 = 32), resulting in a chi-square statistic of 8.0. This yields a p-value significantly below the standard 0.05 threshold, allowing researchers to reject the null hypothesis and conclude that the treatment effect is statistically significant.

Ensure your data consists strictly of matched or paired observations, such as pre-test and post-test scores from the exact same subjects. Pay close attention to the discordant pairs (b and c), as concordant pairs (a and d) do not contribute to the McNemar test statistic numerator. If your total number of discordant pairs (b + c) is small, typically less than 25, consider using the binomial exact test version instead of the standard asymptotic chi-square approximation to maintain analytical validity.