Advanced McNemar Test Calculator

Configure McNemar Test Parameters

1. 2x2 Contingency Table

Enter paired nominal frequencies ($n$).

Cell $n_{00}$ (Both Negative / 0,0):

Cell $n_{01}$ (Row Neg, Col Pos / 0,1):

Cell $n_{10}$ (Row Pos, Col Neg / 1,0):

Cell $n_{11}$ (Both Positive / 1,1):

2. Statistical Options

Configure correction and significance level.

Continuity Correction:

Significance Level ($\alpha$):

Alternative Hypothesis:

3. Execute Test

Review your inputs and click calculate to generate statistical test results.

Paired categorical data
Matched case-control studies
Pre-test / Post-test evaluations

Formula Used

The McNemar test is a non-parametric statistical test applied to paired contingency tables with dichotomous traits. The standard test statistic $\chi^2$ formula with Edwards' continuity correction is defined as:

$$\chi^2 = \frac{(|n_{10} - n_{01}| - 1)^2}{n_{10} + n_{01}}$$

For uncorrected McNemar test:

$$\chi^2 = \frac{(n_{10} - n_{01})^2}{n_{10} + n_{01}}$$

Where $n_{10}$ and $n_{01}$ represent the discordant pair frequencies, following a Chi-squared distribution with $df = 1$ under the null hypothesis.

How to Use This Calculator

Input Contingency Frequencies: Enter your paired observation counts into cells $n_{00}$, $n_{01}$, $n_{10}$, and $n_{11}$. You can also click one of the preset buttons to load sample data instantly.
Select Statistical Options: Choose whether to apply continuity correction (Edwards' correction), select your significance level ($\alpha$), and specify the alternative hypothesis direction.
Calculate: Press the "Calculate Test Statistic" button to view test metrics, Chi-square values, p-values, and hypothesis conclusion instantly at the top of the page.

Comprehensive Guide to McNemar's Test and Paired Data Analysis

McNemar’s test is an essential statistical tool used in categorical data analysis when dealing with paired samples or matched subjects. Unlike independent samples tests such as the Pearson chi-square test, McNemar's test specifically evaluates whether marginal proportions are equal in 2x2 contingency tables with dependent observations. This makes it invaluable in fields such as medicine, psychology, and market research for pre-test and post-test intervention comparisons or matched case-control studies.

Understanding Discordant Pairs

The core mechanism of McNemar's test relies on discordant pairs ($n_{10}$ and $n_{01}$). Concordant pairs ($n_{00}$ and $n_{11}$) indicate subjects where both measurements yielded identical outcomes, providing no information regarding a shift in proportions. Only subjects who changed status between the first and second observation contribute statistical power to evaluate whether the intervention or condition created a measurable change.

Frequently Asked Questions (FAQs)

Use McNemar's test when your data consists of paired or matched categorical responses from the same subjects (e.g., before and after a treatment). Standard chi-square tests assume independent samples and would violate underlying assumptions if applied to paired data.

Edwards' continuity correction adjusts the discrete binomial distribution approximation toward a continuous chi-squared distribution, preventing overestimation of significance when sample sizes are moderate or small.