McNemar's test  overview
This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the righthand column. To practice with a specific method click the button at the bottom row of the table
McNemar's test 


Independent variable  
2 paired groups  
Dependent variable  
One categorical with 2 independent groups  
Null hypothesis  
Let's say that the scores on the dependent variable are scored 0 and 1. Then for each pair of scores, the data allow four options:
Other formulations of the null hypothesis are:
 
Alternative hypothesis  
The alternative hypothesis H_{1} is that for each pair of scores, P(first score of pair is 0 while second score of pair is 1) $\neq$ P(first score of pair is 1 while second score of pair is 0). That is, the probability that a pair of scores switches from 0 to 1 is not the same as the probability that a pair of scores switches from 1 to 0. Other formulations of the alternative hypothesis are:
 
Assumptions  
 
Test statistic  
$X^2 = \dfrac{(b  c)^2}{b + c}$
$b$ is the number of pairs in the sample for which the first score is 0 while the second score is 1, and $c$ is the number of pairs in the sample for which the first score is 1 while the second score is 0  
Sampling distribution of $X^2$ if H_{0} were true  
If $b + c$ is large enough (say, > 20), approximately the chisquared distribution with 1 degree of freedom. If $b + c$ is small, the binomial($n$, $p$) distribution should be used, with $n = b + c$ and $p = 0.5$. In that case the test statistic becomes equal to $b$.  
Significant?  
For test statistic $X^2$:
 
Equivalent to  
 
Example context  
Does a tv documentary about spiders change whether people are afraid (yes/no) of spiders?  
SPSS  
Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples...
 
Jamovi  
Frequencies > Paired Samples  McNemar test
 
Practice questions  