McNemar's test  overview
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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  
$X^2 = \dfrac{(b  c)^2}{b + c}$
Here $b$ 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  