McNemar's test - overview
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McNemar's test |
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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:
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Alternative hypothesis | |
The alternative hypothesis H1 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:
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Assumptions | |
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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 H0 were true | |
If $b + c$ is large enough (say, > 20), approximately the chi-squared 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 $X^2$:
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Equivalent to | |
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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...
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Jamovi | |
Frequencies > Paired Samples - McNemar test
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Practice questions | |