Marginal Homogeneity test / StuartMaxwell test  overview
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Marginal Homogeneity test / StuartMaxwell test  McNemar's test 


Independent variable  Independent variable  
2 paired groups  2 paired groups  
Dependent variable  Dependent variable  
One categorical with $J$ independent groups ($J \geqslant 2$)  One categorical with 2 independent groups  
Null hypothesis  Null hypothesis  
For each category $j$ of the dependent variable:
$\pi_j$ in the first paired group = $\pi_j$ in the second paired group Here $\pi_j$ is the population proportion for category $j$  For each pair of scores, the data allow four options:
Other formulations of the null hypothesis are :
 
Alternative hypothesis  Alternative hypothesis  
For some categories of the dependent variable, $\pi_j$ in the first paired group $\neq$ $\pi_j$ in the second paired group  Alternative hypothesis is that for each pair of scores:
Other formulations of the alternative hypothesis are that, for each pair of scores:
 
Assumptions  Assumptions  
Sample of pairs is a simple random sample from the population of pairs. That is, pairs are independent of one another  Sample of pairs is a simple random sample from the population of pairs. That is, pairs are independent of one another  
Test statistic  Test statistic  
Computing the test statistic is a bit complicated and involves matrix algebra. You probably won't need to calculate it by hand (unless you are following a technical course)  $X^2 = \dfrac{(b  c)^2}{b + c}$
$b$ 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 the test statistic if H0 were true  Sampling distribution of $X^2$ if H0 were true  
Approximately a chisquared distribution with $J  1$ degrees of freedom  If $b + c$ is large enough (say, > 20), approximately a 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?  Significant?  
If we denote the test statistic as $X^2$:
 For test statistic $X^2$:
 
n.a.  Equivalent to  
 
 
Example context  Example context  
Subjects are asked to taste three different types of mayonnaise, and to indicate which of the three types of mayonnaise they like best. They then have to drink a glass of beer, and taste and rate the three types of mayonnaise again. Does drinking a beer change which type of mayonnaise people like best?  Does a tv documentary about spiders change whether people are afraid (yes/no) of spiders?  
SPSS  SPSS  
Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples...
 Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples...
 
n.a.  Jamovi  
  Frequencies > Paired Samples  McNemar test
 
Practice questions  Practice questions  