Marginal Homogeneity test / StuartMaxwell test  overview
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Marginal Homogeneity test / StuartMaxwell test 


Independent variable  
2 paired groups  
Dependent variable  
One categorical with $J$ independent groups ($J \geqslant 2$)  
Null hypothesis  
H_{0}: for each category $j$ of the dependent variable, $\pi_j$ for the first paired group = $\pi_j$ for the second paired group.
Here $\pi_j$ is the population proportion in category $j.$  
Alternative hypothesis  
H_{1}: for some categories of the dependent variable, $\pi_j$ for the first paired group $\neq$ $\pi_j$ for the second paired group.  
Assumptions  
 
Test statistic  
Computing the test statistic is a bit complicated and involves matrix algebra. Unless you are following a technical course, you probably won't need to calculate it by hand.  
Sampling distribution of the test statistic if H_{0} were true  
Approximately the chisquared distribution with $J  1$ degrees of freedom  
Significant?  
If we denote the test statistic as $X^2$:
 
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?  
SPSS  
Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples...
 
Practice questions  