Extending the Stuart-Maxwell Test to Account for Ordinal Category Levels

Stuart (1955) and Maxwell (1970) developed equivalent tests for marginal homogeneity in a two-way classification table where subjects are classified into categories by two separate methods (or judges). While the example used in the original Stuart paper involves ordinal categories, and the literature is full of examples where the Stuart-Maxwell test is applied to ordinal categories, the test itself makes no allowance for the ordinality of category levels, and in fact implicitly treats all category levels as nominal. We present a novel extension of the Stuart-Maxwell test to account for the ordinality of category levels, implemented in R, with demonstration on several data sets.