The Distribution of Higher-Order Interactions in Contingency Tables
Michael Edmund O'Neill · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1980
Summary Lancaster's definition of the absence of second-order interactions in contingency tables produces test statistics which have asymptotic ***x 2 distributions under complete independence, but not (in general) otherwise. This paper obtains the asymptotic distributions of all interaction components in the partitioning of Pearson's x 2, and indicates a test procedure for higher-order interactions when lower-order interactions are found to be significant.