A Note on the Equivalence of Two Test Criteria for Hypotheses in Categorical Data

It is shown in this note that for testing linear hypotheses in categorical data Wald's statistic [1943] is equivalent (i.e., algebraically-identical) to the χ2 1 statistic of Neyman [1949], and for testing nonlinear hypotheses it is equivalent to the χ2 1 statistic using Neyman's linearization technique, whenever these χ2 1 statistics are defined.