Asymptotically favorable methods for testing the equality of certain measures of association in different four-fold tables are deduced from the general theory of χ2-tests as given by Neyman and generalized by Anderson, Goodman and Gold. The tests turn out to be also obtainable by an intuitive use of maximum likelihood estimates as suggested by Wald's large sample theory and include one proposed by Lancaster for testing the second order interaction in a complex contingency table. Applications in the field of drug research and health surveys are indicated.