AbstractThe paper introduces the concept of confounded hypotheses. In particular, it is shown that the test of goodness‐of‐fit is confounded with the test of no interaction in a two‐way classification with one observation per cell. Further, the multiple correlation coefficient is shown to be a good criterion for choosing the best from a class of good tests for non‐additivity. Finally, the question is posed about whether different statistically adequate models do converge in some sense to the same or related mathematical fu