An Incidence Test for k Related Samples

Summary

An incidence test is proposed, which may be viewed as a somewhat more powerful alternative to the familiar F

analysis of variance by ranks. The test is based on the format of the F test. and is subject to the same requisite conditions, but requires a further transformation of the N × k table of ranks into a k × k incidence table, which is treated as a k × k contingency table with fixed marginal sums and ( k – 1) ² degrees of freedom. The ordinary χ ² goodness‐of‐fit criterion is then applied. The test is highly sensitive both to differences in location among the k related samples and to interaction between the identity factor and the treatment factor. The tests is applicable if N ≧ 5 k , and hence represents a large‐sample alternative to the asymptotic version of the F test. The problem of ties is discussed.