Rank-based test procedures for interaction in the two-way layout with one observation per cell

New aligned-rank test procedures for the composite null hypothesis of no interaction effects (without placing restrictions on the two main effects) against appropriate composite general alternatives are developed for the standard two-way layout with a single observation per cell. Relative power performances of the two new aligned-rank procedures and existing tests due to Tukey (1949) and to de Kroon & van der Laan (1981) are examined via Monte Carlo simulation. Extensive power studies conducted on the 5 × 6 and 5 × 9 two-way layouts with one observation per cell show superior performance of the new procedures for a variety of interaction effects. Simulated critical values for the new procedures are provided in settings where the number of levels for each of the factors is between 3 and 9, inclusive.