A Friedman-Type Rank Test for Main Effects in a Two-Factor ANOVA

Abstract

Abstract A distribution-free test is considered for testing main effects in a two-factor ANOVA. Large-sample properties (cell sizes tending to infinity) including efficiencies and the limiting distribution of the test statistic are obtained. For proportional frequencies a simple sum of squares formula is obtained for the test statistic and multiple comparison procedures are given. For general designs the statistic is expressed using generalized inverses. Some tables for the null distribution of the statistic are also given. Key Words: Two-way ANOVADistribution freeMultiple comparisonsFriedmanEfficiency