Using Weighted Rankings in the Analysis of Complete Blocks with Additive Block Effects

The standard nonparametric procedures for testing the hypothesis of no treatment effects in a complete blocks experiment depend entirely on the within-block rankings. If block effects are assumed additive, however, then between-block information may be recovered by weighting these rankings according to their credibility with respect to treatment ordering. (For the special case of only two treatments, the sign test exemplifies use of unweighted rankings and the signed-rank test weighted.) A general family of weighted-rankings test statistics for comparing two or more treatments is presented. They are simple to compute, are strictly distribution free, and have asymptotic chi-squared distributions.