ABSTRACT
This chapter develops nonparametric techniques for one way analysis of variance. This argument addressed the distributions of rank sums associated with each group separately; the argument requires that the joint distribution of the sums of ranks over the various groups be multivariate Gaussian. The calculation requires an understanding of the definition of matrix multiplication, and the associative and distributive properties of matrices, and requires an understanding of the definition of a matrix inverse. A simple case of the general multivariate rank statistic may be constructed by choosing the scores for the rank statistics to be the identity, with the ranks themselves as the scores. Yarnold constructs a continuity correction that is additive on the probability, rather on the statistic, scale. This richness of the sample space, as manifest by the small ratio of the point separation to the marginal standard deviations, implies that continuity correction will have only very limited utility.
