Dj. Best et Jcw. Rayner, NONPARAMETRIC ANALYSIS OF ORDINAL CATEGORICAL RESPONSE DATA WITH FACTORIAL STRUCTURE, Applied Statistics, 47, 1998, pp. 439-446
A simple nonparametric method of analysis for contingency tables with
an ordinal response and factorial treatment structure is described. Th
e method involves a partition of Pearson's X-P(2)-statistic by using o
rthogonal polynomials so that location and dispersion effects are esti
mated for each level of the explanatory variable. Analyses of variance
are then performed on these effects to determine the important factor
s. The methods are applied to two examples, where consumers rate their
liking for a product on an ordered categorical scale, one of which hi
ghlights the need to look at dispersion as well as location effects.