Journal of Applied Mathematics and Decision Sciences
Volume 4 (2000), Issue 1, Pages 83-98

Analysis of singly ordered two-way contingency tables

J. C.W. Rayner1 and D. J. Best2

1School of Mathematics and Applied Statistics, University of Wollongong, Northfields Avenue, NSW 2522, Australia
2CSIRO Mathematical and Information Sciences, PO Box 52, North Ryde NSW 1670, Australia

Copyright © 2000 J. C.W. Rayner and D. J. Best. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Pearson's statistic is investigated for nominal-ordinal two-way contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summand of which is a statistic given by Yates (1948), and examines location effects for the nominal category. The second and subsequent summands reflect the corresponding moments: for example, dispersion, skewness, kurtosis etc. The summands are shown to be weakly optimal in that they are score statistics.