Nonparametric analysis of blocked ordered categories data: some examples revisited

In this paper, we will use Cochran-Mantel-Haenszel (CMH) statistics to analyse four data sets which have appeared in the literature. It is well known that tests based on the CMH statistics are equivalent to certain standard rank tests but here we show how CMH statistics also apply in less standard situations. In particular, examples are given for randomized block designs both with and without missing values, for balanced incomplete block designs, and for supplemented balanced designs. Recent descriptions of CMH statistics have been in Davis [6, Chapter 8] and Agresti [1, Chapter 7, Section 5]. We now give a very brief outline of CMH statistics, mainly from Davis [6, Chapter 8].