Abstract
We consider testing for and against decreasing in transposition in K × K × K contingency tables. We show that when testing for exchangeability against this type of ordering, the asymptotic distribution of the likelihood ratio statistic is that of a convolution of several independent chi-bar square distributions and hence is itself a chi-bar square distribution. We provide expressions for the weighting values and we obtain the least-favorable distribution for testing for this type of ordering. Details are given for the cases K =2 and K =3. An illustrative example is included.
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