145 Note: On a Test for Order

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Abstract
The test described is a simple extension of the procedure of using a single-tailed test when testing for a significant difference between two per-centages or two means. Given N binomial with observed relative frequencies x1/n1> x2/n2 >... > xN/nN, such that n1=n2 ... =nN, and a standard chi-square contingency test value corresponding to a level of significance, [alpha], then the probability that the particular observed ordering under the null hypothesis was due to chance cannot exceed [alpha]/N!. Similarly the significance level [alpha] (F) of the usual analysis of variance test of the hypothesis m1=m2= ... =mk against the alternative hypothesis m1>m2=>...> mk can be strengthened to [alpha](F)/k! , given a set of observed means x .1>x.2> ...> x.k with equal sample sizes.

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