Testing the hypothesis of equality of means, as in a one-way analysis of variance, against the hypothesis of a particular ordering of the means can be done in two ways. One approach uses the maximum likelihood philosophy while the other uses a single degree of freedom contrast with coefficients chosen to be best in some sense. These two methods are applied to some data from a small scale social survey so as to illustrate their calculations and conclusions. Although the single degree of freedom approach may be accused of arbitrariness in scores, still it is relatively more convenient computationally and permits somewhat more comprehensive conclusions.