A technique for incorporating an experimenter's predictions of orderings of the treatment means into an analysis of variance testing procedure is presented. The experimenter's predictions are assessed in terms of a statistic based on the ordering of the means (e.g. Kendall's tau). The product of the significances of this statistic and ofFis used to obtain the significance level. In comparison with other approaches simulations show this to be the most appropriate technique where the experimenter can predict the order of the treatment means but wishes to have reasonable power even if the predicted ordering is wrong.