Department of Statistics, UCLA

Treatment means in factorial experiments are lattice ordered when there is an increase in mean response as the level of any factor is increased, holding the other factors ¯xed. Such means occur naturally in many experiments. A nonparametric test for lattice-ordered means involving a Kendall-type statistic will be summarized for k-factor factorial experiments. Speci¯cally, the form of the test statistic and variance under the null hypothesis will be presented. In addition, a normalized version of the test statistic will be discussed and applied to relevant data.