The extension of the multiple comparisons test to lattice designs

In many investigations, an experimenter is interested in comparing the effects of a number of experimental treatments, such as yields of several new agriculture varieties, results of several different production procedures, or effects of various raw materials on a final product. In this type of investigation, an F test of the mean square for treatments is often used to test the hypothesis that all treatment means are homogeneous. Given that this hypothesis can be rejected, the experimenter would like to make decisions about the significances of individual differences among treatment means considered a pair at a time.