Expected values of mean squares in the analysis of incomplete block experiments and some comments based on them

Abstract

Reference has been made to the logical status of Fisher's null hypothesis that all varieties under test have the same yield on any experimental plot. The types of departures from the null hypothesis, which the ratios of mean squares of varieties to error can detect with a reasonable chance, have been examined in the case of general incomplete block designs. It appears that the test ignores differences in varieties which are, in some sense, attributable to interaction between blocks and treatments. A study of the consequences of non-random allocation of subsets of varieties to block leads to a special property of the BIBD and some PBIBD designs. The effect of random indexing of varieties, i.e., of associating the given varieties with the symbols in which a design is represented, is also considered.