12Experimental Designs
Experimental designs originated in the early years of the 20th century mainly in agricultural field experimentation in connection with open land variety testing. The centre was Rothamsted Experimental Station near London, where Sir Ronald Aylmer Fisher was the head of the statistical department (since 1919). There he wrote one of the first books about statistical design of experiments (Fisher, 1935), a book that was fundamental, and promoted statistical technique and application. The mathematical justification of the methods was not stressed and proofs were often barely sketched or omitted. In this book Fisher also outlined the Lady tasting tea, which is now a famous design of a statistical randomised experiment that uses Fisher’s exact test and is the original exposition of Fisher’s notion of a null hypothesis.
Because soil fertility in trial fields varies enormously, a field is partitioned into so‐called blocks and each block subdivided in plots. It is expected that the soil within the blocks is relatively homogeneous so that yield differences of the varieties planted at the plots of one block are due only to the varieties and not due to soil differences. To ensure homogeneity of soil within blocks, the blocks must not be too large. On the other hand, the plots must be large enough so that harvesting (mainly with machines) is possible. Consequently, only a limited number of plots within the blocks are possible, and only a limited number of varieties ...