Sir Ronald Fisher and the Design of Experiments

Sir Ronald Fisher is rightly regarded as the founder of the modern methods of design and analysis of experiments. It would be wrong, however, to imagine that there had been no development of experimental design before Fisher. In agricultural field trials, as in other experimental work, replication was often used to increase accuracy, and to give some indication of the reliability of the results. Various types of layout for replicated trials, some of which served their objective of further increasing accuracy reasonably well, had been devised from commonsense considerations; arrangement of the separate replicates in blocks was customary, and although some experimenters were in the habit of assigning the treatments systematically in the same order in each block, others adopted more sophisticated and ingenious arrangements designed to eliminate the effects of fertility gradients, etc. Furthermore, some statistically-minded agronomists had been making investigations on uniformity trial data to study the nature and magnitude of the errors in field trials. What was almost completely lacking was any coherent theory on the estimation of errors from the results themselves, except in the simple case of a comparison of two treatments only. It was generally recognised that an estimate of error could then be obtained from the variability of the treatment differences in the different replicates; indeed 'Student' [1908] had derived what is now known as the t-test for testing the significance of a mean or mean difference based on a few replicates, though as Fisher commented in his obituary of 'Student' [1939] this was received by the Pearsonian school with 'weighty apathy'.