By D. J. Finney
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Extra info for An Introduction To The Theory Of Experimental Design
Full enumeration of the commoner partitions has not been completed, a some are very numerous; squares of many transformation sets have at least 200 different (2 3) partitions, and in at least one transformation s t th re are at least 976 different (1,2,3) partitions for each quare. Lakshminarayan (1958) has recently studied tbese properties and has proved some general results. RTITIO Of A 6 X 6 LATIN QU~RE Aal 13d4 Cd4 Dd2 EM Fc3 Bd2 Ca3 FM Ac4 Dd4 Edl Cb4 Fd2 Bel Ed4 Ad3 Da4 Dc4 Ad4 Ea2 Bb3 Fdl d4 Ed3 Dbl Ad4 Fa4 Cc2 Bd4 s Fd4 Ec4 Dd3 Cdl Ba4 Ab2 Higher-order orthogonal partitions of 6 X 6 squares are known, though they appear to be rather rare.
Two points commonly neglected in the theory of analysis of variance are important in practice: i) Experiments are rarely conducted with a real belief in a null hypothesis that certain treatments are identical in effect. The experimenter may be fairly sure that, by making his experiment larger and more precise, he can detect as statistically significant a difference between any two distinct treatmentsl Much more important is estimation of the magnitude of a difference, with a measure of precision to assist judgment of whether the effect is important.
3) referred to an experiment (Kalmus, 1943) on the growth medium to be used for laboratory rearing of Drosophila melanogaster, the species of fruit By the genetic study of which has done so much for the development of the whole subject of genetics. A widely recommended growth medium consisted of agar, cane sugar, and tartaric acid, with small quantities of each of five common salts of magnesium, calcium, ammonium, potassium, and sodium. The experiment concerned the merits of inclusion of each salt; it was 3 X 2' in design, contrasting absence with two alternative amounts of potassium phosphate, and absence with presence of each of the other four salts.