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By D. J. Finney

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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. The "yield" was the number of flies reared and the "plot" a standard unit culture; four plots of each of the 48 treatment combinations were used.

All these 46 Factorial Experiments conclusions could be reached by intelligent appraisal of figures obtained without any sophistication of statistical analysis, and the consistency of results from replicate plots left no doubt about their truth. In order to examine more carefully the average benefit from the higher level of potas ium phosphate as compared with the lower and to evaluate the weight of evidence that this benefit occurred only when Epsom salt was present, appeal to an analysis of variance and a formal test of significance was desirable.

1- 1 1- 1 I- I I-I Total. . . ...... tX I GRECO-LATIN SQUARE Sum of quur .. n Square (1-1)(1 - 3) 1'- 1 letter of the new square occur once in each row and once in each column, but also it occurs once with each letter of the first square. 2 might have wi hed to test simultaneously inoculation by five different techniques Ca, (3, ... , E). 4. 3 also has no orthogonal square. 4 is both permissible and easily computed; thus the two 33 Randomized Blocks and Orthogonal Squares sets of treatments are examined simultaneously in the one experiment.

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