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By D. J. Finney

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Between rabbits, , . , . , , .... Between days .. """, . . , Between treatments , , , , . , , Error. , , ... ' .. , . . . . . 3 3 6 646 . " . " "" , .. " . 15 2,545,75 . NTRATION IN MG. PER 100 CC. E. 8 54 , 2 ±2 . 83/ 4) . Underlying this analysis is the assumption that, for the general tXt Latin square, the yield J ijl: (i, j, k = 1, 2, ... 6) 31 Randomized Block. and Orthogo"al Square. 2). 6) is to be applicable. The expectations of the means squares are then t (12 + - - 2: r2 (3. 7) t- 1 for treatments, with similar expressions for columns and rows.

Latin treatments .. . . Greek treatments ...... Error . . . . 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.

Relative to the normal error. Henceforth for simplicity normality is assumed. Nothing will be said in this book about the transformation of the observed yields, the use of some simpl function of yield instead of the measurement actually made, in order that as umptions underlying the analysis may be more nearly satisfied. Bartlett (1947) and Cochran (1947) have given useful elementary accounts, but much may be found in textbooks and in subsequent pap rs. S VARIANCE COMPONENTS In the interpretation of an anaJy is of variance, the expectations of the mean squares under the randomization procedure that has been used may be required.

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