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By D. J. Finney

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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. This device can be adopted either in order to balance out a third series of block constraints (such as having the inoculations made by five different people), or to introduce a new set of treatments into an experiment that is already in progress, provided that no interaction of the two sets is likely.

Error ...... .... " . 23 115 Total .... .... 1, the treatment component could be subdivid d into 23 separate squares for single and mutually orthogonal contrasts. 1 uffices. Yields are classified according to temperature, and totals of the groups of 48 formed irrespective of quantity of material and period. , the main effect of factor T. Analogous calculations are used on four totals of 36 yields classified by quantity and the two totals of 72 classified according to period. From a classification of yields with respect to temperature and quantity simultaneou Jy, twelve totals of 12 yields per group are form dj the sum of squares with 11 dJ.

7 shows a (3 2) partition of a 6 X 6 Latin square, which could be u ed to incorporate an additional treatment at two levels only or a block constraint with three plots of ach treatment in each block. 8 shows the most extreme partition that exists, (1 4,2), in which suffixes 1, 2, 3, 4 mark four directrices (one letter of each type in each row and each column). 8, other partitions such as (18, 3), (2 8), (2,4), (3 2) can be formed (Finney, 1944, 1946a, 1946b). Orthogonal partitions of Latin squares are of limited use in experi36 Orthogonal Partitions of Latin Square.

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An Introduction To The Theory Of Experimental Design by D. J. Finney

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