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By D. J. Finney

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In laboratory research of a kind that permits observations to be obtained rapidly, the con equent delay may be unimportant, but even so the procedure may be uneconomic (d. 4). In research of a kind that requires a long period for results of one experiment to be obtained, progress would be intolerably slow if optimal conditions could be investigated only by experiments on one factor at a time and if results from one experiment might make nece sary repetition of trials of factors already 41 Factorial Design and Fractional Replication studied.

Ertainly such extreme heterogeneity is most unlikely, but a method of experimentation that wholly prevented even Ie ser heterogeneity of this kind would be a vast improvement. One possibility is to restrict the inv stigation to a single profession; not only might this limit the applicability of the re 'ults, but it would be impossible unless a large number of volunteers from one profession could be secured. The obvious alternative is to stratify the available volunteers according to proiession (or group of professions), and /then to restrict the randomization by requiring that each type of cloth be allocated to 2 farmers, to 3 steelworkers, and 0 on.

2r" u2 11 L Y}- (L YiY Total ..... . .. N - l Here L p Yp 1 J N is written for the total of the fp yields from plots of treatmenl ~ denote summation over p = 1,2, ... I and j = 1,2, ... _p-N-19 Analysis of Variance where 1/ is the general average yield that would be obtained if each treatment could be tried in turn, under identical conditions, on all plots, and (1/ + Tp) is the average yield that would be obtained if treatment p were assigned to every plot. The symbol Yip is u ed to denote that, in the particular randomization adopted, plot j (j = 1, 2, ...

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


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