An Introduction to the Theory of Experimental Design by D. J. Finney

By D. J. Finney

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Extra resources for An Introduction to the Theory of Experimental Design

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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.

Salt was advantageous, and that calcium chloride had no appreciable effect. 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.

5 . . ... .. .... BLOCX D E C A B . II III IV D A C V VI B E A D D B C A C A B D B E E D E C B E C A The treatments are denoted by the letters A, B, C, D, E . i, and (77 + f'Ji) is the average for all treatments on block j alone. The residual t ii is the amount by which Yii differs from a value predicted by adding average block and treatment "effects" to 77; it is compounded of any "interaction" between the relative effects of different treatments and the block classification (d. 2) and of experimental error.

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