Significance Tests which May be Applied to Samples from any Populations: III. The Analysis of Variance Test

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Abstract
Given m batches or blocks, each consisting of n individuals, to which are allocated at random n treatments, a test of the null hypothesis that the treatments are equivalent in their effects may be made without any assumption as to the population form by finding the distribution of W, the ratio of treatment to treatment plus error sums of squares, in the population generated by the chance allocation of the different treatments to the individuals in the batch. The author obtains the first 4 moments of the exact distribution of W, and shows that the usual analysis of variance test may be safely applied when the number of individuals in each batch, and the number of batches, are both not top small. A method of testing the validity of the approximation which this test employs is stated, and modifications of procedure, when necessary, are suggested.

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