An Approximation to the Non-Central Distribution of One-Way Classification Variance-Ratio

A new set of orthogonal polynomials having non-central chi-square distribution as the weight function, is introduced. The distribution of the'one-way classification' variance-ratio under the assumption of nonzero block effects, is given in terms of these polynomials. Population cumulants of order greater than seven are ignored. The effect of non normality on the power of the test is illustrated by way of numerical examples and graphs.