Een permutatietoets voor alternatief verdeelde groot‐heden*

Ph. van Elteren

Statistica Neerlandica, 1963, vol. 17, issue 4, 487-505

Abstract: A permutation test for random variables that assume the values 0 or 1 only (read for the meeting of the Netherlands Statistical Society in 1963). Consider a matrix of stochastically independent random elements xαi (α= lm; i = In) with P[xαi= 1] = 1‐P[xαi= 0] = pαi A permutation test is proposed for the hypothesis H0: pα2=pα2=pαn (α= lm). The statistic of the test is given by the formulas (1.1) and (1.2), its critical region by (1.3). It is shown that this test can be considered as a special case of the method of m rankings of M. Friedman (cf literature [1]) and of a similar test of A. S. C. Ehrenberg (cf [3], [4], [5]). Exact distribution functions (under H0) are tabulated for some special cases (tables 1, 2, 3, 4) and approximations are proposed based on limit theorems for m→∞ (χ2‐distribution) for n→∞ (normal distribution) and on fitting of mean, variance and range (F‐distribution). A consistency theorem is derived for the cases m constant, n→∞ and n constant, m→∞.

Date: 1963
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