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Een permutatietoets voor alternatief verdeelde groot‐heden *
Author(s) -
Elteren Ph.
Publication year - 1963
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1963.tb00329.x
Subject(s) - mathematics , permutation (music) , combinatorics , consistency (knowledge bases) , distribution (mathematics) , constant (computer programming) , test statistic , range (aeronautics) , random permutation , statistics , central limit theorem , random variable , discrete mathematics , statistical hypothesis testing , mathematical analysis , symmetric group , physics , materials science , computer science , acoustics , composite material , programming language
Summary 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 x αi (α= lm; i = In) with P[x αi = 1] = 1‐P[x αi = 0] = p αi A permutation test is proposed for the hypothesis H 0 : p α2 = p α2 = p αn (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 H 0 ) are tabulated for some special cases (tables 1, 2, 3, 4) and approximations are proposed based on limit theorems for m →∞ (χ 2 ‐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 →∞.