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The hypergeometric, the normal and chi‐squared *
Author(s) -
Hemelrijk J.
Publication year - 1967
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.1467-9574.1967.tb00560.x
Subject(s) - mathematics , hypergeometric distribution , simple (philosophy) , approximations of π , distribution (mathematics) , normal distribution , hypergeometric function , combinatorics , statistics , mathematical analysis , philosophy , epistemology
Summary This note describes a numerical investigation of the normal and χ 2 ‐approximations to the hypergeometric distribution, which leads to a surprisingly simple foot rule. If n and r are the two smaller marginal totals, then for the tails of the distribution up to about a probability of 0.07, the normal approximation will in nearly all cases be better than the χ 2 if n + r 1 / 2 N (where N is the grand marginal total) and worse otherwise. Although the two approximations are nearly equivalent, thisfootrule is so simple that it seems worth publishing.