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De gereduceerde X 2 ‐methode *
Author(s) -
Hemelrijk J.
Publication year - 1950
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.1467-9574.1950.tb01051.x
Subject(s) - mathematics , simple (philosophy) , expression (computer science) , elementary theory , square (algebra) , distribution (mathematics) , combinatorics , calculus (dental) , mathematical analysis , computer science , geometry , medicine , philosophy , dentistry , epistemology , programming language
Summary In these notes the author endeavours to describe in elementary form the theory of reduced chi‐square, which formed the subject of two lectures given by Professor N eyman in Amsterdam on the 8th and qth of May, 1950. If the theoretical frequencies occurring as denominators in the usual expression of x 2 are replaced by the observed frequencies, we obtain an expression x' 2 which asymptotically possesses a% % ‐distribution. If the theoretical frequencies depend on a number of parameters these may be estimated by reducing either x 2 or x' 2 to a minimum; mathematically the latter method is often much more tractable. The method of reduced x 2 is illustrated by a simple example in § 2. The importance of this theory is explained in § 3. In §§ 4 and 5 the general formulation of Neyman's theory and its application to the estimation of parameters and the testing of hypotheses are briefly summarized.