Further results on ? 2 for matched samples

1 April 1974

journal article
research article
Published by Taylor & Francis in Scandinavian Actuarial Journal

Vol. 1974 (2) , 115-119
https://doi.org/10.1080/03461238.1974.10408669

Abstract

The problem of χ² tests of a linear hypothesis H₀ for ‘matched samples’ in attribute data has been discussed earlier by the author (Bennett, 1967, 1968). This note presents corresponding results for the hypothesis that the multinomial probabilities p satisfy (c −1) functional restrictions: F ₁(p) = 0, ... , F_C−1(p) = 0. An explicit relationship between the usual ‘goodness-of-fit’ χ² and the modified minimum χ² (=χ*²) of Jeffreys (1938) and Neyman (1949) is demonstrated for this situation. An example of the test for the 2 × 2 × 2 contingency table is given and compared with the solution of Bartlett (1935).

Keywords

This publication has 2 references indexed in Scilit:

The use of minimum χ² as an approximation to the method of maximum likelihood
Mathematical Proceedings of the Cambridge Philosophical Society, 1938
Contingency Table Interactions
Journal of the Royal Statistical Society Series B: Statistical Methodology, 1935