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The size of the chi-square test for the Hardy-Weinberg law

Title
The size of the chi-square test for the Hardy-Weinberg law
Authors
Kang S.-H.Shin D.
Ewha Authors
신동완강승호
SCOPUS Author ID
신동완scopus
Issue Date
2004
Journal Title
Human Heredity
ISSN
0001-5652JCR Link
Citation
Human Heredity vol. 58, no. 1, pp. 10 - 17
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
Many scientific problems can be formulated in terms of a statistical model indexed by parameters, only some of which are of scientific interest and the other parameters, called nuisance parameters, are not of interest in themselves. For testing the Hardy-Weinberg law, a relation among genotype and allele probabilities is of interest and allele probabilities are of no interest and now nuisance parameters. In this paper we investigate how the size (the maximum of the type I error rate over the nuisance parameter space) of the chi-square test for the Hardy-Weinberg law is affected by the nuisance parameters. Whether the size is well controlled or not under the nominal level has been frequently investigated as basic components of statistical tests. The size represents the type I error rate at the worst case. We prove that the size is always greater than the nominal level as the sample size increases. Extensive computations show that the size of the chi-squared test (worst type I error rate over the nuisance parameter space) deviates more upwardly from the nominal level as the sample size gets larger. The value at which the maximum of the type I error rate was found moves closer to the edges of the the nuisance parameter space with increasing sample size. An exact test is recommended as an alternative when the type I error is inflated. Copyright © 2004 S. Karger AG, Basel.
DOI
10.1159/000081452
Appears in Collections:
자연과학대학 > 통계학전공 > Journal papers
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