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

Seung Ho Kang, Dongwan Shin

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)10-17
Number of pages8
JournalHuman Heredity
Volume58
Issue number1
DOIs
Publication statusPublished - 2004 Dec 31

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Chi-Square Distribution
Sample Size
Alleles
Statistical Models
Genotype

All Science Journal Classification (ASJC) codes

  • Medicine(all)
  • Genetics
  • Genetics(clinical)

Cite this

Kang, Seung Ho ; Shin, Dongwan. / The size of the chi-square test for the Hardy-Weinberg law. In: Human Heredity. 2004 ; Vol. 58, No. 1. pp. 10-17.
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The size of the chi-square test for the Hardy-Weinberg law. / Kang, Seung Ho; Shin, Dongwan.

In: Human Heredity, Vol. 58, No. 1, 31.12.2004, p. 10-17.

Research output: Contribution to journalArticle

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