Genetics. Jun 2001; 158(2): 875–883.

# An unconditional exact test for the Hardy-Weinberg equilibrium law: sample-space ordering using the Bayes factor.

Universidad del Cauca, Popayan, Cauca, Colombia.

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cited by other articles in PMC.

## Abstract

Much forensic inference based upon DNA evidence is made assuming that the Hardy-Weinberg equilibrium (HWE) is valid for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, each having advantages and limitations. The limitations become more obvious when testing for deviation within multiallelic DNA loci is attempted. Here we present an exact test for HWE in the biallelic case, based on the ratio of weighted likelihoods under the null and alternative hypotheses, the Bayes factor. This test does not depend on asymptotic results and minimizes a linear combination of type I and type II errors. By ordering the sample space using the Bayes factor, we also define a significance (evidence) index, P value, using the weighted likelihood under the null hypothesis. We compare it to the conditional exact test for the case of sample size n = 10. Using the idea under the method of chi(2) partition, the test is used sequentially to test equilibrium in the multiple allele case and then applied to two short tandem repeat loci, using a real Caucasian data bank, showing its usefulness.

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## Selected References

###### These references are in PubMed. This may not be the complete list of references from this article.

- Guo SW, Thompson EA. Performing the exact test of Hardy-Weinberg proportion for multiple alleles. Biometrics. 1992 Jun;48(2):361–372. [PubMed]
- Hernández JL, Weir BS. A disequilibrium coefficient approach to Hardy-Weinberg testing. Biometrics. 1989 Mar;45(1):53–70. [PubMed]
- Ayres KL, Balding DJ. Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient. Heredity (Edinb) 1998 Jun;80(Pt 6):769–777. [PubMed]
- Cannings C, Edwards AW. Expected genotypic frequencies in a small sample: deviation from Hardy-Weinberg equilibrium. Am J Hum Genet. 1969 May;21(3):245–247. [PMC free article] [PubMed]
- Maiste PJ, Weir BS. A comparison of tests for independence in the FBI RFLP data bases. Genetica. 1995;96(1-2):125–138. [PubMed]
- Deka R, Jin L, Shriver MD, Yu LM, DeCroo S, Hundrieser J, Bunker CH, Ferrell RE, Chakraborty R. Population genetics of dinucleotide (dC-dA)n.(dG-dT)n polymorphisms in world populations. Am J Hum Genet. 1995 Feb;56(2):461–474. [PMC free article] [PubMed]
- Devlin B, Risch N, Roeder K. Response. Science. 1991 Aug 30;253(5023):1039–1041. [PubMed]
- Devlin B, Risch N, Roeder K. Statistical evaluation of DNA fingerprinting: a critique of the NRC's report. Science. 1993 Feb 5;259(5096):748–837. [PubMed]
- Devlin B, Risch N, Roeder K. NRC report on DNA typing. Science. 1993 May 21;260(5111):1057–1059. [PubMed]
- Devlin B, Risch N, Roeder K. Disequilibrium mapping: composite likelihood for pairwise disequilibrium. Genomics. 1996 Aug 15;36(1):1–16. [PubMed]
- Shoemaker J, Painter I, Weir BS. A Bayesian characterization of Hardy-Weinberg disequilibrium. Genetics. 1998 Aug;149(4):2079–2088. [PMC free article] [PubMed]
- Vieland VJ. Bayesian linkage analysis, or: how I learned to stop worrying and love the posterior probability of linkage. Am J Hum Genet. 1998 Oct;63(4):947–954. [PMC free article] [PubMed]
- Weber JL, Kwitek AE, May PE, Wallace MR, Collins FS, Ledbetter DH. Dinucleotide repeat polymorphisms at the D17S250 and D17S261 loci. Nucleic Acids Res. 1990 Aug 11;18(15):4640–4640. [PMC free article] [PubMed]

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