gofhwex {EQUIVNONINF} R Documentation

## Critical constants of the exact UMPU test for approximate compatibility of a SNP genotype distribution with the Hardy-Weinberg model

### Description

The function computes the critical constants defining the uniformly most powerful unbiased test for equivalence of the population distribution of the three genotypes distinguishable in terms of a single nucleotide polymorphism (SNP), to a distribution being in Hardy-Weinberg equilibrium (HWE).
The test is conditional on the total count S of alleles of the kind of interest, and the parameter θ, in terms of which equivalence shall be established, is defined by θ = \frac{π_2^2}{π_1(1-π_1-π_2)}, with π_1 and π_2 denoting the population frequence of homozygotes of the 1st kind and heterozygotes, respectively.

### Usage

gofhwex(alpha,n,s,del1,del2)


### Arguments

 alpha significance level n number of genotyped individuals s observed count of alleles of the kind of interest del1 absolute value of the lower equivalence limit to θ/4 - 1 del2 upper equivalence limit to θ/4 - 1

### Value

 alpha significance level n number of genotyped individuals s observed count of alleles of the kind of interest del1 absolute value of the lower equivalence limit to θ/4 - 1 del2 upper equivalence limit to θ/4 - 1 C1 left-hand limit of the critical interval for the observed number X_2 of heterozygotes C2 right-hand limit of the critical interval for the observed number X_2 GAM1 probability of rejecting the null hypothesis when it turns out that X_2=C_1 GAM2 probability of rejecting the null hypothesis for X_2=C_2

### Author(s)

Stefan Wellek <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>

### References

Wellek S: Tests for establishing compatibility of an observed genotype distribution with Hardy-Weinberg equilibrium in the case of a biallelic locus. Biometrics 60 (2004), 694-703.

Goddard KAB, Ziegler A, Wellek S: Adapting the logical basis of tests for Hardy-Weinberg equilibrium to the real needs of association studies in human and medical genetics. Genetic Epidemiology 33 (2009), 569-580.

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 9.4.2.

### Examples

gofhwex(0.05,475,429,1-1/1.96,0.96)


[Package EQUIVNONINF version 1.0.2 Index]