An Alternate Multinomial Assessment of the Accuracy of the χ 2 Test of Goodness of Fit

Radlow, Robert; Alf, Edward F.

doi:10.2307/2285440

Cited by 40 publications

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“…The general question of whether probability itself should be used as a test statistic for ordering the potential outcomes of a discrete-valued experiment as opposed to using the likelihood ratio, x 2 , or other measures including Bayesian approaches has been examined by several authors (Gibbons and Pratt 1975;Radlow and Alf 1975;Horn 1977;Davis 1986;Cressie and Read 1989;Montoya-Delgado et al 2001 ;Maiste and Weir 2004;Wakefield 2009), and it is unlikely that the discussion will end here. However, it is hoped that the visualization provided in Figure 2 and the accompanying discussions will at least help to clarify some of the differences and raise the possibility that the likelihood ratio may be a closer fit to what most population geneticists aim to do when testing for goodness of fit to HW proportions.…”

Section: Discussionmentioning

confidence: 99%

“…The last option is by far the most widely used (Elston and Forthofer 1977;Louis and Dempster 1987;Chakraborty and Zhong 1994;Weir 1996;Wigginton et al 2005) and implemented in the GENEPOP software package (Rousset 2008). The idea of using the null-hypothesis probability as the test statistic was originally suggested in the context of rectangular contingency tables (Freeman and Halton 1951), but this idea has been criticized for its lack of discrimination between the null hypothesis and alternatives (Gibbons and Pratt 1975;Radlow and Alf 1975;Cressie and Read 1989). For example, suppose a particular sample was found to have a very low probability under the null hypothesis of HW.…”

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confidence: 99%

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Exact Tests for Hardy–Weinberg Proportions

Engels

2009

Genetics

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Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments. This requirement is especially common when the sample includes multiple alleles and sparse data, thus rendering asymptotic methods, such as the common x 2 -test, unreliable. Such an exact test can be performed using the likelihood ratio as its test statistic rather than the more commonly used probability test. Conceptual advantages in using the likelihood ratio are discussed. A substantially improved algorithm is described to permit the performance of a full-enumeration exact test on sample sizes that are too large for previous methods. An improved Monte Carlo algorithm is also proposed for samples that preclude full enumeration. These algorithms are about two orders of magnitude faster than those currently in use. Finally, methods are derived to compute the number of possible samples with a given set of allele counts, a useful quantity for evaluating the feasibility of the full enumeration procedure. Software implementing these methods, ExactoHW, is provided. W HEN studying the genetics of a population, one of the first questions to be asked is whether the genotype frequencies fit Hardy-Weinberg (HW) expectations. They will fit HW if the population is behaving like a single randomly mating unit without intense viability selection acting on the sampled loci. In addition, testing for HW proportions is often used for quality control in genotyping, as the test is sensitive to misclassifications or undetected null alleles. Traditionally, geneticists have relied on test statistics with asymptotic x 2 -distributions to test for goodness-of-fit with respect to HW proportions. However, as pointed out by several authors (Elston and Forthofer 1977;Emigh 1980;Louis and Dempster 1987;Hernandez and Weir 1989;Guo and Thompson 1992;Chakraborty and Zhong 1994;Rousset and Raymond 1995;Aoki 2003;Maiste and Weir 2004;Wigginton et al. 2005;Kang 2008;Rohlfs and Weir 2008), these asymptotic tests quickly become unreliable when samples are small or when rare alleles are involved. The latter situation is increasingly common as techniques for detecting large numbers of alleles become widely used. Moreover, loci with large numbers of alleles are intentionally selected for use in DNA identification techniques (e.g., Weir 1992). The result is often sparse-matrix data for which the asymptotic methods cannot be trusted.A solution to this problem is to use an exact test (Levene 1949;Haldane 1954) analogous to Fisher's exact test for independence in a 2 3 2 contingency table and its generalization to rectangular tables (Freeman and Halton 1951). In this approach, one considers only potential outcomes that have the same allele frequencies as observed, thus greatly reducing the number of outcomes that must be analyzed. One then identifies all such outcomes that deviate from the HW null hypothesis by at least as much the observed sample...

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Exact Tests for Hardy–Weinberg Proportions

Engels

2009

Genetics

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“…Subjects were then classified as always left, significantly left, ambi-preferent, significantly right, or always right based on the model given by McGrew and Marchant [1997]. w 2 goodness-of-fit tests were performed using exact probabilities [Radlow & Alf, 1975] to assess whether head and hand preference distributions differed from an unbiased hypothetical distribution of 25% left preferent, 50% ambi-preferent or mixed preferent, and 25% right preferent as defined by Annett [2006].…”

Section: Discussionmentioning

confidence: 99%

Laterality in semi‐free‐ranging black and white ruffed lemurs (Varecia variegata variegata): head‐tilt correlates with hand use during feeding

Nelson

O'Karma

Ruperti³

et al. 2009

American J Primatol

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Previous studies in human and chimpanzee infants have identified a predictive relationship between early rightward head orientation and later right hand use. Data from lemurs suggest a leftward bias in hand preference, but there are no data on head positioning. The purpose of this study was to examine the relationship between head and hand preferences in the black and white ruffed lemur (Varecia variegata variegata). Ruffed lemurs rotate the head vertically during chewing in a behavior called head-tilting. Frequency of head-tilting and bouts of unimanual hand use were measured during normal feeding in a semi-free-ranging population of lemurs. Subjects were provisioned at feeding platforms twice daily with fresh fruits, vegetables, and other food items. Sampling was spontaneous and all observations were videotaped. No group-level bias was found for head-tilting, but a left hand bias emerged for hand use. A positive relationship was found between direction of head-tilting preference and direction of hand use preference such that left head-tilts increased as left hand use increased. Furthermore, left head-tilts increased as the degree of hand preference lateralization increased. When the hand used to bring food to the mouth just before head-tilting was examined, there was a strong bias for the left hand to precede left head-tilts. For right head-tilts, however, lemurs were equally likely to use either hand before head-tilting. Overall a strong relationship was found between the left hand and left head-tilting in black and white ruffed lemurs, suggesting a common link between these behaviors. However, the direction of bias was different from that seen in human and chimpanzee studies. Additional studies on patterns of laterality would be informative for understanding how laterality has changed across the primate order and the adaptive significance of laterality in primates.

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“…, with ϑ estimated by CMLE) ϑ -VDJ model? In an initial approach we conducted an exact chi-square goodness of fit test [25] separately for each Y stratum, using as expected probabilities the CP values under the optimal model. As a second analysis, we calculated a single global chi-square goodness of fit statistic G , conditioned on the marginal distribution of Y , using as expected probabilities the CP values under the optimal model multiplied by the ratio ( Y total frequency/ n ).…”

Section: Methodsmentioning

confidence: 99%

The Multiple Shark Ig H Chain Genes Rearrange and Hypermutate Autonomously

Zhu

Feng

Weedon

et al. 2011

The Journal of Immunology

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Sharks and skates are representatives of the earliest vertebrates with an immune system based on V(D)J rearrangement. They possess a unique Ig gene organization consisting of 15 to >50 individual IgM loci, each with one VH, two DH, one JH and one set of constant region exons. The present study attempts to understand how multiple Ig genes are regulated with respect to rearrangement initiation and to targeting during somatic hypermutation. The linkage of three single-copy IgH genes was determined, and single-cell genomic PCR studies in a neonatal animal was used to examine any relationship between relative gene position and likelihood of rearrangement. Our results show that 1–3 IgH genes are activated independently of linkage or allelic position and the data best fit with a probability model based on the hypothesis that V(D)J rearrangement occurs as a sequence of trials within the B cell. In the neonatal cell set two closely related IgH, G2A and G2B, rearranged at similar frequencies and their membrane forms were expressed at similar levels, like in other young animals. However, older animals displayed a bias in favor of the G2A isotype, which suggests that although rearrangement at G2A and G2B was randomly initiated during primary repertoire generation, the two very similar IgM sequences appear to be differentially expressed with age and exposure to antigen. We performed genomic single-cell PCR on B cells from an immunized individual to study AID targeting and found that hypermutation, like V(D)J rearrangement, occurred independently among the many shark IgH.

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An Alternate Multinomial Assessment of the Accuracy of the χ 2 Test of Goodness of Fit

Cited by 40 publications

References 0 publications

Exact Tests for Hardy–Weinberg Proportions

Exact Tests for Hardy–Weinberg Proportions

Laterality in semi‐free‐ranging black and white ruffed lemurs (Varecia variegata variegata): head‐tilt correlates with hand use during feeding

The Multiple Shark Ig H Chain Genes Rearrange and Hypermutate Autonomously

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