POWSIM: a computer program for assessing statistical power when testing for genetic differentiation

Knowledge of statistical power is essential for sampling design and data evaluation when testing for genetic differentiation. Yet, such information is typically missing in studies of conservation and evolutionary genetics, most likely because of complex interactions between the many factors that affect power. powsim is a 32‐bit Windows/DOS simulation‐based computer program that estimates power (and α error) for chi‐square and Fisher's exact tests when evaluating the hypothesis of genetic homogeneity. Optional combinations include the number of samples, sample sizes, number of loci and alleles, allele frequencies, and degree of differentiation (quantified as F_ST). powsim is available at http://www.zoologi.su.se/~ryman .     

A Comparison of the Three Conditional Exact Tests in Two‐way Contingency Tables Using the Unconditional Exact Power

The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact test, the exact chi‐squared test and the exact likelihood ratio test are popular and can be implemented in software StatXact. In this paper we investigate which test is the best in small samples in terms of the unconditional exact power. In equal sample cases it is proved that the three tests produce the same unconditional exact power. A symmetry of the unconditional exact power is also found. In unequal sample cases the unconditional exact powers of the three tests are computed and compared. In most cases the Fisher's exact test turns out to be best, but we characterize some cases in which the exact likelihood ratio test has the highest unconditional exact power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stratified Fisher's exact test and its sample size calculation

Chi‐squared test has been a popular approach to the analysis of a 2 × 2 table when the sample sizes for the four cells are large. When the large sample assumption does not hold, however, we need an exact testing method such as Fisher's test. When the study population is heterogeneous, we often partition the subjects into multiple strata, so that each stratum consists of homogeneous subjects and hence the stratified analysis has an improved testing power. While Mantel–Haenszel test has been widely used as an extension of the chi‐squared test to test on stratified 2 × 2 tables with a large‐sample approximation, we have been lacking an extension of Fisher's test for stratified exact testing. In this paper, we discuss an exact testing method for stratified 2 × 2 tables that is simplified to the standard Fisher's test in single 2 × 2 table cases, and propose its sample size calculation method that can be useful for designing a study with rare cell frequencies.     

Conjunctival melanoma copy number alterations and correlation with mutation status,tumor features,and clinical outcome

Relatively little is known about the genetic aberrations of conjunctival melanomas (CoM) and their correlation with clinical and histomorphological features as well as prognosis. The aim of this large collaborative multicenter study was to determine potential key biomarkers for metastatic risk and any druggable targets for high metastatic risk CoM. Using Affymetrix single nucleotide polymorphism genotyping arrays on 59 CoM, we detected frequent amplifications on chromosome (chr) 6p and deletions on 7q, and characterized mutation‐specific copy number alterations. Deletions on chr 10q11.21‐26.2, a region harboring the tumor suppressor genes, PDCD4, SUFU, NEURL1, PTEN, RASSF4, DMBT1, and C10orf90 and C10orf99, significantly correlated with metastasis (Fisher's exact, p ≤ 0.04), lymphatic invasion (Fisher's exact, p ≤ 0.02), increasing tumor thickness (Mann–Whitney, p ≤ 0.02), and BRAF mutation (Fisher's exact, p ≤ 0.05). This enhanced insight into CoM biology is a step toward identifying patients at risk of metastasis and potential therapeutic targets for systemic disease.     

Letter to the Editor

Regarding Paper “Stratified Fisher's exact test and its sample size calculation” by Sin‐Ho Jung Biometrical Journal (2014) 56 (1): 129–140 Article: http://dx.doi.org/10.1002/bimj.201300048     

Determination of diagnostic species with statistical fidelity measures

Abstract. Statistical measures of fidelity, i.e. the concentration of species occurrences in vegetation units, are reviewed and compared. The focus is on measures suitable for categorical data which are based on observed species frequencies within a vegetation unit compared with the frequencies expected under random distribution. Particular attention is paid to Bruelheide's u value. It is shown that its original form, based on binomial distribution, is an asymmetric measure of fidelity of a species to a vegetation unit which tends to assign comparatively high fidelity values to rare species. Here, a hypergeometric form of u is introduced which is a symmetric measure of the joint fidelity of species to a vegetation unit and vice versa. It is also shown that another form of the binomial u value may be defined which measures the asymmetric fidelity of a vegetation unit to a species. These u values are compared with phi coefficient, chi‐square, G statistic and Fisher's exact test. Contrary to the other measures, phi coefficient is independent of the number of relevés in the data set, and like the hypergeometric form of u and the chi‐square it is little affected by the relative size of the vegetation unit. It is therefore particularly useful when comparing species fidelity values among differently sized data sets and vegetation units. However, unlike the other measures it does not measure any statistical significance and may produce unreliable results for small vegetation units and small data sets. The above measures, all based on the comparison of observed/expected frequencies, are compared with the categorical form of the Dufrêne‐Legendre Indicator Value Index, an index strongly underweighting the fidelity of rare species. These fidelity measures are applied to a data set of 15 989 relevés of Czech herbaceous vegetation. In a small subset of this data set which simulates a phytosociological table, we demonstrate that traditional table analysis fails to determine diagnostic species of general validity in different habitats and large areas. On the other hand, we show that fidelity calculations used in conjunction with large data sets can replace expert knowledge in the determination of generally valid diagnostic species. Averaging positive fidelity values for all species within a vegetation unit is a useful approach to measure quality of delimination of the vegetation unit. We propose a new way of ordering species in synoptic species‐by‐relevé tables, using fidelity calculations.     

Associations of single nucleotide polymorphisms in candidate genes with the polled trait in Datong domestic yaks

The domestic yak (Bos grunniens) is an iconic symbol of animal husbandry at high altitudes. Yaks exhibit unique external characteristics including long hair and large horns. However, hornless yaks can be found in different breeds and different populations. The hornless trait is also known as polled, and the POLL locus has been fine‐mapped to chromosome 1 in cattle (Bos taurus), although the underlying genetic basis of the polled trait is still unclear in the yak. Thus, we performed an association study to identify the genetic polymorphisms responsible for the polled trait in the yak. Fifty polled Datong domestic yaks and 51 horned individuals were selected randomly from a huge herd and were used as the case and control groups respectively for the association analysis. Twelve genes located in the candidate region of the POLL locus in cattle were used as references to detect DNA polymorphisms related to yak polledness, which were analyzed by sequencing and a high‐resolution melting test. We applied Fisher's exact test and haplotype analysis to show that a 147‐kb segment that included three protein‐coding genes C1H21orf62, GCFC1 and SYNJ1 was the most likely location of the POLL mutation in domestic yaks.     

Enthesopathy formation in the humerus: Data from known age‐at‐death and known occupation skeletal collections

Enthesopathies, in the guise of musculoskeletal skeletal stress markers (MSM), have been widely used to reconstruct activity levels in human skeletal populations. In general, studies have focused on their presence in the upper limb, which is used in the majority of daily activities. The aim of this study was to use some of the attachment sites on the humerus to explore the relationship between enthesopathy formation, activity, and the ageing process. The skeletal sample used in this study comprised male adult skeletons with known age‐at‐death and known occupations from the late‐19th and early‐20th century cemeteries in Portugal. The enthesopathies were recorded as either present or absent. Statistical analysis using Fishers exact tests and logistic regression was undertaken to determine whether associations could be found between specific activities or socioeconomic status (manual or nonmanual workers), and age and enthesopathy presence. Left and right sides were analyzed separately. Fisher's exact tests were used to determine the relationship between activity and enthesopathy, and they demonstrated no association between activity and enthesopathies (P > 0.01). The results of the logistic regression established that age was the single most significant factor in enthesopathy formation (P > 0.05). This study found that, in these samples, age‐at‐death, and therefore age‐related degeneration rather than degeneration caused by activities, was the primary cause of enthesopathy formation. Considering the difficulties of reliably ageing adult human skeletal remains, this is a major issue for studies of activity using enthesopathies. Am J Phys Anthropol, 2010. © 2009 Wiley‐Liss, Inc.     

Intra‐ and interpopulation genetic differentiation and gene flow in a group of isolated populations of Bradybaena fruticum (O. F. Müller, 1774) in South Poland

Intra‐ and interpopulation variation was studied, by means of cellulose acetate allozyme electrophoresis, on 16 populations of helicoid snail Bradybaena fruticum (O. F. Müller, 1774) in South Poland. Four enzyme systems, coded by seven loci, were analysed. Calculated with Fisher's technique and Ohta's D‐statistics, four cases of linkage disequilibrium were detected, reflecting population subdivision. The mean number of alleles per locus equalled 2.16 and the mean expected heterozygosity was 0.287. Exact multipopulation and multilocus tests for Hardy–Weinberg equilibrium indicated a statistically significant homozygote excess in all the loci and all populations but three. Each population, however, was at Hardy–Weinberg equilibrium for most loci, though the values of f (F_IS) were usually high. Homozygote excess was ascribed partly to inbreeding and partly to Wahlund's effect (spatial subdivision of population; at least two cohorts of adult, reproducing snails), disrupting selection in this polymorphic species not excluded. F‐statistics showed relatively low values of θ (F_ST ; mean for all loci = 0.224) and those of Nm usually below 1 (mean 0.866). Pairwise values of either θ or Cavalli‐Sforza and Edwards arc distance were statistically significantly associated with geographic distances. Contrary to this, no geographic pattern of interpopulation differences was detected by correspondence analysis on allele frequencies, non‐linear multidimensional scaling, UPGMA clustering or neighbour‐joining trees constructed on θ and Cavalli‐Sforza and Edwards arc distance. Accordingly, some most distant populations were more similar to one another than the close ones.     

塔克尔莫乎尔沙漠银沙槐群落主要植物的种间关系

根据野外调查的样地数据资料,运用2×2列联表的Fisher精确检验、Pearson相关系数和Spearman秩相关系数检验,并结合DCA排序,分析塔克尔莫乎尔沙漠银沙槐群落主要植物种群之间的种间关系。结果表明:Fisher精确检验有3个种对呈显著正关联,3个种对呈显著负关联;Pearson相关系数检验有1个种对呈显著正相关,12个种对呈显著负相关;Spearman秩相关系数检验,有14个种对存在显著相关,其中负相关13对,占所有种对数的14.29%,正相关1对,占所有种对数的1.1%。银沙槐群落种间关系相对松散,反映出植物群落随着环境变化其物种组成也发生相应变化,正向着相对稳定独立的无关联方向发展。     

Nonparametric Two-Sample Tests for General Clinical Data

Starting from the discussion of a practical example a unifying concept for the derivation of meaningfully interpretable nonparametric tests for the two-sample case is developed which may well be adapted for other designs, too. This methodology covers other well-known procedures, e.g. Fisher's exact test, the Wilcoxon-Mann-Whitney and Gehan's tests, and may furthermore be extended to all situations sharing the same fundamental structural property of the sample space, namely its strict order induced by the substantial problem under study. The resulting test procedure is discussed for a randomization argument, exact and approximate, as well as for the general specific test problem. A numerical example is provided.     

Facultative and non‐facultative sex ratio adjustments in a dimorphic bird species

If parental allocation to each offspring sex has the same cost/benefit ratio, Fisher's hypothesis predicts a sex ratio biased towards the cheaper sex. However, in dimorphic birds there is little evidence for this, especially at hatching. We investigated the pre‐fledgling 1) sex ratio, 2) body condition and 3) sex‐differential mortality in a population of the glossy ibis Plegadis falcinellus, in southern Spain between 2001 and 2011. We defined two age groups for the period between hatching and fledging. We also compared pre‐fledgling with the autumn sex ratio. Metabolic rates were estimated by the doubly labeled water (DLW) technique to establish that sons (the bigger sex) were 18% more energy demanding than daughters, and to compute the predicted Fisher's sex ratio (0.465). As population size increased between years, body condition decreased in both sexes, and mortality increased more for daughters than sons prior to fledging. At the same time, the proportion of males among chicks close to fledging increased (average sex ratio: 0.606) while the proportion close to hatching decreased (average sex ratio: 0.434, in line with Fisher's prediction). Furthermore, the proportions of males at fledging and the following autumn were negatively correlated across years. We suggest that, as population density increased and conditions worsened the larger sex had relatively higher survival. These differences in survival produce a shift from a facultative female‐biased sex ratio at hatching into a non‐facultative male‐biased sex ratio of fledglings. Additionally, the excess of males at fledging was counterbalanced by sex‐related dispersal during the autumn. Overall, glossy ibis sex ratio is a product of a combination of facultative and non‐facultative adjustments triggered by environmental conditions, driven by rapid population growth, and mediated by highly interrelated life‐history traits such as body condition, mortality, and dispersal.     

Common pitfalls when testing additivity of treatment mixtures with chi‐square analyses

Studying interactions of multiple pesticides applied simultaneously in a mixture is a common task in phytopathology. Statistical methods are employed to test whether the treatment components influence each other's efficacy in a promotive or inhibitory way (synergistic or antagonistic interaction) or rather act independent of one another (additivity). The trouble is that widely used procedures based on chi‐square tests are often seriously flawed, either because people apply them in a preposterous way or because the method simply does not fit the problem at hand. Browsing recent volumes of entomological journals, we found that numerous researchers have (in all likelihood unwittingly) analysed their data as if they had had a sample size of 100 or, equally bad, a sample size of one! We show how to avoid such poor practices and further argue that chi‐square testing is, even if applied correctly (meaning that no technical errors are made), a limited purpose tool for assessing treatment interactions.     

Testing for Homogeneity in Meta‐Analysis I. The One‐Parameter Case: Standardized Mean Difference

Summary Meta‐analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to warrant their combination into an overall result. Cochran’s Q statistic is frequently used for this homogeneity test. It is often assumed that Q follows a chi‐square distribution under the null hypothesis of homogeneity, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. Here, we present an expansion for the mean of Q under the null hypothesis that is valid when the effect and the weight for each study depend on a single parameter, but for which neither normality nor independence of the effect and weight estimators is needed. This expansion represents an order O(1/n) correction to the usual chi‐square moment in the one‐parameter case. We apply the result to the homogeneity test for meta‐analyses in which the effects are measured by the standardized mean difference (Cohen’s d‐statistic). In this situation, we recommend approximating the null distribution of Q by a chi‐square distribution with fractional degrees of freedom that are estimated from the data using our expansion for the mean of Q. The resulting homogeneity test is substantially more accurate than the currently used test. We provide a program available at the Paper Information link at the Biometrics website http://www.biometrics.tibs.org for making the necessary calculations.     

An Investigation on the Allelic Chi‐Square Test Used in Genetic Association Studies

Case‐control studies are primary study designs used in genetic association studies. Sasieni (Biometrics 1997, 53, 1253–1261) pointed out that the allelic chi‐square test used in genetic association studies is invalid when Hardy‐Weinberg equilibrium (HWE) is violated in a combined population. It is important to know how much type I error rate is deviated from the nominal level under violated HWE. We examine bounds of type I error rate of the allelic chi‐square test. We also investigate power of the goodness‐of‐fit test for HWE which can be used as a guideline for selecting an appropriate test between the allelic chi‐square test and the modified allelic chi‐square test, the latter of which was proposed for cases of violated HWE. In small samples, power is not large enough to detect the Wright's inbreeding model of small values of inbreeding coefficient. Therefore, when the null hypothesis of HWE is barely accepted, the modified test should be considered as an alternative method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Species co‐occurrence analysis: pairwise versus matrix‐level approaches

Veech (2013, Global Ecology and Biogeography, 22 , 252–260) introduced a formula to calculate the probability of two species co‐occurring in various sites under the assumption of statistical independence between the two distributional patterns. He presented his model as a new procedure, a ‘pairwise approach’, different from analyses of whole presence–absence matrices to examine patterns of co‐occurrence. Here I show that: (1) Veech's method is identical to Fisher's exact test, a standard procedure for measuring the statistical association between two discrete variables; (2) in a broad sense, the pairwise approach is very similar to early analyses of spatial association, such as the one advanced by Forbes in 1907; (3) implicit in Veech's formula is a sampling scheme that is indistinguishable from well‐known matrix‐level null models that randomize the distribution of species among equiprobable sites; (4) pairwise co‐occurrence patterns can be analysed using any matrix‐level null model, so pairwise comparisons are not limited to using Veech's formula. The methodological distinction that Veech proposed between pairwise and matrix‐level approaches does not in fact exist, although the conceptual distinction between the two approaches is still a debated topic.     

Characterization of microsatellite markers for Couch's spadefoot toad (Scaphiopus couchii) and cross‐amplification in other species of the family Scaphiopodidae

I developed 12 di‐ and tetranucleotide microsatellite loci for Couch's spadefoot toad (Scaphiopus couchii). These loci have 3–37 alleles per locus and observed heterozygosities ranging from 0.157 to 0.941 among 85 individuals from four populations. Global and within‐population exact tests do not reveal departure from Hardy–Weinberg expectations and all loci pairs are in linkage equilibrium. These independent markers will be useful for studies of population structure and kinship in this commonly studied amphibian. Additionally, several of these loci may be applicable for studies of other North American toads of the family Scaphiopodidae.     

Prevalence of oral mucosal lesions in institutionalized elderly people in Mashhad, Northeast Iran

doi: 10.1111/j.1741‐2358.2011.00588.x
Prevalence of oral mucosal lesions in institutionalized elderly people in Mashhad, Northeast Iran Objective: The aim of this study was to determine the prevalence of oral mucosal lesions in institutionalized elderly people in Mashhad, northeast of Iran. Background: This study was conducted to assess the prevalence of oral lesions in the institutionalized elderly. Methods: In this survey, we studied all of the nursing homes in Mashhad; a total of five encompassing 237 residents. The subjects were examined and lesions recorded in a designed checklist. T‐test, chi‐square and Fisher’s exact tests were used for the analysis. Results: The mean age of the patients was 79.59 ± 8.88. Ninety‐eight per cent of cases had at least one oral mucosal lesion. The most common lesions were fissured tongue (66.5%), atrophic glossitis (48.8%), sublingual varicosity (42%) and xerostomia (38%). There was no significant difference in the prevalence of denture‐related lesions (DRLs) between men and women (p > 0.05). Xerostomia was more prevalent in 70–79‐year‐old than in 60–69‐year‐old subjects. No case of oral malignant lesion was detected. Discussion: These findings revealed a higher prevalence of oral mucosal lesions in Mashhad city compared with other studies conducted in other major cities in Iran and abroad. The results emphasise the necessity of national programmes towards oral health promotion.     

Asymptotic distribution of the lod score for familial data

Using a linkage model with mixed parental mating types between a trait locus and a marker locus the asymptotic null distribution of the statistic U = 2ln(10)Z(theta) was stimulated and compared to the chi square type distribution function 1/2 + 1/2 Pr [chi 2(1) less than mu]. The stimulation results show that the chi square approximation fits the asymptotic null distribution well when both loci are predominated by either one of the two alleles at their loci, respectively, or the linkage phase tends to disequilibrium.     

Hommel's procedure in linear time

Hommel's and Hochberg's procedures for familywise error control are both derived as shortcuts in a closed testing procedure with the Simes local test. Hommel's shortcut is exact but takes quadratic time in the number of hypotheses. Hochberg's shortcut takes only linear time after the P‐values are sorted, but is conservative. In this paper, we present an exact shortcut in linear time on sorted P‐values, combining the strengths of both procedures. The novel shortcut also applies to a robust variant of Hommel's procedure that does not require the assumption of the Simes inequality.