Test Statistics (test + statistics)

Distribution by Scientific Domains

Kinds of Test Statistics

  • proposed test statistics

  • Selected Abstracts


    EVOLUTION, Issue 10 2009
    Brittny Calsbeek
    A central assumption of quantitative genetic theory is that the breeder's equation (R=GP,1S) accurately predicts the evolutionary response to selection. Recent studies highlight the fact that the additive genetic variance,covariance matrix (G) may change over time, rendering the breeder's equation incapable of predicting evolutionary change over more than a few generations. Although some consensus on whether G changes over time has been reached, multiple, often-incompatible methods for comparing G matrices are currently used. A major challenge of G matrix comparison is determining the biological relevance of observed change. Here, we develop a "selection skewers"G matrix comparison statistic that uses the breeder's equation to compare the response to selection given two G matrices while holding selection intensity constant. We present a bootstrap algorithm that determines the significance of G matrix differences using the selection skewers method, random skewers, Mantel's and Bartlett's tests, and eigenanalysis. We then compare these methods by applying the bootstrap to a dataset of laboratory populations of Tribolium castaneum. We find that the results of matrix comparison statistics are inconsistent based on differing a priori goals of each test, and that the selection skewers method is useful for identifying biologically relevant G matrix differences. [source]

    The Limiting Density of Unit Root Test Statistics: A Unifying Technique

    Mithat Gonen
    In this note we introduce a simple principle to derive a constructive expression for the density of the limiting distribution, under the null hypothesis, of unit root statistics for an AR(1)-process in a variety of situations. We consider the case of unknown mean and reconsider the well-known situation where the mean is zero. For long-range dependent errors we indicate how the principle might apply again. We also show that in principle the method also works for a near unit root case. Weak convergence and subsequent Karhunen-Loeve expansion of the weak limit of the partial sum process of the errors plays an important role, along with the evaluation of a certain normal type integral with complex mean and variance. For independent and long range dependent errors this weak limit is ordinary and fractional Brownian motion respectively. AMS 1991 subject classification. Primary 62M10; secondary 62E20. [source]

    Trimmed Weighted Simes' Test for Two One-Sided Hypotheses With Arbitrarily Correlated Test Statistics

    Werner Brannath
    Abstract The two-sided Simes test is known to control the type I error rate with bivariate normal test statistics. For one-sided hypotheses, control of the type I error rate requires that the correlation between the bivariate normal test statistics is non-negative. In this article, we introduce a trimmed version of the one-sided weighted Simes test for two hypotheses which rejects if (i) the one-sided weighted Simes test rejects and (ii) both p -values are below one minus the respective weighted Bonferroni adjusted level. We show that the trimmed version controls the type I error rate at nominal significance level , if (i) the common distribution of test statistics is point symmetric and (ii) the two-sided weighted Simes test at level 2, controls the level. These assumptions apply, for instance, to bivariate normal test statistics with arbitrary correlation. In a simulation study, we compare the power of the trimmed weighted Simes test with the power of the weighted Bonferroni test and the untrimmed weighted Simes test. An additional result of this article ensures type I error rate control of the usual weighted Simes test under a weak version of the positive regression dependence condition for the case of two hypotheses. This condition is shown to apply to the two-sided p -values of one- or two-sample t -tests for bivariate normal endpoints with arbitrary correlation and to the corresponding one-sided p -values if the correlation is non-negative. The Simes test for such types of bivariate t -tests has not been considered before. According to our main result, the trimmed version of the weighted Simes test then also applies to the one-sided bivariate t -test with arbitrary correlation. [source]

    Testing association for markers on the X chromosome,

    Gang Zheng
    Abstract Test statistics for association between markers on autosomal chromosomes and a disease have been extensively studied. No research has been reported on performance of such test statistics for association on the X chromosome. With 100,000 or more single-nucleotide polymorphisms (SNPs) available for genome-wide association studies, thousands of them come from the X chromosome. The X chromosome contains rich information about population history and linkage disequilibrium. To identify X-linked marker susceptibility to a disease, it is important to study properties of various statistics that can be used to test for association on the X chromosome. In this article, we compare performance of several approaches for testing association on the X chromosome, and examine how departure from Hardy-Weinberg equilibrium would affect type I error and power of these association tests using X-linked SNPs. The results are applied to the X chromosome of Klein et al. [2005], a genome-wide association study with 100K SNPs for age-related macular degeneration. We found that a SNP (rs10521496) covered by DIAPH2, known to cause premature ovarian failure (POF) in females, is associated with age-related macular degeneration. Genet. Epidemiol. 2007. Published 2007 Wiley-Liss, Inc. [source]

    A minimum sample size required from Schmidt hammer measurements

    Tomasz Niedzielski
    Abstract The Schmidt hammer is a useful tool applied by geomorphologists to measure rock strength in field conditions. The essence of field application is to obtain a sufficiently large dataset of individual rebound values, which yields a meaningful numerical value of mean strength. Although there is general agreement that a certain minimum sample size is required to proceed with the statistics, the choice of size (i.e. number of individual impacts) was usually intuitive and arbitrary. In this paper we show a simple statistical method, based on the two-sample Student's t -test, to objectively estimate the minimum number of rebound measurements. We present the results as (1) the ,mean' and ,median' solutions, each providing a single estimate value, and (2) the empirical probability distribution of such estimates based on many field samples. Schmidt hammer data for 14 lithologies, 13,81 samples for each, with each sample consisting of 40 individual readings, have been evaluated, assuming different significance levels. The principal recommendations are: (1) the recommended minimum sample size for weak and moderately strong rock is 25; (2) a sample size of 15 is sufficient for sandstones and shales; (3) strong and coarse rocks require 30 readings at a site; (4) the minimum sample size may be reduced by one-third if the context of research allows for higher significance level for test statistics. Interpretations based on less than 10 readings from a site should definitely be avoided. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    GMM with Weak Identification

    ECONOMETRICA, Issue 5 2000
    James H. Stock
    This paper develops asymptotic distribution theory for GMM estimators and test statistics when some or all of the parameters are weakly identified. General results are obtained and are specialized to two important cases: linear instrumental variables regression and Euler equations estimation of the CCAPM. Numerical results for the CCAPM demonstrate that weak-identification asymptotics explains the breakdown of conventional GMM procedures documented in previous Monte Carlo studies. Confidence sets immune to weak identification are proposed. We use these results to inform an empirical investigation of various CCAPM specifications; the substantive conclusions reached differ from those obtained using conventional methods. [source]

    A critical evaluation of genomic control methods for genetic association studies

    Tony Dadd
    Abstract Population stratification is an important potential confounder of genetic case-control association studies. For replication studies, limited availability of samples may lead to imbalanced sampling from heterogeneous populations. Genomic control (GC) can be used to correct ,2 test statistics which are presumed to be inflated by a factor ,; this may be estimated by a summary ,2 value (,median or ,mean) from a set of unlinked markers. Many studies applying GC methods have used fewer than 50 unlinked markers and an important question is whether this can adequately correct for population stratification. We assess the behavior of GC methods in imbalanced case-control studies using simulation. SNPs are sampled from two subpopulations with intra-continental levels of FST (,0.005) and sampling schemata ranging from balanced to completely imbalanced between subpopulations. The sampling properties of ,median and ,mean are explored using 6,1,600 unlinked markers to estimate Type 1 error and power empirically. GC corrections based on the ,2 -distribution (GCmedian or GCmean) can be anti-conservative even when more than 100 single nucleotide polymorphisms (SNPs) are genotyped and realistic levels of population stratification exist. The GCF procedure performs well over a wider range of conditions, only becoming anti-conservative at low levels of , and with fewer than 25 SNPs genotyped. A substantial loss of power can arise when population stratification is present, but this is largely independent of the number of SNPs used. A literature survey shows that most studies applying GC have used GCmedian or GCmean, rather than GCF, which is the most appropriate GC correction method. Genet. Epidemiol. 2009. © 2008 Wiley Liss, Inc. [source]

    Bivariate combined linkage and association mapping of quantitative trait loci

    Jeesun Jung
    Abstract In this paper, bivariate/multivariate variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL), based on combinations of pedigree and population data. Suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In the region, multiple markers such as single nucleotide polymorphisms are typed. Two regression models, "genotype effect model" and "additive effect model", are proposed to model the association between the markers and the trait locus. The linkage information, i.e., recombination fractions between the QTL and the markers, is modeled in the variance and covariance matrix. By analytical formulae, we show that the "genotype effect model" can be used to model the additive and dominant effects simultaneously; the "additive effect model" only takes care of additive effect. Based on the two models, F -test statistics are proposed to test association between the QTL and markers. By analytical power analysis, we show that bivariate models can be more powerful than univariate models. For moderate-sized samples, the proposed models lead to correct type I error rates; and so the models are reasonably robust. As a practical example, the method is applied to analyze the genetic inheritance of rheumatoid arthritis for the data of The North American Rheumatoid Arthritis Consortium, Problem 2, Genetic Analysis Workshop 15, which confirms the advantage of the proposed bivariate models. Genet. Epidemiol. 2008. © 2008 Wiley-Liss, Inc. [source]

    Testing association for markers on the X chromosome,

    Gang Zheng
    Abstract Test statistics for association between markers on autosomal chromosomes and a disease have been extensively studied. No research has been reported on performance of such test statistics for association on the X chromosome. With 100,000 or more single-nucleotide polymorphisms (SNPs) available for genome-wide association studies, thousands of them come from the X chromosome. The X chromosome contains rich information about population history and linkage disequilibrium. To identify X-linked marker susceptibility to a disease, it is important to study properties of various statistics that can be used to test for association on the X chromosome. In this article, we compare performance of several approaches for testing association on the X chromosome, and examine how departure from Hardy-Weinberg equilibrium would affect type I error and power of these association tests using X-linked SNPs. The results are applied to the X chromosome of Klein et al. [2005], a genome-wide association study with 100K SNPs for age-related macular degeneration. We found that a SNP (rs10521496) covered by DIAPH2, known to cause premature ovarian failure (POF) in females, is associated with age-related macular degeneration. Genet. Epidemiol. 2007. Published 2007 Wiley-Liss, Inc. [source]

    Gene-dropping vs. empirical variance estimation for allele-sharing linkage statistics

    Jeesun Jung
    Abstract In this study, we compare the statistical properties of a number of methods for estimating P -values for allele-sharing statistics in non-parametric linkage analysis. Some of the methods are based on the normality assumption, using different variance estimation methods, and others use simulation (gene-dropping) to find empirical distributions of the test statistics. For variance estimation methods, we consider the perfect variance approximation and two empirical variance estimates. The simulation-based methods are gene-dropping with and without conditioning on the observed founder alleles. We also consider the Kong and Cox linear and exponential models and a Monte Carlo method modified from a method for finding genome-wide significance levels. We discuss the analytical properties of these various P -value estimation methods and then present simulation results comparing them. Assuming that the sample sizes are large enough to justify a normality assumption for the linkage statistic, the best P -value estimation method depends to some extent on the (unknown) genetic model and on the types of pedigrees in the sample. If the sample sizes are not large enough to justify a normality assumption, then gene-dropping is the best choice. We discuss the differences between conditional and unconditional gene-dropping. Genet. Epidemiol. 2006. © 2006 Wiley-Liss, Inc. [source]

    Resampling-based multiple hypothesis testing procedures for genetic case-control association studies,

    Bingshu E. Chen
    Abstract In case-control studies of unrelated subjects, gene-based hypothesis tests consider whether any tested feature in a candidate gene,single nucleotide polymorphisms (SNPs), haplotypes, or both,are associated with disease. Standard statistical tests are available that control the false-positive rate at the nominal level over all polymorphisms considered. However, more powerful tests can be constructed that use permutation resampling to account for correlations between polymorphisms and test statistics. A key question is whether the gain in power is large enough to justify the computational burden. We compared the computationally simple Simes Global Test to the min,P test, which considers the permutation distribution of the minimum p -value from marginal tests of each SNP. In simulation studies incorporating empirical haplotype structures in 15 genes, the min,P test controlled the type I error, and was modestly more powerful than the Simes test, by 2.1 percentage points on average. When disease susceptibility was conferred by a haplotype, the min,P test sometimes, but not always, under-performed haplotype analysis. A resampling-based omnibus test combining the min,P and haplotype frequency test controlled the type I error, and closely tracked the more powerful of the two component tests. This test achieved consistent gains in power (5.7 percentage points on average), compared to a simple Bonferroni test of Simes and haplotype analysis. Using data from the Shanghai Biliary Tract Cancer Study, the advantages of the newly proposed omnibus test were apparent in a population-based study of bile duct cancer and polymorphisms in the prostaglandin-endoperoxide synthase 2 (PTGS2) gene. Genet. Epidemiol. 2006. Published 2006 Wiley-Liss, Inc. [source]

    Haplotype association analysis for late onset diseases using nuclear family data

    Chun Li
    Abstract In haplotype-based association studies for late onset diseases, one attractive design is to use available unaffected spouses as controls (Valle et al. [1998] Diab. Care 21:949,958). Given cases and spouses only, the standard expectation-maximization (EM) algorithm (Dempster et al. [1977] J. R. Stat. Soc. B 39:1,38) for case-control data can be used to estimate haplotype frequencies. But often we will have offspring for at least some of the spouse pairs, and offspring genotypes provide additional information about the haplotypes of the parents. Existing methods may either ignore the offspring information, or reconstruct haplotypes for the subjects using offspring information and discard data from those whose haplotypes cannot be reconstructed with high confidence. Neither of these approaches is efficient, and the latter approach may also be biased. For case-control data with some subjects forming spouse pairs and offspring genotypes available for some spouse pairs or individuals, we propose a unified, likelihood-based method of haplotype inference. The method makes use of available offspring genotype information to apportion ambiguous haplotypes for the subjects. For subjects without offspring genotype information, haplotypes are apportioned as in the standard EM algorithm for case-control data. Our method enables efficient haplotype frequency estimation using an EM algorithm and supports probabilistic haplotype reconstruction with the probability calculated based on the whole sample. We describe likelihood ratio and permutation tests to test for disease-haplotype association, and describe three test statistics that are potentially useful for detecting such an association. Genet. Epidemiol. 2006. © 2006 Wiley-Liss, Inc. [source]

    Analysis of single-locus tests to detect gene/disease associations,

    Kathryn Roeder
    Abstract A goal of association analysis is to determine whether variation in a particular candidate region or gene is associated with liability to complex disease. To evaluate such candidates, ubiquitous Single Nucleotide Polymorphisms (SNPs) are useful. It is critical, however, to select a set of SNPs that are in substantial linkage disequilibrium (LD) with all other polymorphisms in the region. Whether there is an ideal statistical framework to test such a set of ,tag SNPs' for association is unknown. Compared to tests for association based on frequencies of haplotypes, recent evidence suggests tests for association based on linear combinations of the tag SNPs (Hotelling T2 test) are more powerful. Following this logical progression, we wondered if single-locus tests would prove generally more powerful than the regression-based tests? We answer this question by investigating four inferential procedures: the maximum of a series of test statistics corrected for multiple testing by the Bonferroni procedure, TB, or by permutation of case-control status, TP; a procedure that tests the maximum of a smoothed curve fitted to the series of of test statistics, TS; and the Hotelling T2 procedure, which we call TR. These procedures are evaluated by simulating data like that from human populations, including realistic levels of LD and realistic effects of alleles conferring liability to disease. We find that power depends on the correlation structure of SNPs within a gene, the density of tag SNPs, and the placement of the liability allele. The clearest pattern emerges between power and the number of SNPs selected. When a large fraction of the SNPs within a gene are tested, and multiple SNPs are highly correlated with the liability allele, TS has better power. Using a SNP selection scheme that optimizes power but also requires a substantial number of SNPs to be genotyped (roughly 10,20 SNPs per gene), power of TP is generally superior to that for the other procedures, including TR. Finally, when a SNP selection procedure that targets a minimal number of SNPs per gene is applied, the average performances of TP and TR are indistinguishable. Genet. Epidemiol. © 2005 Wiley-Liss, Inc. [source]

    Power and robustness of linkage tests for quantitative traits in general pedigrees

    Wei-Min Chen
    Abstract There are numerous statistical methods for quantitative trait linkage analysis in human studies. An ideal such method would have high power to detect genetic loci contributing to the trait, would be robust to non-normality in the phenotype distribution, would be appropriate for general pedigrees, would allow the incorporation of environmental covariates, and would be appropriate in the presence of selective sampling. We recently described a general framework for quantitative trait linkage analysis, based on generalized estimating equations, for which many current methods are special cases. This procedure is appropriate for general pedigrees and easily accommodates environmental covariates. In this report, we use computer simulations to investigate the power and robustness of a variety of linkage test statistics built upon our general framework. We also propose two novel test statistics that take account of higher moments of the phenotype distribution, in order to accommodate non-normality. These new linkage tests are shown to have high power and to be robust to non-normality. While we have not yet examined the performance of our procedures in the context of selective sampling via computer simulations, the proposed tests satisfy all of the other qualities of an ideal quantitative trait linkage analysis method. Genet. Epidemiol. © 2004 Wiley-Liss, Inc. [source]

    Genetic association tests with age at onset

    L. Hsu
    Abstract Many diseases or traits exhibit a varying age at onset. Recent data examples of prostate cancer and childhood diabetes show that compared to simply treating the disease outcome as affected vs. unaffected, incorporation of age-at-onset information into the transmission/disequilibrium type of test (TDT) does not appear to change the results much. In this paper, we evaluate the power of TDT as a function of age at onset, and show that age-at-onset information is most useful when the disease is common, or the relative risk associated with the high-risk genotype varies with age. Moreover, an extremely old unaffected subject can contribute substantially to the power of the TDT, sometimes as much as old-onset subjects. We propose a modified test statistic for testing no association between the marker at the candidate locus and age at onset. The simulation study was conducted to evaluate the finite sample properties of proposed and the TDT test statistics under various sampling schemes for trios of parents and offspring, as well as for sibling clusters where unaffected siblings were used as controls. Genet Epidemiol 24:118,127, 2003. © 2003 Wiley-Liss, Inc. [source]

    Tests for genetic association using family data

    Mei-Chiung Shih
    Abstract We use likelihood-based score statistics to test for association between a disease and a diallelic polymorphism, based on data from arbitrary types of nuclear families. The Nonfounder statistic extends the transmission disequilibrium test (TDT) to accommodate affected and unaffected offspring, missing parental genotypes, phenotypes more general than qualitative traits, such as censored survival data and quantitative traits, and residual correlation of phenotypes within families. The Founder statistic compares observed or inferred parental genotypes to those expected in the general population. Here the genotypes of affected parents and those with many affected offspring are weighted more heavily than unaffected parents and those with few affected offspring. We illustrate the tests by applying them to data on a polymorphism of the SRD5A2 gene in nuclear families with multiple cases of prostate cancer. We also use simulations to compare the power of these family-based statistics to that of the score statistic based on Cox's partial likelihood for censored survival data, and find that the family-based statistics have considerably more power when there are many untyped parents. The software program FGAP for computing test statistics is available at http://www.stanford.edu/dept/HRP/epidemiology/FGAP. Genet. Epidemiol. 22:128,145, 2002. © 2002 Wiley-Liss, Inc. [source]

    Inferences for Selected Location Quotients with Applications to Health Outcomes

    Gemechis Dilba Djira
    The location quotient (LQ) is an index frequently used in geography and economics to measure the relative concentration of activities. This quotient is calculated in a variety of ways depending on which group is used as a reference. Here, we focus on a simultaneous inference for the ratios of the individual proportions to the overall proportion based on binomial data. This is a multiple comparison problem and inferences for LQs with adjustments for multiplicity have not been addressed before. The comparisons are negatively correlated. The quotients can be simultaneously tested against unity, and simultaneous confidence intervals can be constructed for the LQs based on existing probability inequalities and by directly using the asymptotic joint distribution of the associated test statistics. The proposed inferences are appropriate for analysis based on sample surveys. Two real data sets are used to demonstrate the application of multiplicity-adjusted LQs. A simulation study is also carried out to assess the performance of the proposed methods to achieve a nominal coverage probability. For the LQs considered, the coverage of the simple Bonferroni-adjusted Fieller intervals for LQs is observed to be almost as good as the coverage of the method that directly takes the correlations into account. El cociente de localización (LQ) es un índice de uso frecuente en las disciplinas de Geografía y Economía para medir la concentración relativa de actividades. El cálculo del cociente se realiza de una variedad de formas, dependiendo del grupo que se utilice como referencia. El presente artículo aborda el problema de realizar inferencias simultáneas con tasas que describen proporciones individuales en relación a proporciones globales, para el caso de datos en escala binomial. Este problema puede ser caracterizado como uno de tipo de comparaciones múltiples (multiple comparison problem). Salvo el estudio presente, no existen precedentes de métodos diseñados para realizar inferencias de LQ que estén ajustados para abordar comparaciones múltiples. Las comparaciones están correlacionadas negativamente. Los cocientes pueden ser evaluados simultáneamente para verificar la propiedad de unidad (unity), y se pueden construir intervalos de confianza simultáneos para un LQ basado en la desigualdad de probabilidades existentes y por medio del uso directo de la distribución asintótica conjunta (asymtotic joint distribution) de los test o pruebas estadísticas asociadas. El tipo de inferencias propuestas por los autores son las adecuadas para el análisis de encuestas por muestreo. Para demostrar la aplicación del LQ desarrollado por el estudio, se utilizan dos conjuntos de datos del mundo real. Asimismo se lleva a cabo un estudio de simulación para evaluar el desempeño de los métodos propuestos con el fin de alcanzar una probabilidad de cobertura nominal (nominal coverage). Para los LQs seleccionados, la cobertura de los intervalos de confianza simples Fieller-Bonferroni ajustados para LQ, producen resultados casi tan buenos como la cobertura de métodos que toma en cuenta las correlaciones directamente. [source]

    Random fields,Union intersection tests for detecting functional connectivity in EEG/MEG imaging

    HUMAN BRAIN MAPPING, Issue 8 2009
    Felix Carbonell
    Abstract Electrophysiological (EEG/MEG) imaging challenges statistics by providing two views of the same underlying spatio-temporal brain activity: a topographic view (EEG/MEG) and tomographic view (EEG/MEG source reconstructions). It is a common practice that statistical parametric mapping (SPM) for these two situations is developed separately. In particular, assessing statistical significance of functional connectivity is a major challenge in these types of studies. This work introduces statistical tests for assessing simultaneously the significance of spatio-temporal correlation structure between ERP/ERF components as well as that of their generating sources. We introduce a greatest root statistic as the multivariate test statistic for detecting functional connectivity between two sets of EEG/MEG measurements at a given time instant. We use some new results in random field theory to solve the multiple comparisons problem resulting from the correlated test statistics at each time instant. In general, our approach using the union-intersection (UI) principle provides a framework for hypothesis testing about any linear combination of sensor data, which allows the analysis of the correlation structure of both topographic and tomographic views. The performance of the proposed method is illustrated with real ERP data obtained from a face recognition experiment. Hum Brain Mapp 2009. © 2009 Wiley-Liss, Inc. [source]

    Permutation tests for factorially designed neuroimaging experiments

    HUMAN BRAIN MAPPING, Issue 3 2004
    John Suckling
    Abstract Permutation methods for analysis of functional neuroimaging data acquired as factorially designed experiments are described and validated. The F ratio was estimated for main effects and interactions at each voxel in standard space. Critical values corresponding to probability thresholds were derived from a null distribution sampled by appropriate permutation of observations. Spatially informed, cluster-level test statistics were generated by applying a preliminary probability threshold to the voxel F maps and then computing the sum of voxel statistics in each of the resulting three-dimensional clusters, i.e., cluster "mass." Using simulations comprising two between- or within-subject factors each with two or three levels, contaminated by Gaussian and non-normal noise, the voxel-wise permutation test was compared to the standard parametric F test and to the performance of the spatially informed statistic using receiver operating characteristic (ROC) curves. Validity of the permutation-testing algorithm and software is endorsed by almost identical performance of parametric and permutation tests of the voxel-level F statistic. Permutation testing of suprathreshold voxel cluster mass, however, was found to provide consistently superior sensitivity to detect simulated signals than either of the voxel-level tests. The methods are also illustrated by application to an experimental dataset designed to investigate effects of antidepressant drug treatment on brain activation by implicit sad facial affect perception in patients with major depression. Antidepressant drug effects in left amygdala and ventral striatum were detected by this software for an interaction between time (within-subject factor) and group (between-subject factor) in a representative two-way factorial design. Hum. Brain Mapping 22:193,205, 2004. © 2004 Wiley-Liss, Inc. [source]

    Exact multivariate tests for brain imaging data

    HUMAN BRAIN MAPPING, Issue 1 2002
    Rita Almeida
    Abstract In positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) data sets, the number of variables is larger than the number of observations. This fact makes application of multivariate linear model analysis difficult, except if a reduction of the data matrix dimension is performed prior to the analysis. The reduced data set, however, will in general not be normally distributed and therefore, the usual multivariate tests will not be necessarily applicable. This problem has not been adequately discussed in the literature concerning multivariate linear analysis of brain imaging data. No theoretical foundation has been given to support that the null distributions of the tests are as claimed. Our study addresses this issue by introducing a method of constructing test statistics that follow the same distributions as when the data matrix is normally distributed. The method is based on the invariance of certain tests over a large class of distributions of the data matrix. This implies that the method is very general and can be applied for different reductions of the data matrix. As an illustration we apply a test statistic constructed by the method now presented to test a multivariate hypothesis on a PET data set. The test rejects the null hypothesis of no significant differences in measured brain activity between two conditions. The effect responsible for the rejection of the hypothesis is characterized using canonical variate analysis (CVA) and compared with the result obtained by using univariate regression analysis for each voxel and statistical inference based on size of activations. The results obtained from CVA and the univariate method are similar. Hum. Brain Mapping 16:24,35, 2002. © 2002 Wiley-Liss, Inc. [source]

    Inconsistencies between reported test statistics and p- values in two psychiatry journals

    David Berle
    Abstract A recent survey of the British Medical Journal (BMJ) and Nature revealed that inconsistencies in reported statistics were common. We sought to replicate that survey in the psychiatry literature. We checked the consistency of reported t -test, F -test and ,2 -test values with their corresponding p -values in the 2005 issues of the Australian and New Zealand Journal of Psychiatry (ANZJP) and compared this with the issues of the ANZJP from 2000, and with a similar journal, Acta Psychiatrica Scandinavica (APS). A reported p -value was ,inconsistent' if it differed (at its reported number of decimal places) from our calculated p -values (using three different software packages), which we based on the reported test statistic and degrees of freedom. Of the 546 results that we checked, 78 (14.3%) of the p -values were inconsistent with the corresponding degrees of freedom and test statistic. Similar rates of inconsistency were found in APS and ANZJP, and when comparing the ANZJP between 2000 and 2005. The percentages of articles with at least one inconsistency were 8.5% for ANZJP 2005, 9.9% for ANZJP 2000 and 12.1% for APS. We conclude that inconsistencies in p -values are common and may reflect errors of analysis and rounding, typographic errors or typesetting errors. Suggestions for reducing the occurrence of such inconsistencies are provided. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Deterministic assembly of land snail communities according to species size and diet

    Brandon Schamp
    Summary 1.,We investigated whether coexisting snail species in 145 treeless fen communities in the Western Carpathian Mountains differed more in size and diet than would be expected by chance, as predicted for traits commonly associated with competition and differential resource acquisition under limiting similarity theory. 2.,Contrary to expectations, coexisting snail species were no more different in body size than expected by chance under a null model. However, variation in body size played a significant role in structuring snail communities: coexisting snail species were significantly more similar with respect to body size. 3.,We developed two new test statistics to expand our investigation of limiting similarity to include diet, a nominal trait. We tested whether communities of snails were characterized by a greater richness of diet, and whether different diets were represented more or less evenly within communities. Communities of snails were significantly less evenly distributed than expected by chance, with detritivores being over-represented relative to predatory strategies. 4.,We also examined the effect of water pH and conductivity, herbaceous cover, and bryophyte and vascular plant richness, on these trends by examining how the effect size of our tests varied across these gradients. Convergence in species size increased with increasing habitat pH. Specifically, smaller snail species were over-represented in fen communities in general, and this effect was accentuated in increasingly calcareous fens. 5.,Theory predicts that traits related strongly to environmental conditions are more likely to be convergent. Our findings support this suggestion, as small snail species have an advantage in tolerating freezing conditions over winter when refuges are limited. 6.,These results add to the growing body of literature demonstrating that variation in body size and diet play a strong role in structuring communities, although frequently in ways not predicted by limiting similarity theory. Finally, our results increase our understanding of how species are assembled non-randomly into communities with respect to important traits. [source]

    Computation and analysis of multiple structural change models

    Jushan Bai
    In a recent paper, Bai and Perron (1998) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most least-squares operations of order O(T2) for any number of breaks. Our method can be applied to both pure and partial structural change models. Second, we consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and the errors across segments. Third, we address the issue of testing for structural changes under very general conditions on the data and the errors. Fourth, we address the issue of estimating the number of breaks. Finally, a few empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Assessing the forecasting accuracy of alternative nominal exchange rate models: the case of long memory

    David Karemera
    Abstract This paper presents an autoregressive fractionally integrated moving-average (ARFIMA) model of nominal exchange rates and compares its forecasting capability with the monetary structural models and the random walk model. Monthly observations are used for Canada, France, Germany, Italy, Japan and the United Kingdom for the period of April 1973 through December 1998. The estimation method is Sowell's (1992) exact maximum likelihood estimation. The forecasting accuracy of the long-memory model is formally compared to the random walk and the monetary models, using the recently developed Harvey, Leybourne and Newbold (1997) test statistics. The results show that the long-memory model is more efficient than the random walk model in steps-ahead forecasts beyond 1 month for most currencies and more efficient than the monetary models in multi-step-ahead forecasts. This new finding strongly suggests that the long-memory model of nominal exchange rates be studied as a viable alternative to the conventional models.,,Copyright © 2006 John Wiley & Sons, Ltd. [source]

    New Improved Tests for Cointegration with Structural Breaks

    Joakim Westerlund
    C12; C32; C33 Abstract., This article proposes Lagrange multiplier-based tests for the null hypothesis of no cointegration. The tests are general enough to allow for heteroskedastic and serially correlated errors, deterministic trends, and a structural break of unknown timing in both the intercept and slope. The limiting distributions of the test statistics are derived, and are found to be invariant not only with respect to the trend and structural break, but also with respect to the regressors. A small Monte Carlo study is also conducted to investigate the small-sample properties of the tests. The results reveal that the tests have small size distortions and good power relative to other tests. [source]

    Blockwise empirical entropy tests for time series regressions

    Francesco Bravo
    Abstract., This paper shows how the empirical entropy (also known as exponential likelihood or non-parametric tilting) method can be used to test general parametric hypothesis in time series regressions. To capture the weak dependence of the observations, the paper uses blocking techniques which are also used in the bootstrap literature on time series. Monte Carlo evidence suggests that the proposed test statistics have better finite-sample properties than conventional test statistics such as the Wald statistic. [source]

    The Mathematical Assessment of Long-Range Linguistic Relationships

    Brett Kessler
    Language classification differs from biological cladistics in that monogenesis cannot be assumed. Before a cladogram or family tree can be accepted, linguists must be convinced that the languages are related at all. Morpheme tables, or word lists, provide a good framework for investigating relatedness, but methodologies for quantifying and assessing the data statistically are still being developed. The comparative method furnished a viable statistic, recurrent sound correspondences, but by no means to see whether they exceeded levels expected by chance. Organizing correspondences into contingency tables permitted hypothesis testing, with Monte Carlo resampling methods providing the flexibility to support a wide variety of test statistics, including different ways of computing sound recurrences and phonetic similarity. Thus, techniques from both the comparative method and multilateral comparison can be deployed with rigorous numeric assessment. Experiments seek to increase the power of the tests to explore new hypotheses and verify long-range language relationships. [source]

    Power for detecting genetic divergence: differences between statistical methods and marker loci

    MOLECULAR ECOLOGY, Issue 8 2006
    Abstract Information on statistical power is critical when planning investigations and evaluating empirical data, but actual power estimates are rarely presented in population genetic studies. We used computer simulations to assess and evaluate power when testing for genetic differentiation at multiple loci through combining test statistics or P values obtained by four different statistical approaches, viz. Pearson's chi-square, the log-likelihood ratio G -test, Fisher's exact test, and an FST -based permutation test. Factors considered in the comparisons include the number of samples, their size, and the number and type of genetic marker loci. It is shown that power for detecting divergence may be substantial for frequently used sample sizes and sets of markers, also at quite low levels of differentiation. The choice of statistical method may be critical, though. For multi-allelic loci such as microsatellites, combining exact P values using Fisher's method is robust and generally provides a high resolving power. In contrast, for few-allele loci (e.g. allozymes and single nucleotide polymorphisms) and when making pairwise sample comparisons, this approach may yield a remarkably low power. In such situations chi-square typically represents a better alternative. The G -test without Williams's correction frequently tends to provide an unduly high proportion of false significances, and results from this test should be interpreted with great care. Our results are not confined to population genetic analyses but applicable to contingency testing in general. [source]

    On testing predictions of species relative abundance from maximum entropy optimisation

    OIKOS, Issue 4 2010
    Stephen H. Roxburgh
    A randomisation test is described for assessing relative abundance predictions from the maximum entropy approach to biodiversity. The null model underlying the test randomly allocates observed abundances to species, but retains key aspects of the structure of the observed communities; site richness, species composition, and trait covariance. Three test statistics are used to explore different characteristics of the predictions. Two are based on pairwise comparisons between observed and predicted species abundances (RMSE, RMSESqrt). The third statistic is novel and is based on community-level abundance patterns, using an index calculated from the observed and predicted community entropies (EDiff). Validation of the test to quantify type I and type II error rates showed no evidence of bias or circularity, confirming the dependencies quantified by Roxburgh and Mokany (2007) and Shipley (2007) have been fully accounted for within the null model. Application of the test to the vineyard data of Shipley et al. (2006) and to an Australian grassland dataset indicated significant departures from the null model, suggesting the integration of species trait information within the maximum entropy framework can successfully predict species abundance patterns. The paper concludes with some general comments on the use of maximum entropy in ecology, including a discussion of the mathematics underlying the Maxent optimisation algorithm and its implementation, the role of absent species in generating biased predictions, and some comments on determining the most appropriate level of data aggregation for Maxent analysis. [source]

    Exponential Tilting with Weak Instruments: Estimation and Testing,

    Mehmet Caner
    Abstract This article analyses exponential tilting estimator with weak instruments in a nonlinear framework. Our paper differs from the previous literature in the context of consistency proof. Tests that are robust to the identification problem are also analysed. These are Anderson,Rubin and Kleibergen types of test statistics. We also conduct a simulation study wherein we compare empirical likelihood and continuous updating-based tests with exponential tilting (ET)-based ones. The designs involve GARCH(1,1) and contaminated structural errors. We find that ET-based Kleibergen test has the best size among these competitors. [source]