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Null Hypothesis (null + hypothesis)
Kinds of Null Hypothesis Selected AbstractsIntracellular Staphylococcus aureus and antibiotic resistance: Implications for treatment of staphylococcal osteomyelitisJOURNAL OF ORTHOPAEDIC RESEARCH, Issue 1 2006J. Kent Ellington Abstract Staphylococcus aureus is responsible for 80% of human osteomyelitis. It can invade and persist within osteoblasts. Antibiotic resistant strains of S. aureus make successful treatment of osteomyelitis difficult. Null Hypothesis: antibiotic sensitivities of S. aureus do not change after exposure to the osteoblast intracellular environment. Human and mouse osteoblast cultures were infected and S. aureus cells were allowed to invade. Following times 0, 12, 24, and 48 h (,± the addition of erythromycin, clindamycin, and rifampin at times 0 or 12 h), the osteoblasts were lysed and intracellular bacteria enumerated. Transmission electron microscopy was performed on extracellular and intracellular S. aureus cells. In mouse osteoblasts, administration of bacteriostatic antibiotics at time 0 prevented the increase in intracellular S. aureus. If the antibiotics were delayed 12 h, this did not occur. When rifampin (bactericidal) was introduced at time 0 to human and mouse osteoblasts, there was a significant decrease in number of intracellular S. aureus within osteoblasts compared to control. If rifampin was delayed 12 h, this did not occur. Significant time-dependent S. aureus structural changes were observed after exposure to the osteoblast intracellular environment. These studies demonstrate that once S. aureus is established intracellularly for 12 h, the bacteria are less sensitive to antibiotics capable of eukaryotic cell penetration (statistically significant). These antibiotic sensitivity changes could be due in part to the observed structural changes. This leads to the rejection of our null hypotheses that the antibiotic sensitivities of S. aureus are unaltered by their location. © 2005 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res [source] Nested distributions of bat flies (Diptera: Streblidae) on Neotropical bats: artifact and specificity in host-parasite studiesECOGRAPHY, Issue 3 2009Bruce D. Patterson We examined the structure of ectoparasitic bat fly infestations on 31 well-sampled bat species, representing 4 Neotropical families. Sample sizes varied from 22 to 1057 bats per species, and bat species were infested by 4 to 27 bat fly species. Individual bats supported smaller infracommunities (the set of parasites co-occurring on an individual host), ranging from 1 to 5 fly species in size, and no bat species had more than 6 bat fly species characteristically associated with it (its primary fly species). Nestedness analyses used system temperature (BINMATNEST algorithm) because it is particularly well-suited for analysis of interaction networks, where parasite records may be nested among hosts and host individuals simultaneously nested among parasites. Most species exhibited very low system temperatures (mean 3.14°; range 0.14,12.28°). Simulations showed that nested structure for all 31 species was significantly stronger than simulated values under 2 of the 3 null hypotheses, and about half the species were also nested under the more stringent conditions of the third null hypothesis. Yet this structure disappears when analyses are restricted to "primary" associations of fly species (flies on their customary host species), which exclude records thought to be atypical, transient, or potential contaminants. Despite comprising a small fraction of total parasite records, such anomalies represent a considerable part of the statistical state-space, offering the illusion of significant ecological structure. Only well understood and well documented systems can make distinctions between primary and other occurrence records. Generally, nestedness appears best developed in host-parasite systems where infestations are long-term and accumulate over time. Dynamic, short-term infestations by highly mobile parasites like bat flies may appear to be nested, but such structure is better understood in terms of host specificity and accidental occurrences than in terms of prevalence, persistence, or hierarchical niche relations of the flies. [source] "What exactly are you inferring?"ENVIRONMENTAL TOXICOLOGY & CHEMISTRY, Issue 5 2008A closer look at hypothesis testing Abstract This critical review describes the confused application of significance tests in environmental toxicology and chemistry that often produces incorrect inferences and indefensible regulatory decisions. Following a brief review of statistical testing theory, nine recommendations are put forward. The first is that confidence intervals be used instead of hypothesis tests whenever possible. The remaining recommendations are relevant if hypothesis tests are used. They are as follows: Define and justify Type I and II error rates a priori; set and justify an effect size a priori; do not confuse p(E | H0) and p(H0 | E); design tests permitting Positive Predictive Value estimation; publish negative results; estimate a priori, not post hoc, power; as warranted by study goals, favor null hypotheses that are not conventional nil hypotheses; and avoid definitive inferences from isolated tests. [source] The relationship between baseline value and its change: problems in categorization and the proposal of a new methodEUROPEAN JOURNAL OF ORAL SCIENCES, Issue 4 2005Yu-Kang Tu Oral health researchers have shown great interest in the relationship between the initial status of diseases and subsequent changes following treatment. Two main approaches have been adopted to provide evidence of a positive association between baseline values and their changes following treatment. One approach is to use correlation or regression to test the relationship between baseline measurements and subsequent change (correlation/regression approach). The second approach is to categorize the lesions into subgroups, according to threshold values, and subsequently compare the treatment effects across the two (or more) subgroups (categorization approach). However, the correlation/regression approach suffers a methodological weakness known as mathematical coupling. Consequently, the statistical procedure of testing the null hypothesis becomes inappropriate. Categorization seems to avoid the problem of mathematical coupling, although it still suffers regression to the mean. We show, first, how the appropriate null hypothesis may be established to analyze the relationship between baseline values and change in the correlation approach and, second, we use computer simulations to investigate the impact of regression to the mean on the significance testing of the differences in the average treatment effects (or average baseline values) in the categorization approach. Data available from previous literature are reanalyzed by testing the appropriate null hypotheses and the results are compared to those from testing the usual (incorrect) null hypothesis. The results indicate that both the correlation and categorization approaches can give rise to misleading conclusions and that more appropriate methods, such as Oldham's method and our new approach of deriving the correct null hypothesis, should be adopted. [source] ENVIRONMENTAL NICHE EQUIVALENCY VERSUS CONSERVATISM: QUANTITATIVE APPROACHES TO NICHE EVOLUTIONEVOLUTION, Issue 11 2008Dan L. Warren Environmental niche models, which are generated by combining species occurrence data with environmental GIS data layers, are increasingly used to answer fundamental questions about niche evolution, speciation, and the accumulation of ecological diversity within clades. The question of whether environmental niches are conserved over evolutionary time scales has attracted considerable attention, but often produced conflicting conclusions. This conflict, however, may result from differences in how niche similarity is measured and the specific null hypothesis being tested. We develop new methods for quantifying niche overlap that rely on a traditional ecological measure and a metric from mathematical statistics. We reexamine a classic study of niche conservatism between sister species in several groups of Mexican animals, and, for the first time, address alternative definitions of "niche conservatism" within a single framework using consistent methods. As expected, we find that environmental niches of sister species are more similar than expected under three distinct null hypotheses, but that they are rarely identical. We demonstrate how our measures can be used in phylogenetic comparative analyses by reexamining niche divergence in an adaptive radiation of Cuban anoles. Our results show that environmental niche overlap is closely tied to geographic overlap, but not to phylogenetic distances, suggesting that niche conservatism has not constrained local communities in this group to consist of closely related species. We suggest various randomization tests that may prove useful in other areas of ecology and evolutionary biology. [source] Analysis of multilocus models of associationGENETIC EPIDEMIOLOGY, Issue 1 2003B. Devlin Abstract It is increasingly recognized that multiple genetic variants, within the same or different genes, combine to affect liability for many common diseases. Indeed, the variants may interact among themselves and with environmental factors. Thus realistic genetic/statistical models can include an extremely large number of parameters, and it is by no means obvious how to find the variants contributing to liability. For models of multiple candidate genes and their interactions, we prove that statistical inference can be based on controlling the false discovery rate (FDR), which is defined as the expected number of false rejections divided by the number of rejections. Controlling the FDR automatically controls the overall error rate in the special case that all the null hypotheses are true. So do more standard methods such as Bonferroni correction. However, when some null hypotheses are false, the goals of Bonferroni and FDR differ, and FDR will have better power. Model selection procedures, such as forward stepwise regression, are often used to choose important predictors for complex models. By analysis of simulations of such models, we compare a computationally efficient form of forward stepwise regression against the FDR methods. We show that model selection includes numerous genetic variants having no impact on the trait, whereas FDR maintains a false-positive rate very close to the nominal rate. With good control over false positives and better power than Bonferroni, the FDR-based methods we introduce present a viable means of evaluating complex, multivariate genetic models. Naturally, as for any method seeking to explore complex genetic models, the power of the methods is limited by sample size and model complexity. Genet Epidemiol 25:36,47, 2003. © 2003 Wiley-Liss, Inc. [source] ,The National Stream Quality Accounting Network: a flux-based approach to monitoring the water quality of large riversHYDROLOGICAL PROCESSES, Issue 7 2001Richard P. Hooper Abstract Estimating the annual mass flux at a network of fixed stations is one approach to characterizing water quality of large rivers. The interpretive context provided by annual flux includes identifying source and sink areas for constituents and estimating the loadings to receiving waters, such as reservoirs or the ocean. Since 1995, the US Geological Survey's National Stream Quality Accounting Network (NASQAN) has employed this approach at a network of 39 stations in four of the largest river basins of the USA: the Mississippi, the Columbia, the Colorado and the Rio Grande. In this paper, the design of NASQAN is described and its effectiveness at characterizing the water quality of these rivers is evaluated using data from the first 3 years of operation. A broad range of constituents was measured by NASQAN, including trace organic and inorganic chemicals, major ions, sediment and nutrients. Where possible, a regression model relating concentration to discharge and season was used to interpolate between chemical observations for flux estimation. For water-quality network design, the most important finding from NASQAN was the importance of having a specific objective (that is, estimating annual mass flux) and, from that, an explicitly stated data analysis strategy, namely the use of regression models to interpolate between observations. The use of such models aided in the design of sampling strategy and provided a context for data review. The regression models essentially form null hypotheses for concentration variation that can be evaluated by the observed data. The feedback between network operation and data collection established by the hypothesis tests places the water-quality network on a firm scientific footing. Published in 2001 by John Wiley & Sons, Ltd. [source] Wobbles, humps and sudden jumps: a case study of continuity, discontinuity and variability in early language developmentINFANT AND CHILD DEVELOPMENT, Issue 1 2007Marijn van Dijk Abstract Current individual-based, process-oriented approaches (dynamic systems theory and the microgenetic perspective) have led to an increase of variability-centred studies in the literature. The aim of this article is to propose a technique that incorporates variability in the analysis of the shape of developmental change. This approach is illustrated by the analysis of time serial language data, in particular data on the development of preposition use, collected from four participants. Visual inspection suggests that the development of prepositions-in-contexts shows a characteristic pattern of two phases, corresponding with a discontinuity. Three criteria for testing such discontinuous phase-wise change in individual data are presented and applied to the data. These are: (1) the sub-pattern criterion, (2) the peak criterion and (3) the membership criterion. The analyses rely on bootstrap and resampling procedures based on various null hypotheses. The results show that there are some indications of discontinuity in all participants, although clear inter-individual differences have been found, depending on the criteria used. In the discussion we will address several fundamental issues concerning (dis)continuity and variability in individual-based, process-oriented data sets. Copyright © 2007 John Wiley & Sons, Ltd. [source] Neutral theory: a historical perspectiveJOURNAL OF EVOLUTIONARY BIOLOGY, Issue 6 2007E. G. LEIGH JR Abstract To resolve a panselectionist paradox, the population geneticist Kimura invented a neutral theory, where each gene is equally likely to enter the next generation whatever its allelic type. To learn what could be explained without invoking Darwinian adaptive divergence, Hubbell devised a similar neutral theory for forest ecology, assuming each tree is equally likely to reproduce whatever its species. In both theories, some predictions worked; neither theory proved universally true. Simple assumptions allow neutral theorists to treat many subjects still immune to more realistic theory. Ecologists exploit far fewer of these possibilities than population geneticists, focussing instead on species abundance distributions, where their predictions work best, but most closely match non-neutral predictions. Neutral theory cannot explain adaptive divergence or ecosystem function, which ecologists must understand. By addressing new topics and predicting changes in time, however, ecological neutral theory can provide probing null hypotheses and stimulate more realistic theory. [source] Selection of evolutionary models for phylogenetic hypothesis testing using parametric methodsJOURNAL OF EVOLUTIONARY BIOLOGY, Issue 4 2001B. C. Emerson Recent molecular studies have incorporated the parametric bootstrap method to test a priori hypotheses when the results of molecular based phylogenies are in conflict with these hypotheses. The parametric bootstrap requires the specification of a particular substitutional model, the parameters of which will be used to generate simulated, replicate DNA sequence data sets. It has been both suggested that, (a) the method appears robust to changes in the model of evolution, and alternatively that, (b) as realistic model of DNA substitution as possible should be used to avoid false rejection of a null hypothesis. Here we empirically evaluate the effect of suboptimal substitution models when testing hypotheses of monophyly with the parametric bootstrap using data sets of mtDNA cytochrome oxidase I and II (COI and COII) sequences for Macaronesian Calathus beetles, and mitochondrial 16S rDNA and nuclear ITS2 sequences for European Timarcha beetles. Whether a particular hypothesis of monophyly is rejected or accepted appears to be highly dependent on whether the nucleotide substitution model being used is optimal. It appears that a parameter rich model is either equally or less likely to reject a hypothesis of monophyly where the optimal model is unknown. A comparison of the performance of the Kishino,Hasegawa (KH) test shows it is not as severely affected by the use of suboptimal models, and overall it appears to be a less conservative method with a higher rate of failure to reject null hypotheses. [source] A comparative study of transformational leadership in nursing development units and conventional clinical settingsJOURNAL OF NURSING MANAGEMENT, Issue 2 2000A. Bowles RMN Aims This is a comparative study of the leadership provided by nurse managers and leaders in Nursing Development Units and conventional clinical settings in England. Background Nursing development units (NDUs) were originally conceived as centres of nursing excellence, innovation and leadership development. This article describes the first published use of a leadership practices inventory (LPI) explicitly based upon a model of transformational leadership. This style of leadership has been commended as highly effective and suitable for nursing. Methods The use of the LPI was piloted as a postal questionnaire and as a schedule for telephone interviewing, these pilots supported the use of telephone interviewing in the main study. Two matched samples of 70 nurses in total were recruited from across England, comprising 14 nurse leaders and 56 of their day to day colleagues. Data was collected by telephone interviewing over a 6-week period between February and April 1998. Six null hypotheses were developed to identify significant inter-group differences in leadership behaviour. Descriptive and inferential data analysis techniques were employed using SPSS for Windows. Findings The leadership provided by NDU leaders was evaluated more highly than non-NDU leaders. A higher level of congruence between self and observer evaluations was shown by NDU leaders. Statistically significant inter-group differences were apparent in three of the five practices of exemplary leadership and in the overall leadership behaviour. NDU leaders show greater self awareness and are more transformational than their non-NDU counterparts. The limitations of the study design are discussed. Conclusions NDU leaders provide leadership of a more transformational nature than their counterparts working in conventional settings. This finding suggests that NDU leaders have enhanced leadership potential and that formalizing nursing development within NDUs may promote the emergence of transformational leadership and provide a microculture in which it might flourish. The LPI is regarded as a useful, adaptable tool suitable for use in UK nursing applications including research, leadership development and education. [source] Intracellular Staphylococcus aureus and antibiotic resistance: Implications for treatment of staphylococcal osteomyelitisJOURNAL OF ORTHOPAEDIC RESEARCH, Issue 1 2006J. Kent Ellington Abstract Staphylococcus aureus is responsible for 80% of human osteomyelitis. It can invade and persist within osteoblasts. Antibiotic resistant strains of S. aureus make successful treatment of osteomyelitis difficult. Null Hypothesis: antibiotic sensitivities of S. aureus do not change after exposure to the osteoblast intracellular environment. Human and mouse osteoblast cultures were infected and S. aureus cells were allowed to invade. Following times 0, 12, 24, and 48 h (,± the addition of erythromycin, clindamycin, and rifampin at times 0 or 12 h), the osteoblasts were lysed and intracellular bacteria enumerated. Transmission electron microscopy was performed on extracellular and intracellular S. aureus cells. In mouse osteoblasts, administration of bacteriostatic antibiotics at time 0 prevented the increase in intracellular S. aureus. If the antibiotics were delayed 12 h, this did not occur. When rifampin (bactericidal) was introduced at time 0 to human and mouse osteoblasts, there was a significant decrease in number of intracellular S. aureus within osteoblasts compared to control. If rifampin was delayed 12 h, this did not occur. Significant time-dependent S. aureus structural changes were observed after exposure to the osteoblast intracellular environment. These studies demonstrate that once S. aureus is established intracellularly for 12 h, the bacteria are less sensitive to antibiotics capable of eukaryotic cell penetration (statistically significant). These antibiotic sensitivity changes could be due in part to the observed structural changes. This leads to the rejection of our null hypotheses that the antibiotic sensitivities of S. aureus are unaltered by their location. © 2005 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res [source] On the use of non-local prior densities in Bayesian hypothesis testsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2010Valen E. Johnson Summary., We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities that are used to define alternative hypotheses in many Bayesian tests assign non-negligible probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in favour of true alternative hypotheses, but only sublinear accumulation of evidence in favour of true null hypotheses. Thus, it is often impossible for such tests to provide strong evidence in favour of a true null hypothesis, even when moderately large sample sizes have been obtained. We review asymptotic convergence rates of Bayes factors in testing precise null hypotheses and propose two new classes of prior densities that ameliorate the imbalance in convergence rates that is inherited by most Bayesian tests. Using members of these classes, we obtain analytic expressions for Bayes factors in linear models and derive approximations to Bayes factors in large sample settings. [source] Power and sample size for nested analysis of molecular varianceMOLECULAR ECOLOGY, Issue 19 2009BENJAMIN M. FITZPATRICK Abstract Analysis of molecular variance (amova) is a widely used tool for quantifying the contribution of various levels of population structure to patterns of genetic variation. Implementations of amova use permutation tests to evaluate null hypotheses of no population structure within groups and between groups. With few populations per group, between-group structure might be impossible to detect because only a few permutations of the sampled populations are possible. In fact, with fewer than six total populations, permutation tests will never result in P -values <0.05 for higher-level population structure. I present minimum numbers of replicates calculated from multinomial coefficients and an r script that can be used to evaluate the minimum P -value for any sampling scheme. While it might seem counterintuitive that a large sample of individuals is uninformative about hierarchical structure, the power to detect between-group differences depends on the number of populations per group and investigators should sample appropriately. [source] Statistical hypothesis testing in intraspecific phylogeography: nested clade phylogeographical analysis vs. approximate Bayesian computationMOLECULAR ECOLOGY, Issue 2 2009ALAN R. TEMPLETON Abstract Nested clade phylogeographical analysis (NCPA) and approximate Bayesian computation (ABC) have been used to test phylogeographical hypotheses. Multilocus NCPA tests null hypotheses, whereas ABC discriminates among a finite set of alternatives. The interpretive criteria of NCPA are explicit and allow complex models to be built from simple components. The interpretive criteria of ABC are ad hoc and require the specification of a complete phylogeographical model. The conclusions from ABC are often influenced by implicit assumptions arising from the many parameters needed to specify a complex model. These complex models confound many assumptions so that biological interpretations are difficult. Sampling error is accounted for in NCPA, but ABC ignores important sources of sampling error that creates pseudo-statistical power. NCPA generates the full sampling distribution of its statistics, but ABC only yields local probabilities, which in turn make it impossible to distinguish between a good fitting model, a non-informative model, and an over-determined model. Both NCPA and ABC use approximations, but convergences of the approximations used in NCPA are well defined whereas those in ABC are not. NCPA can analyse a large number of locations, but ABC cannot. Finally, the dimensionality of tested hypothesis is known in NCPA, but not for ABC. As a consequence, the ,probabilities' generated by ABC are not true probabilities and are statistically non-interpretable. Accordingly, ABC should not be used for hypothesis testing, but simulation approaches are valuable when used in conjunction with NCPA or other methods that do not rely on highly parameterized models. [source] Fire-mediated interactions between shrubs in a South American temperate savannahOIKOS, Issue 9 2009Fernando Biganzoli We examined spatial patterns of fire-caused mortality and after-fire establishment of two dominant shrub species, Baccharis dracunculifolia and Eupatorium buniifolium in a humid temperate South American savannah. Our objective was to determine whether fires mediate in interactions between these two species. After a natural fire burned a large tract of savannah, we established two plots (respectively 550 and 500 m2) within which we mapped all surviving and dead shrubs as well as all individuals of shrub species that recruited in the following year. We used techniques of point-pattern analysis to test specific null hypotheses about spatial associations in the distribution, mortality, and establishment of shrubs. Results support the notions that fire mediates interactions between these two species. Fire-caused death of E. buniifolium tended to occur selectively in the vicinities of Baccharis individuals, and recruitment of B. dracunculifolia tended to be concentrated in the places of dead shrubs. These responses, however, were contingent on local abundances of shrubs which depend in part from the recent fire history. Anthropogenic perturbation of the natural fire regime would have therefore distorted the role of fire mediated interactions as drivers of the dynamics of the vegetation of this temperate savannah. [source] Power and sample size when multiple endpoints are consideredPHARMACEUTICAL STATISTICS: THE JOURNAL OF APPLIED STATISTICS IN THE PHARMACEUTICAL INDUSTRY, Issue 3 2007Stephen Senn Abstract A common approach to analysing clinical trials with multiple outcomes is to control the probability for the trial as a whole of making at least one incorrect positive finding under any configuration of true and false null hypotheses. Popular approaches are to use Bonferroni corrections or structured approaches such as, for example, closed-test procedures. As is well known, such strategies, which control the family-wise error rate, typically reduce the type I error for some or all the tests of the various null hypotheses to below the nominal level. In consequence, there is generally a loss of power for individual tests. What is less well appreciated, perhaps, is that depending on approach and circumstances, the test-wise loss of power does not necessarily lead to a family wise loss of power. In fact, it may be possible to increase the overall power of a trial by carrying out tests on multiple outcomes without increasing the probability of making at least one type I error when all null hypotheses are true. We examine two types of problems to illustrate this. Unstructured testing problems arise typically (but not exclusively) when many outcomes are being measured. We consider the case of more than two hypotheses when a Bonferroni approach is being applied while for illustration we assume compound symmetry to hold for the correlation of all variables. Using the device of a latent variable it is easy to show that power is not reduced as the number of variables tested increases, provided that the common correlation coefficient is not too high (say less than 0.75). Afterwards, we will consider structured testing problems. Here, multiplicity problems arising from the comparison of more than two treatments, as opposed to more than one measurement, are typical. We conduct a numerical study and conclude again that power is not reduced as the number of tested variables increases. Copyright © 2007 John Wiley & Sons, Ltd. [source] Misprescription and misuse of one-tailed testsAUSTRAL ECOLOGY, Issue 4 2009CELIA M. LOMBARDI Abstract One-tailed statistical tests are often used in ecology, animal behaviour and in most other fields in the biological and social sciences. Here we review the frequency of their use in the 1989 and 2005 volumes of two journals (Animal Behaviour and Oecologia), their advantages and disadvantages, the extensive erroneous advice on them in both older and modern statistics texts and their utility in certain narrow areas of applied research. Of those articles with data sets susceptible to one-tailed tests, at least 24% in Animal Behaviour and at least 13% in Oecologia used one-tailed tests at least once. They were used 35% more frequently with nonparametric methods than with parametric ones and about twice as often in 1989 as in 2005. Debate in the psychological literature of the 1950s established the logical criterion that one-tailed tests should be restricted to situations where there is interest only in results in one direction. ,Interest' should be defined; however, in terms of collective or societal interest and not by the individual investigator. By this ,collective interest' criterion, all uses of one-tailed tests in the journals surveyed seem invalid. In his book Nonparametric Statistics, S. Siegel unrelentingly suggested the use of one-tailed tests whenever the investigator predicts the direction of a result. That work has been a major proximate source of confusion on this issue, but so are most recent statistics textbooks. The utility of one-tailed tests in research aimed at obtaining regulatory approval of new drugs and new pesticides is briefly described, to exemplify the narrow range of research situations where such tests can be appropriate. These situations are characterized by null hypotheses stating that the difference or effect size does not exceed, or is at least as great as, some ,amount of practical interest'. One-tailed tests rarely should be used for basic or applied research in ecology, animal behaviour or any other science. [source] Resampling-Based Empirical Bayes Multiple Testing Procedures for Controlling Generalized Tail Probability and Expected Value Error Rates: Focus on the False Discovery Rate and Simulation StudyBIOMETRICAL JOURNAL, Issue 5 2008Sandrine Dudoit Abstract This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP (q,g) = Pr(g (Vn,Sn) > q), and generalized expected value (gEV) error rates, gEV (g) = E [g (Vn,Sn)], for arbitrary functions g (Vn,Sn) of the numbers of false positives Vn and true positives Sn. Of particular interest are error rates based on the proportion g (Vn,Sn) = Vn /(Vn + Sn) of Type I errors among the rejected hypotheses, such as the false discovery rate (FDR), FDR = E [Vn /(Vn + Sn)]. The proposed procedures offer several advantages over existing methods. They provide Type I error control for general data generating distributions, with arbitrary dependence structures among variables. Gains in power are achieved by deriving rejection regions based on guessed sets of true null hypotheses and null test statistics randomly sampled from joint distributions that account for the dependence structure of the data. The Type I error and power properties of an FDR-controlling version of the resampling-based empirical Bayes approach are investigated and compared to those of widely-used FDR-controlling linear step-up procedures in a simulation study. The Type I error and power trade-off achieved by the empirical Bayes procedures under a variety of testing scenarios allows this approach to be competitive with or outperform the Storey and Tibshirani (2003) linear step-up procedure, as an alternative to the classical Benjamini and Hochberg (1995) procedure. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] On Identification of the Number of Best Treatments Using the Newman-Keuls TestBIOMETRICAL JOURNAL, Issue 5 2008Samuel S. Wu Abstract In this paper, we provide a stochastic ordering of the Studentized range statistics under a balanced one-way ANOVA model. Based on this result we show that, when restricted to the multiple comparisons with the best, the Newman,Keuls (NK) procedure strongly controls experimentwise error rate for a sequence of null hypotheses regarding the number of largest treatment means. In other words, the NK procedure provides an upper confidence bound for the number of best treatments. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] FDR Control by the BH Procedure for Two-Sided Correlated Tests with Implications to Gene Expression Data AnalysisBIOMETRICAL JOURNAL, Issue 1 2007Anat Reiner-Benaim Abstract The multiple testing problem attributed to gene expression analysis is challenging not only by its size, but also by possible dependence between the expression levels of different genes resulting from co-regulations of the genes. Furthermore, the measurement errors of these expression levels may be dependent as well since they are subjected to several technical factors. Multiple testing of such data faces the challenge of correlated test statistics. In such a case, the control of the False Discovery Rate (FDR) is not straightforward, and thus demands new approaches and solutions that will address multiplicity while accounting for this dependency. This paper investigates the effects of dependency between bormal test statistics on FDR control in two-sided testing, using the linear step-up procedure (BH) of Benjamini and Hochberg (1995). The case of two multiple hypotheses is examined first. A simulation study offers primary insight into the behavior of the FDR subjected to different levels of correlation and distance between null and alternative means. A theoretical analysis follows in order to obtain explicit upper bounds to the FDR. These results are then extended to more than two multiple tests, thereby offering a better perspective on the effect of the proportion of false null hypotheses, as well as the structure of the test statistics correlation matrix. An example from gene expression data analysis is presented. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Controlling False Discoveries in Multidimensional Directional Decisions, with Applications to Gene Expression Data on Ordered CategoriesBIOMETRICS, Issue 2 2010Wenge Guo Summary Microarray gene expression studies over ordered categories are routinely conducted to gain insights into biological functions of genes and the underlying biological processes. Some common experiments are time-course/dose-response experiments where a tissue or cell line is exposed to different doses and/or durations of time to a chemical. A goal of such studies is to identify gene expression patterns/profiles over the ordered categories. This problem can be formulated as a multiple testing problem where for each gene the null hypothesis of no difference between the successive mean gene expressions is tested and further directional decisions are made if it is rejected. Much of the existing multiple testing procedures are devised for controlling the usual false discovery rate (FDR) rather than the mixed directional FDR (mdFDR), the expected proportion of Type I and directional errors among all rejections. Benjamini and Yekutieli (2005,,Journal of the American Statistical Association,100, 71,93) proved that an augmentation of the usual Benjamini,Hochberg (BH) procedure can control the mdFDR while testing simple null hypotheses against two-sided alternatives in terms of one-dimensional parameters. In this article, we consider the problem of controlling the mdFDR involving multidimensional parameters. To deal with this problem, we develop a procedure extending that of Benjamini and Yekutieli based on the Bonferroni test for each gene. A proof is given for its mdFDR control when the underlying test statistics are independent across the genes. The results of a simulation study evaluating its performance under independence as well as under dependence of the underlying test statistics across the genes relative to other relevant procedures are reported. Finally, the proposed methodology is applied to a time-course microarray data obtained by Lobenhofer et al. (2002,,Molecular Endocrinology,16, 1215,1229). We identified several important cell-cycle genes, such as DNA replication/repair gene MCM4 and replication factor subunit C2, which were not identified by the previous analyses of the same data by Lobenhofer et al. (2002) and Peddada et al. (2003,,Bioinformatics,19, 834,841). Although some of our findings overlap with previous findings, we identify several other genes that complement the results of Lobenhofer et al. (2002). [source] Screening for Partial Conjunction HypothesesBIOMETRICS, Issue 4 2008Yoav Benjamini Summary We consider the problem of testing for partial conjunction of hypothesis, which argues that at least u out of n tested hypotheses are false. It offers an in-between approach to the testing of the conjunction of null hypotheses against the alternative that at least one is not, and the testing of the disjunction of null hypotheses against the alternative that all hypotheses are not null. We suggest powerful test statistics for testing such a partial conjunction hypothesis that are valid under dependence between the test statistics as well as under independence. We then address the problem of testing many partial conjunction hypotheses simultaneously using the false discovery rate (FDR) approach. We prove that if the FDR controlling procedure in Benjamini and Hochberg (1995, Journal of the Royal Statistical Society, Series B 57, 289,300) is used for this purpose the FDR is controlled under various dependency structures. Moreover, we can screen at all levels simultaneously in order to display the findings on a superimposed map and still control an appropriate FDR measure. We apply the method to examples from microarray analysis and functional magnetic resonance imaging (fMRI), two application areas where the need for partial conjunction analysis has been identified. [source] Quantifying Genomic Imprinting in the Presence of LinkageBIOMETRICS, Issue 4 2006Quentin Vincent Summary Genomic imprinting decreases the power of classical linkage analysis, in which paternal and maternal transmissions of marker alleles are equally weighted. Several methods have been proposed for taking genomic imprinting into account in the model-free linkage analysis of binary traits. However, none of these methods are suitable for the formal identification and quantification of genomic imprinting in the presence of linkage. In addition, the available methods are designed for use with pure sib-pairs, requiring artificial decomposition in cases of larger sibships, leading to a loss of power. We propose here the maximum likelihood binomial method adaptive for imprinting (MLB-I), which is a unified analytic framework giving rise to specific tests in sibships of any size for (i) linkage adaptive to imprinting, (ii) genomic imprinting in the presence of linkage, and (iii) partial versus complete genomic imprinting. In addition, we propose an original measure for quantifying genomic imprinting. We have derived and validated the distribution of the three tests under their respective null hypotheses for various genetic models, and have assessed the power of these tests in simulations. This method can readily be applied to genome-wide scanning, as illustrated here for leprosy sibships. Our approach provides a novel tool for dissecting genomic imprinting in model-free linkage analysis, and will be of considerable value for identifying and evaluating the contribution of imprinted genes to complex diseases. [source] Closure Procedures for Monotone Bi-Factorial Dose,Response DesignsBIOMETRICS, Issue 1 2005M. Hellmich Summary Two goals of multiple-dose factorial trials are (i) demonstrating improved effectiveness of a fixed combination over each of its components as well as (ii) identifying a safe and effective dose range. The authors address both goals though with focus on the second by closure procedures that guarantee strong control of the familywise error rate. Two different families of null hypotheses are investigated for bi-factorial dose,response designs that are monotone with respect to the matrix partial order. One is suitable to find the minimum effective dose(s) and the other one is large enough to identify the highest effective dose step(s). Likelihood ratio tests and appropriate multiple contrast tests are applied to an unbalanced clinical trial example taken from Hung (2000, Statistics in Medicine19, 2079,2087). Full computer code written in the R language is available from the Internet. [source] Sequential Tests for Noninferiority and SuperiorityBIOMETRICS, Issue 1 2003W. Brannath Summary. The problem of simultaneous sequential tests for noninferiority and superiority of a treatment, as compared to an active control, is considered in terms of continuous hierarchical families of one-sided null hypotheses, in the framework of group sequential and adaptive two-stage designs. The crucial point is that the decision boundaries for the individual null hypotheses may vary over the parameter space. This allows one to construct designs where, e.g., a rigid stopping criterion is chosen, rejecting or accepting all individual null hypotheses simultaneously. Another possibility is to use monitoring type stopping boundaries, which leave some flexibility to the experimenter: he can decide, at the interim analysis, whether he is satisfied with the noninferiority margin achieved at this stage, or wants to go for more at the second stage. In the case where he proceeds to the second stage, he may perform midtrial design modifications (e.g., reassess the sample size). The proposed approach allows one to "spend," e.g., less of , for an early proof of noninferiority than for an early proof of superiority, and is illustrated by typical examples. [source] Nested distributions of bat flies (Diptera: Streblidae) on Neotropical bats: artifact and specificity in host-parasite studiesECOGRAPHY, Issue 3 2009Bruce D. Patterson We examined the structure of ectoparasitic bat fly infestations on 31 well-sampled bat species, representing 4 Neotropical families. Sample sizes varied from 22 to 1057 bats per species, and bat species were infested by 4 to 27 bat fly species. Individual bats supported smaller infracommunities (the set of parasites co-occurring on an individual host), ranging from 1 to 5 fly species in size, and no bat species had more than 6 bat fly species characteristically associated with it (its primary fly species). Nestedness analyses used system temperature (BINMATNEST algorithm) because it is particularly well-suited for analysis of interaction networks, where parasite records may be nested among hosts and host individuals simultaneously nested among parasites. Most species exhibited very low system temperatures (mean 3.14°; range 0.14,12.28°). Simulations showed that nested structure for all 31 species was significantly stronger than simulated values under 2 of the 3 null hypotheses, and about half the species were also nested under the more stringent conditions of the third null hypothesis. Yet this structure disappears when analyses are restricted to "primary" associations of fly species (flies on their customary host species), which exclude records thought to be atypical, transient, or potential contaminants. Despite comprising a small fraction of total parasite records, such anomalies represent a considerable part of the statistical state-space, offering the illusion of significant ecological structure. Only well understood and well documented systems can make distinctions between primary and other occurrence records. Generally, nestedness appears best developed in host-parasite systems where infestations are long-term and accumulate over time. Dynamic, short-term infestations by highly mobile parasites like bat flies may appear to be nested, but such structure is better understood in terms of host specificity and accidental occurrences than in terms of prevalence, persistence, or hierarchical niche relations of the flies. [source] Methods to account for spatial autocorrelation in the analysis of species distributional data: a reviewECOGRAPHY, Issue 5 2007Carsten F. Dormann Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species' distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix. [source] Survival rates in a natural population of the damselfly Ceriagrion tenellum: effects of sex and female phenotypeECOLOGICAL ENTOMOLOGY, Issue 4 2001Jose A. Andrés Summary 1. Ceriagrion tenellum females show genetic colour polymorphism. Androchrome (erythrogastrum) females are brightly (male-like) coloured while gynochrome females (typica and melanogastrum) show cryptic colouration. 2. Several hypotheses have been proposed to explain the existence of more than one female morph in damselfly populations. The reproductive isolation and intraspecific mimicry hypotheses predict greater survival of gynochrome females, while the density dependent hypothesis predicts no differential survival between morphs. 3. Mature males had greater recapture probability than females while the survival probability was similar for both sexes. Survival and recapture rates were similar for androchrome and gynochrome females. 4. Gynochrome females showed greater mortality or migration rate than androchrome females during the pre-reproductive period. This result is not predicted by the above hypotheses or by the null hypothesis that colour polymorphism is only maintained by random factors: founder effects, genetic drift, and migration. [source] Co-occurrence of ectoparasites of marine fishes: a null model analysisECOLOGY LETTERS, Issue 1 2002Nicholas J. Gotelli We used null model analysis to test for nonrandomness in the structure of metazoan ectoparasite communities of 45 species of marine fish. Host species consistently supported fewer parasite species combinations than expected by chance, even in analyses that incorporated empty sites. However, for most analyses, the null hypothesis was not rejected, and co-occurrence patterns could not be distinguished from those that might arise by random colonization and extinction. We compared our results to analyses of presence,absence matrices for vertebrate taxa, and found support for the hypothesis that there is an ecological continuum of community organization. Presence,absence matrices for small-bodied taxa with low vagility and/or small populations (marine ectoparasites, herps) were mostly random, whereas presence,absence matrices for large-bodied taxa with high vagility and/or large populations (birds, mammals) were highly structured. Metazoan ectoparasites of marine fishes fall near the low end of this continuum, with little evidence for nonrandom species co-occurrence patterns. [source] | |||||||||||||||||||||||||||||||||||||