Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth

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Simultaneous inference in general parametric models.

Summary: DnaSP is a software package for the analysis of DNA polymorphism data. Present version introduces several new modules and features which, among other options allow: (1) handling big data sets (∼5 Mb per sequence); (2) conducting a large number of coalescent-based tests by Monte Carlo computer simulations; (3) extensive analyses of the genetic differentiation and gene flow among populations; (4) analysing the evolutionary pattern of preferred and unpreferred codons; (5) generating graphical outputs for an easy visualization of results. Availability: The software package, including complete documentation and examples, is freely available to academic users from: http://www.ub.es/dnasp

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DnaSP, DNA polymorphism analyses by the coalescent and other methods.

Regression models are frequently used to develop diagnostic, prognostic, and health resource utilization models in clinical, health services, outcomes, pharmacoeconomic, and epidemiologic research, and in a multitude of non-health-related areas. Regression models are also used to adjust for patient heterogeneity in randomized clinical trials, to obtain tests that are more powerful and valid than unadjusted treatment comparisons.

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Regression Modeling Strategies

On robust estimation of the location parameter

writing in the first issue of TREE, Ryder’ brought the term ‘Evolutionarily Significant Unit’ (ESU) to the attention of a broad audience of ecologists and evolutionary biologists. The ESU concept was developed to provide a rational basis for prioritizing taxa for conservation effort (e.g. captive breeding), given that resources are limited and that existing taxonomy may not adequately reflect underlying genetic diversity*. With the explicit recognition of the genetic component of biodiversity in conservation legislation of many countries and in the Convention on Biological Diversity, the ESU concept is set to become increasingly significant for conservation of natural as well as captive populations.

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Defining ‘Evolutionarily Significant Units’ for conservation

A statistical test for detecting genetic differentiation of subpopulations is described that uses molecular variation in samples of DNA sequences from two or more localities. The statistical significance of the test is determined with Monte Carlo simulations. The power of the test to detect genetic differentiation in a selectively neutral Wright-Fisher island model depends on both sample size and the rates of migration, mutation, and recombination. It is found that the power of the test is substantial with samples of size 50, when 4Nm less than 10, where N is the subpopulation size and m is the fraction of migrants in each subpopulation each generation. More powerful tests are obtained with genes with recombination than with genes without recombination.

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A statistical test for detecting geographic subdivision.

Since the seminal papers by Huber in the 1960s, M-estimation methods (also known as estimating equation methods) have been increasingly important for asymptotic analysis and approximate inference. This article illustrates the breadth and generality of the M-estimation approach, thereby facilitating its use inpractice and in the classroom as a unifying approach to the study of large-sample inference.

The Calculus of M-Estimation

For testing problems of the form H 0: v = v 0 with unknown nuisance parameter θ, various methods are used to deal with θ. The simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance. In other problems, such as the 2 × 2 contingency table, one conditions on a sufficient statistic for 0 and proceeds as in Fisher's exact test. Because neither of these standard methods is appropriate for all situations, this article suggests a new method for handling the unknown θ. This new method is a simple modification of the formal definition of a p value that involves taking a maximum over the nuisance parameter space of a p value obtained for the case when θ is known. The suggested modification is to restrict the maximization to a confidence set for the nuisance parameter. After giving a brief justification, we give various examples to show how this new method gives improved results for 2 × 2 tabl...

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P Values Maximized Over a Confidence Set for the Nuisance Parameter

Generalizations of Rao's score test are receiving increased attention, especially in the econometrics and biostatistics literature. These generalizations are able to account for certain model inadequacies or lack of knowledge by use of empirical variance estimates. This article shows how the various forms of the generalized test statistic arise from Taylor expansion of the estimating equations. The general estimating equations structure unifies a variety of applications and helps suggest new areas of application.

On Generalized Score Tests

P-values are useful statistical measures of evidence against a null hypothesis. In contrast to other statistical estimates, however, their sample-to-sample variability is usually not considered or estimated, and therefore not fully appreciated. Via a systematic study of log-scale p-value standard errors, bootstrap prediction bounds, and reproducibility probabilities for future replicate p-values, we show that p-values exhibit surprisingly large variability in typical data situations. In addition to providing context to discussions about the failure of statistical results to replicate, our findings shed light on the relative value of exact p-values vis-a-vis approximate p-values, and indicate that the use of *, **, and *** to denote levels 0.05, 0.01, and 0.001 of statistical significance in subject-matter journals is about the right level of precision for reporting p-values when judged by widely accepted rules for rounding statistical estimates.

https://amstat.tandfonline.com/doi/pdf/10.1198/tas.2011.10129

Dennis D. Boos

Papers

A statistical test for detecting geographic subdivision.

The Calculus of M-Estimation

P Values Maximized Over a Confidence Set for the Nuisance Parameter

On Generalized Score Tests

P-Value Precision and Reproducibility.