Statistical hypothesis testing

About: Statistical hypothesis testing is a research topic. Over the lifetime, 19580 publications have been published within this topic receiving 1037815 citations. The topic is also known as: statistical hypothesis testing & confirmatory data analysis.

Statistical Analysis of fMRI Time-Series: A Critical Review of the GLM Approach.

Abstract: Functional magnetic resonance imaging (fMRI) is one of the most widely used tools to study the neural underpinnings of human cognition. Standard analysis of fMRI data relies on a general linear model (GLM) approach to separate stimulus induced signals from noise. Crucially, this approach relies on a number of assumptions about the data which, for inferences to be valid, must be met. The current paper reviews the GLM approach to analysis of fMRI time-series, focusing in particular on the degree to which such data abides by the assumptions of the GLM framework, and on the methods that have been developed to correct for any violation of those assumptions. Rather than biasing estimates of effect size, the major consequence of non-conformity to the assumptions is to introduce bias into estimates of the variance, thus affecting test statistics, power, and false positive rates. Furthermore, this bias can have pervasive effects on both individual subject and group-level statistics, potentially yielding qualitatively different results across replications, especially after the thresholding procedures commonly used for inference-making.

New Statistical Tests of Neutrality for DNA Samples from a Population

Abstract: The purpose of this paper is to develop statistical tests of the neutral model of evolution against a class of alternative models with the common characteristic of having an excess of mutations that occurred a long time ago or a reduction of recent mutations compared to the neutral model. This class of population genetics models include models for structured populations, models with decreasing effective population size and models of selection and mutation balance. Four statistical tests were proposed in this paper for DNA samples from a population. Two of these tests, one new and another a modification of an existing test, are based on EWENS' sampling formula, and the other two new tests make use of the frequencies of mutations of various classes. Using simulated samples and regression analyses, the critical values of these tests can be computed from regression equations. This approach for computing the critical values of a test was found to be appropriate and quite effective. We examined the powers of these four tests using simulated samples from structured populations, populations with linearly decreasing sizes and models of selection and mutation balance and found that they are more powerful than existing statistical tests of the neutral model of evolution.

A simulation-based approach to two-stage stochastic programming with recourse

Abstract: In this paper we consider stochastic programming problems where the objective function is given as an expected value function. We discuss Monte Carlo simulation based approaches to a numerical solution of such problems. In particular, we discuss in detail and present numerical results for two-stage stochastic programming with recourse where the random data have a continuous (multivariate normal) distribution. We think that the novelty of the numerical approach developed in this paper is twofold. First, various variance reduction techniques are applied in order to enhance the rate of convergence. Successful application of those techniques is what makes the whole approach numerically feasible. Second, a statistical inference is developed and applied to estimation of the error, validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests

Abstract: Nonparametric two-sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being designed and analyzed, both for the unidimensional and the multivariate setting. In this short survey, we focus on test statistics that involve the Wasserstein distance. Using an entropic smoothing of the Wasserstein distance, we connect these to very different tests including multivariate methods involving energy statistics and kernel based maximum mean discrepancy and univariate methods like the Kolmogorov–Smirnov test, probability or quantile (PP/QQ) plots and receiver operating characteristic or ordinal dominance (ROC/ODC) curves. Some observations are implicit in the literature, while others seem to have not been noticed thus far. Given nonparametric two-sample testing’s classical and continued importance, we aim to provide useful connections for theorists and practitioners familiar with one subset of methods but not others.