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.

An Exact Test for Multiple Inequality and Equality Constraints in the Linear Regression Model

Abstract: In this article we consider the linear regression model y = Xβ + e, where e is N(0, σ2I). In this context we derive exact tests of the form H: Rβ ≥ r versus K: β ∈ RK for the case in which θ2 is unknown. We extend these results to consider hypothesis tests of the form H: R1β ≥ r1 and R2β = r2 versus K: (β ∈ RK . For each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming. For both tests we derive their exact distribution as a weighted sum of Snedecor's F distributions normalized by the numerator degrees of freedom of each F distribution of the sum. A methodology for computing critical values as well as probability values for the tests is discussed. The relationship between this testing framework and the multivariate one-sided hypothesis testing literature is also discussed. In this context we show that for any size of the hypothesis test H: λ = 0 versus K: β ∈ RK the test statistic and critical value obtained a...

The appropriate use of null hypothesis testing.

Abstract: The many criticisms of null hypothesis testing suggest when it is not useful and what is should not be used for. This article explores when and why its use is appropriate. Null hypothesis testing is insufficient when size of effect is important, but it is ideal for testing ordinal claims relating the order of conditions, which are common in psychology. Null hypothesis testing also is insufficient for determining beliefs, but it is ideal for demonstrating sufficient evidential strength to support an ordinal claim, with sufficient evidence being 1 criterion for a finding entering the corpus of legitimate findings in psychology. The line between sufficient and insufficient evidence is currently set at p < .05; there is little reason for allowing experimenters to select their own value of alpha. Thus null hypothesis testing is an optimal method for demonstrating sufficient evidence for an ordinal claim.

Statistics for the Behavioral and Social Sciences: A Brief Course

Abstract: Chapter 1 - Displaying the Order in a Group of Numbers Using Tables and Graphs Chapter 2 - The Mean, Variance, Standard Deviation, and Z Scores Chapter 3 - Correlation and Prediction Chapter 4 - Some Key Ingredients for Inferential Statistics: The Normal Curve, Sample Versus Population, and Probability Chapter 5 - Introduction to Hypothesis Testing Chapter 6 - Hypothesis Tests with Means of Samples Chapter 7 - Making Sense of Statistical Significance: Effect Size and Statistical Power Chapter 8 - Introduction to the t Test: Single Sample and Dependent Means Chapter 9 - The t Test for Independent Means Chapter 10 - Introduction to the Analysis of Variance Chapter 11- Chi-Square Tests and Strategies When Population Distributions Are Not Normal Chapter 12 - Applying Statistical Methods in Your Own Research Project

New likelihood test methods for change detection in image sequences

Abstract: Modeling the image as a piecewise linear gray-value function of the pixel coordinates considerably improved a change detection test based previously on a piecewise constant gray-value function. These results encouraged investigations into modeling the picture as a mosaic of patches where the gray-value function within each patch is described as a second-order bivariate polynomial of the pixel coordinates. Such a more appropriate model allowed the assumption to be made that the remaining gray-value variation within each patch can be attributed to noise related to the sensing and digitizing devices, independent of the individual image frames in a sequence. This assumption made it possible to relate the likelihood test for change detection to well-known statistical tests ( t test, F test), facilitating the determination of threshold values related to a priori confidence limits.

Bayesian clustering and product partition models

Abstract: Summary. We present a decision theoretic formulation of product partition models (PPMs) that allows a formal treatment of different decision problems such as estimation or hypothesis testing and clustering methods simultaneously. A key observation in our construction is the fact that PPMs can be formulated in the context of model selection. The underlying partition structure in these models is closely related to that arising in connection with Dirichlet processes. This allows a straightforward adaptation of some computational strategies--originally devised for nonparametric Bayesian problems-to our framework. The resulting algorithms are more flexible than other competing alternatives that are used for problems involving PPMs. We propose an algorithm that yields Bayes estimates of the quantities of interest and the groups of experimental units. We explore the application of our methods to the detection of outliers in normal and Student t regression models, with clustering structure equivalent to that induced by a Dirichlet process prior. We also discuss the sensitivity of the results considering different prior distributions for the partitions.