Topic
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.
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01 Jan 2018
TL;DR: This tutorial paper provides basic demonstrations of the strength of raincloud plots and similar approaches, outlines potential modifications for their optimal use, and provides open-source code for their streamlined implementation in R, Python and Matlab.
Abstract: Across scientific disciplines, there is a rapidly growing recognition of the need for more statistically robust, transparent approaches to data visualization. Complementary to this, many scientists have called for plotting tools that accurately and transparently convey key aspects of statistical effects and raw data with minimal distortion. Previously common approaches, such as plotting conditional mean or median barplots together with error-bars have been criticized for distorting effect size, hiding underlying patterns in the raw data, and obscuring the assumptions upon which the most commonly used statistical tests are based. Here we describe a data visualization approach which overcomes these issues, providing maximal statistical information while preserving the desired 'inference at a glance' nature of barplots and other similar visualization devices. These "raincloud plots" can visualize raw data, probability density, and key summary statistics such as median, mean, and relevant confidence intervals in an appealing and flexible format with minimal redundancy. In this tutorial paper, we provide basic demonstrations of the strength of raincloud plots and similar approaches, outline potential modifications for their optimal use, and provide open-source code for their streamlined implementation in R, Python and Matlab ( https://github.com/RainCloudPlots/RainCloudPlots). Readers can investigate the R and Python tutorials interactively in the browser using Binder by Project Jupyter.
505 citations
Book•
01 Jan 2004
TL;DR: This book provides a valuable primer that delineates what the authors know, what they would like to know, and the limits of what they can know, when they try to learn about a system that is composed of other learners.
Abstract: 1. The Interactive Learning Problem 2. Reinforcement and Regret 3. Equilibrium 4. Conditional No-Regret Learning 5. Prediction, Postdiction, and Calibration 6. Fictitious Play and Its Variants 7. Bayesian Learning 8. Hypothesis Testing 9. Conclusion
504 citations
TL;DR: The knockoff filter is introduced, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables, and empirical results show that the resulting method has far more power than existing selection rules when the proportion of null variables is high.
Abstract: In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR) - the expected fraction of false discoveries among all discoveries - is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper introduces the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method achieves exact FDR control in finite sample settings no matter the design or covariates, the number of variables in the model, or the amplitudes of the unknown regression coefficients, and does not require any knowledge of the noise level. As the name suggests, the method operates by manufacturing knockoff variables that are cheap - their construction does not require any new data - and are designed to mimic the correlation structure found within the existing variables, in a way that allows for accurate FDR control, beyond what is possible with permutation-based methods. The method of knockoffs is very general and flexible, and can work with a broad class of test statistics. We test the method in combination with statistics from the Lasso for sparse regression, and obtain empirical results showing that the resulting method has far more power than existing selection rules when the proportion of null variables is high.
503 citations
TL;DR: The method derives from observing that in general, a Bayes factor can be written as the product of a quantity called the Savage-Dickey density ratio and a correction factor; both terms are easily estimated from posterior simulation.
Abstract: We present a simple method for computing Bayes factors. The method derives from observing that in general, a Bayes factor can be written as the product of a quantity called the Savage-Dickey density ratio and a correction factor; both terms are easily estimated from posterior simulation. In some cases it is possible to do these computations without ever evaluating the likelihood.
502 citations
TL;DR: Here it is drawn attention to the Savage-Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors.
499 citations