Abstract
Tests for dependence of continuous, discrete and mixed continuous-discrete variables are ubiquitous in science. The goal of this paper is to derive Bayesian alternatives to frequentist null hypothesis significance tests for dependence. In particular, we will present three Bayesian tests for dependence of binary, continuous and mixed variables. These tests are nonparametric and based on the Dirichlet Process, which allows us to use the same prior model for all of them. Therefore, the tests are “consistent” among each other, in the sense that the probabilities that variables are dependent computed with these tests are commensurable across the different types of variables being tested. By means of simulations with artificial data, we show the effectiveness of the new tests.
Highlights
Tests for dependence of continuous, discrete and mixed continuous-discrete variables are fundamental in science
The usage of null-hypothesis significance tests (NHST) often relies on the wrong assumptions that p-values are a reasonable proxy to the probability of the null hypothesis and that statistical significance implies practical significance
To address the issue of how to choose the prior parameters in case of lack of information, we propose the use of the Imprecise Dirichlet Process (IDP) [4]
Summary
Tests for dependence of continuous, discrete and mixed continuous-discrete variables are fundamental in science. The standard way to statistically assess if two (or more) variables are dependent is by using null-hypothesis significance tests (NHST), such as χ2 -test, Kendall’s τ, etc. An NHST computes the probability of getting the observed (or a larger) value of the statistics under the assumption that the null hypothesis of independence is true, which is obviously not the same as the probability of variables being dependent on each other, given the observed data. Another common problem is that the claimed statistical significance might have no practical impact. The usage of NHST often relies on the wrong assumptions that p-values are a reasonable proxy to the probability of the null hypothesis and that statistical significance implies practical significance
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