Bayesanova: An R package for Bayesian Inference in the Analysis of Variance via Markov Chain Monte Carlo in Gaussian Mixture Models

Abstract

This paper introduces the R package [bayesanova](https://CRAN.R-project.org/package=bayesanova), which performs Bayesian inference in the analysis of variance (ANOVA). Traditional ANOVA based on null hypothesis significance testing (NHST) is prone to overestimating effects and stating effects if none are present. Bayesian ANOVAs developed so far are based on Bayes factors (BF), which also enforce a hypothesis testing stance. Instead, the Bayesian ANOVA implemented in bayesanova focusses on effect size estimation and is based on a Gaussian mixture with known allocations, for which full posterior inference for the component parameters is implemented via Markov-Chain-Monte-Carlo (MCMC). Inference for the difference in means, standard deviations and effect sizes between each of the groups is obtained automatically. Estimation of the parameters instead of hypothesis testing is embraced via the region of practical equivalence (ROPE), and helper functions provide checks of the model assumptions and visualization of the results.