Truncating the Likelihood Allows Outlier Exclusion Without Overestimating the Evidence in the Bayes Factor t-Test

The purpose of outlier exclusion is to improve data quality and prevent modelmisspecification. However, procedures to identify and exclude outliers may bring unwantedside effects such as an increase in the Type I error rate. Here we study the side effects ofoutlier exclusion procedures on the Bayes factor hypothesis test. We focus on the Bayesianindependent samples t-test and show how outlier exclusion procedures may inflate theBayes factor, resulting in conclusions that are overconfident. Researchers therefore findthemselves on the horns of a dilemma: spurious effects and an inflation of evidence canoccur both as a result of retaining outliers and as a result of removing extremeobservations. To resolve the dilemma, we propose to truncate the likelihood function andembed the procedure in the Bayesian model-averaged t-test. Simulations demonstrate theadequacy of the proposed solution. The methodology has been implemented in the Rpackage RoBTT and in JASP.