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 model misspecification. However, procedures to identify and exclude outliers may bring unwanted side effects such as an increase in the Type I error rate. Here we study the side effects of outlier exclusion procedures on the Bayes factor hypothesis test. We focus on the Bayesian independent samples t test and show how outlier exclusion procedures may inflate the Bayes factor, resulting in conclusions that are overconfident. Researchers therefore find themselves on the horns of a dilemma: spurious effects and an inflation of evidence can occur both as a result of retaining outliers and as a result of removing extreme observations. To resolve the dilemma, we propose to truncate the likelihood function and embed the procedure in the Bayesian model-averaged t test. Simulations demonstrate the behavior of the proposed solution. The methodology has been implemented in the R package RoBTT and in JASP. (PsycInfo Database Record (c) 2025 APA, all rights reserved).