This stand-alone tutorial gives an introduction to the QTEST 2.1 public domain software package for the specification and statistical analysis of certain order-constrained probabilistic choice models. Like its predecessors, QTEST 2.1 allows a user to specify a variety of probabilistic models of binary responses and to carry out state-of-the-art frequentist order-constrained hypothesis tests within a Graphical User Interface (GUI). QTEST 2.1 automatizes the mathematical characterization of so-called “random preference models”, adds some parallel computing capabilities, and, most importantly, adds tools for Bayesian inference and model selection. In this tutorial, we provide an in-depth introduction to the Bayesian features: We review order-constrained Bayesian p-values, DIC and Bayes factors, building on the data, models, and prior QTEST based frequentist data analyses of an earlier (frequentist) tutorial by Regenwetter et al. (2014).