Hierarchical Bayesian modeling is a powerful and promising tool that aids experimental psychologists to flexibly build and evaluate interpretable statistical models that consider inter-individual and inter-trial variability. This article offers several examples of hierarchical Bayesian modeling to introduce the idea and to show its implementation with R and Stan. As a tutorial, it uses data from well-known experimental paradigms in perceptual and cognitive psychology. Specifically, I present linear models for correct response time data from a mental rotation task, probit models for binary choice data from two psychophysical tasks, and drift diffusion models for both response time and binary choice data from an Eriksen flanker task. The R and Stan scripts and data are available on the Open Science Framework repository at https://doi.org/10.17605/osf.io/2zxs6. The importance of model selection and the potential functions of open data practices in statistical modeling are also briefly discussed.