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In this paper, we develop generalized hierarchical Bayesian ANOVA, to assist experimental researchers in the behavioral and social sciences in the analysis of experiments with within- and between-subjects factors. The method alleviates several limitations of classical ANOVA, still commonly employed in those fields of research. An accompanying R Package for BANOVA is developed. It offers statistical routines and several easy-to-use functions for estimation of hierarchical Bayesian ANOVA models that are tailored to the analysis of experimental research. MCMC simulation is used to simulate posterior samples of the parameters of each model specified by the user. The core program is written in R and JAGS. After preparing the data in the required format, users simply select an appropriate model, and can estimate it without any advanced coding being required. The main aim of the R package is to offer freely accessible resources for hierarchical Bayesian ANOVA analysis, which makes it easy to use for applied researchers.