Compositional changes of cell types are main drivers of biological processes. Their detection through single-cell experiments is difficult due to the compositionality of the data and low sample sizes. We introduce scCODA ( https://github.com/theislab/scCODA ), a Bayesian model addressing these issues enabling the study of complex cell type effects in disease, and other stimuli. scCODA demonstrated excellent detection performance, while reliably controlling for false discoveries, and identified experimentally verified cell type changes that were missed in original analyses.