Single-cell transcriptomics is a versatile tool for exploring heterogeneous cell populations, but as with all genomics experiments, batch effects can hamper data integration and interpretation. The success of batch-effect correction is often evaluated by visual inspection of low-dimensional embeddings, which are inherently imprecise. Here we present a user-friendly, robust and sensitive k-nearest-neighbor batch-effect test (kBET; https://github.com/theislab/kBET) for quantification of batch effects. We used kBET to assess commonly used batch-regression and normalization approaches, and to quantify the extent to which they remove batch effects while preserving biological variability. We also demonstrate the application of kBET to data from peripheral blood mononuclear cells (PBMCs) from healthy donors to distinguish cell-type-specific inter-individual variability from changes in relative proportions of cell populations. This has important implications for future data-integration efforts, central to projects such as the Human Cell Atlas.