When comparing biological conditions using mass cytometry data, a key challenge is to identify cellular populations that change in abundance. Here, we present a computational strategy for detecting 'differentially abundant' populations by assigning cells to hyperspheres, testing for significant differences between conditions and controlling the spatial false discovery rate. Our method (http://bioconductor.org/packages/cydar) outperforms other approaches in simulations and finds novel patterns of differential abundance in real data.