Single cell Higher Order Testing (scHOT) is an R package that facilitates testing changes in higher order structure of gene expression along either a developmental trajectory or across space. scHOT is general and modular in nature, can be run in multiple data contexts such as along a continuous trajectory, between discrete groups, and over spatial orientations; as well as accommodate any higher order measurement such as variability or correlation. scHOT meaningfully adds to first order effect testing, such as differential expression, and provides a framework for interrogating higher order interactions from single cell data.