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Convex rank tests are coarsenings of the hyperplane arrangement associated to the symmetric group. Semigraphoids are combinatorial structures that correspond to squares and hexagons on a polytope known as the permutohedron. These objects - convex rank tests and semigraphoids - are equivalent, and this result allows us to answer a question posed by Postnikov, Reiner, and Williams. No prior knowledge of hyperplane arrangements or permutohedra will be assumed.

This work originated in collaboration with the Pourqui\'{e} lab at the Stowers Institute in Kansas City. We describe the experiments conducted to identify the molecular components of biological clocks, and explain how the convex rank test called the cyclohedron test contributes to time course microarray data analysis.