  Distinguishing between uniform and non-uniform sample distributions is a
common problem in directional data analysis; however for many tests,
non-uniform distributions exist that fail uniformity rejection. By merging
directional statistics with frame theory, we find that probabilistic tight
frames yield non-uniform distributions that minimize directional potentials,
leading to failure of uniformity rejection for the Bingham test. Finally, we
apply our results to model patterns found in granular rod experiments.
