  In exploratory data analysis of known classes of high dimensional data, a
central question is how distinct are the classes? The Direction Projection
Permutation (DiProPerm) hypothesis test provides an answer to this that is
directly connected to a visual analysis of the data. In this paper, we propose
an improved DiProPerm test that solves 3 major challenges of the original
version. First, we implement only balanced permutations to increase the test
power for data with strong signals. Second, our mathematical analysis leads to
an adjustment to correct the null behavior of both balanced and the
conventional all permutations. Third, new confidence intervals (reflecting
permutation variation) for test significance are also proposed for comparison
of results across different contexts. This improvement of DiProPerm inference
is illustrated in the context of comparing cancer types in examples from The
Cancer Genome Atlas.
