replicating Krishnamoorthy's simulation to test the second-order James.  Seems to work like their results, with the exception of the tests where n = c(2,3,2).  Present results are higher than results provided in Krishnamoorthy.
Result from the small simulation that I did to check the James Second Order.
start of re-writing the Naive Anova function with summary statistics
corrected "estimator" to "test"