Date: Oct 21, 2012 5:42 AM
Author: Luis A. Afonso
Subject: The J-B test again (and again. . . )

The J-B test again (and again)

The Jarque-Bera Test shouldn?t be taken as a Goodness-of Fit one (Gof). The reason is evident: when we add two quantities and check if the result doesn?t exceed a certain value, the critical value, we loss track of each individually.
It?s vital to keep in mind that we start with a sample which the distribution is unknown.
When we fail to reject by J-B test we can assert that the total, only it, of the Skewness and Excess Kurtosis are in conformity with those normal data shows. So we are not allowed to say whatever concerning theses parameters values individually, as it was demanded by the test. Conclusion: the test is not a Gof one. In fact, a too large Skewness to be normal can be associated with a sufficiently small Kurtosis in order that the sum could indicate, wrongly, that there is no sufficient evidence to reject normality.

Luis A. Afonso