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Topic: The Jarque-Bera Normality Test, indeed?
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Luis A. Afonso

Posts: 4,617
From: LIsbon (Portugal)
Registered: 2/16/05
The Jarque-Bera Normality Test, indeed?
Posted: Sep 28, 2013 6:42 AM
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The Jarque-Bera Normality Test, indeed?


A type I error is made when we are lead not to reject a false null hypothesis, for example to ascribe Normality, i.e., a Gauss distribution, of a Chi-squared (or whatever) Distribution data, gathering trash, the Jarque-Bera is sometimes accused, with all reason, to allow. Surely the reason behind is because the test statistics is a two-parameters estimates sum, namely skewness and kurtosis, to which a trade-off between them is present at an unknown proportion, and consequently it can easily happens that one could be so large that will hide the absurd smallness, in terms of normality, the other have.
It should be noted that the Cumulative Distribution Function be obtained from rigorously normal data does not invalidate the criticism at all. In fact the test is on a unknown distribution to see though is normal, not to confirm that normal data is bounded by a test statistics critical value. One can avoid promptly this circular reasoning to justify the test validity. We made a step further from the XIII century Scholasticism, I mean.

Luis A. Afonso



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