Johannes Hain (Aug. 2010) Comparison of Common Tests for Normality (pg.59)
There is a different approach than Jarque-Bera?s to test normality through Skewness and Kurtosis: the tests are performed separately, each parameter in turn. A rectangle of no significance is obtained with significance alpha´=0.0253 and 0.0050 for each side. The 0.05 and 0.01 compound alpha are then obtained approximately (alpha= 1-sqrt(1-alpha´), Sidak). Note that the procedure demands a not checked feature namely the parameter´s tests independence.