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D'Agostino & Pearson (1973) gave percentage points of the distribution of b2 for independent observations from a common univariate normal distribution. Their results can be adequately approximated, when the first three moments of the distribution of b2 have been determined, by fitting a linear function of the reciprocal of a X2 variable and then using the Wilson-Hilferty transformation. Evidence is presented suggesting that the same method of approximation is satisfactory for the b2 statistic calculated from any set of linear-least-squares residuals, on the hypothesis of normal homoscedastic errors.
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Anscombe et al. (1983) studied this question.
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