A Transformation to Normality for the Skewness Coefficient in Normal Samples

D'Agostino's formula to transform$g_{1}$to normality, in normal samples of size n, is based on Johnson SU transformation. It can be used for n ≥ 8 but does not take into account the fact that the range of$g_{1}$is bounded by$A_{n}=\pm (n-2)/\sqrt{(n-1)}$, so it loses accuracy for extreme percentage points. In this paper we propose first to transform the range of$g_{1}$to ±∞ by means of a logit function and then to make a Johnson SU transformation to normality. The transformation proposed can be applied for n ≥ 4 and it is slightly more accurate than D'Agostino's formula for n ≥ 8, avoiding the lateral effect of that transformation. A polynomial improvement, tables and approximate formulae to carry out the transformation are given in this paper, as well as some empirical comparative results, between the mentioned transformations.