Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 3, 387--398

A TRANSFORMATION TO NORMALITY FOR THE SKEWNESS COEFFICIENT IN NORMAL SAMPLES

By

RAM\'ON ARDANUY, MAR\'IA M. SOLDEVILLA and QUINT\'IN MART\'IN Universidad de Salamanca, Salamanca

SUMMARY. D'Agostino's formula to transform g1 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 g1 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 g1 to ±a 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.

AMS (1991) subject classification. 62E15, 62E20, 62Q05, 62F03.

Key words and phrases. D'Agostino's formula, percentage points, skewness, test for normality, transformations to normality.

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