Re: Standards for "Skewness"

[David A. Heiser]

Skewness is only well defined for univariate distributions. The Johnson SU distribution approximation for the skewness distribution converts a Pearson skewness measure to a normal distribution Z value. As with all large data sets, a small skewness will show up as indicationg that the departure from normality is significant.   Bollen in his book in page 421 gives D'Agostino's formulas for the computation. I can give you a version in BASIC if you are interested. It is generally accepted that D'Agostino's approximation gives reasonably accurate results for samples with N>8.   In the multivariate world, skewness is not clear. You may have only one variable out of p-1 variables that is highly skew, and a multivariate test will show no significance. The effects are mediated by the covariance and averaging effects of the matrix of the data as a whole. The whole (as a single number) poorly represents individual variable skewness.   Bollen's formula 9.78 is wrong. It does not correspond to Mardia's outstanding work on multivariate skewness measures. I am working on this issue now.   DAH                 ----- Original Message ----- From: Ronald B. Livingston To: [EMAIL PROTECTED] Sent: Monday, December 20, 1999 11:25 AM Subject: Standards for "Skewness" Hello:      Are there "standards" for describing the skew of a distribution?  For example, 0 to 1 = mild; 1 - 2 = moderate, etc.  I am aware of tests of significance for skew, but with large samples practically any skew is significant. Any references would be appreciated.   Sincerely,   Ron