[S] Summary : Tests for Normality

sinclair, andrew (asinclair@edfman.co.uk)
Tue, 10 Nov 1998 10:37:00 +0000

Thanks for the very helpful suggestions, and in some cases code,
got to (in no particular order) :
Mark Salmon, Richard Lockhart, Kenneth Butler, Don McKenzie,
Viswanath Devanarayan, David J Cummins and Andrew White.

I summarise here the tests that were mentioned, with _my_ interpretation
of the comments that were made about them (apologies for not attributing
individual comments, and possibly scrambling them !? ).

Anderson-Darling A-squared - widely used in financial data.

Bera-Jarque / Kiefer-Salmon - used in econometrics,
similar form to Bowman-Shenton statistic.

Bowman-Shenton KS-squared - based on joint distribution of the 3rd and 4th

Brown and Hettmansperger - recently developed, see their 1996 paper [3].
Splus code written by Viswanath Devanarayan and David J Cummins available.

Chi-squared goodness-of-fit - a general goodness of fit test, unlikely to
be powerful for this specific application.

Kolmogorov-Smirnov - "For testing normality, the Kolmogorov-Smirnov test is
a historical curiosity. It should never be used." [1]

Quantile-quantile plots vs Normal - simple visual test.

Shapiro Wilk - sensitive to general alternatives.

T3 plots - method by Sucharita Ghosh. Code available, I believe there is a
paper ?

References mentioned were:

[1] D'Agostino and M.A. Stephens eds., Marcel Dekker, Goodness of Fit

[2] Bowman, K.O. and L.R. Shenton. 1975. Omnibus test contours for
departures from
normality based on b1 and b2. Biometrika 62:243-50

[3] Brown and Hettmansperger, JASA, December 1996, vol 91, No. 436, pp.

[4] Greene,W. Econometric Analysis

The original question :

> Does anyone know of code/ references for tests of normality ?
> I am aware of qqnorm plots, Kolmogorov Smirnoff and chi squared
> goodness of fit tests. I need procedures that give a specific p-values,
> and preferably are sensitive to alternatives with fat tails (which is not
> true for K-S in my experience).
> Many thanks for any advice - I will summarise responses that
> are sent to me only.
> Andrew

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