Date:         Fri, 11 Feb 2005 09:15:22 +0000
Reply-To:     Jeremy Miles <jnvm1@york.ac.uk>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Jeremy Miles <jnvm1@york.ac.uk>
Subject:      Re: Statistics Question
Comments: To: Marta García-Granero <biostatistics@terra.es>
In-Reply-To:  <154789717.20050211094805@terra.es>
Content-Type: text/plain; charset="iso-8859-1"; format=flowed

At 08:48 11/02/2005, Marta García-Granero wrote:
>Hi
>
>MK> Yours is a good example of the fact that ANOVA is not nearly
>MK> as robust against violations of normality as is often believed,
>MK> e.g., in my own field of social psychology. ANOVA is fairly robust
>MK> against violations of kurtosis, but is much more sensitive toward
>MK> violations of symmetry.
>
>I have read just the opposite. ANOVA is considered to be quite robust
>against violations of symmetry (as a matter of fact, Levene test is an
>ANOVA on the absolute values of the residuals, with are really
>assymetric). On the other hand, high kurtosis lowers efficiency (not
>validity) of the ANOVA. High kurtosis happens when outliers are
>present (standard deviation is increased, and p values too). Non
>parametric methods handle outliers quite well (replacing them by the
>lowest/highest ranks), that's why they give better results for
>leptokurtic distributions.

Rand Wilcox has done a lot of work on this.  If you are interested, have a
look at, for example, Introduction to Robust Estimation and Hypothesis
Testing, by Wilcox, published by Acadmic Press, or his paper:

Wilcox, R. R (1998).  How many discoveries have been lost by ignoring modern
    statistical methods?  American Psychologist, 53 (3), 300-314.


JM







Jeremy Miles
mailto:jnvm1@york.ac.uk             http://www-users.york.ac.uk/~jnvm1/
Dept of Health Sciences (Area 4),  University of York,  York,  YO10 5DD
Phone: 01904 321375       Mobile: 07941 228018         Fax 01904 321320