[R] Problems with normality req. for ANOVA

[Michael Dewey]

At 19:31 02/08/2010, wwreith wrote:

>I am testing normality on the studetized residuals that are 
>generated after performing ANOVA and yes I used Levene's test to see 
>if the variances can be assumed equal. They infact are not, but I 
>have found a formula for determining whether the p-value for ANOVA 
>will become larger or smaller as a result of unequal variances and 
>unequal sample sizes. Fortuneately it turns out the p-value is 
>greater. Despite this the ANOVA test is still significant with p=.000.

Well perhaps this is starting a new hare but surely if you have shown 
the variances are unequal you have already shown the treatment(s) 
made a difference?


>The problem I have is that I am expected, by my client, to find a 
>similiar formula that states which way the p-value would be pushed 
>by a lack of normality. Despite numerous citations that ANOVA is 
>robust to departures of normality my client does not care. They want 
>numerical proof. This lead to looking for a method for estimating 
>the effects non normality would have on the p-value for ANOVA. In 
>other words can I build a confidence interval for the p-value? Hence 
>the error term I am speaking of would be a the margin or error for 
>p-value confidence interval.
>
>William W. Reith III
>
>Business Analytics
>J9 SAC (757)-203-3400  Best Contact From 7:00am-4:00pm
>J9 Office (757)-203-3772
>Booz Office (757) 466-3253
>Mobile (434)-989-7948
>
>________________________________
>From: David Winsemius [via R] 
>[ml-node+2310616-1859960724-371040 at n4.nabble.com]
>Sent: Monday, August 02, 2010 1:33 PM
>To: Reith, William [USA]
>Subject: Re: Problems with normality req. for ANOVA
>
>
>On Aug 2, 2010, at 9:33 AM, wwreith wrote:
>
> >
> > I am conducting an experiment with four independent variables each
> > of which
> > has three or more factor levels. The sample size is quite large i.e.
> > several
> > thousand. The dependent variable data does not pass a normality test
> > but
> > "visually" looks close to normal so is there a way to compute the
> > affect
> > this would have on the p-value for ANOVA or is there a way to
> > perform an
> > nonparametric test in R that will handle this many independent
> > variables.
> > Simply saying ANOVA is robust to small departures from normality is
> > not
> > going to be good enough for my client.
>
>The statistical assumption of normality for linear models do not apply
>to the distribution of the dependent variable, but rather to the
>residuals after a model is estimated. Furthermore, it is the
>homoskedasticity assumption that is more commonly violated and also
>greater threat to validity. (And if you don't already know both of
>these points, then you desperately need to review your basic modeling
>practices.)
>
> >  I need to compute an error amount for
> > ANOVA or find a nonparametric equivalent.
>
>You might get a better answer if you expressed the first part of that
>question in unambiguous terminology.  What is "error amount"?
>
>For the second part, there is an entire Task View on Robust
>Statistical Methods.
>
>--
>
>David Winsemius, MD
>West Hartford, CT
>
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Michael Dewey
http://www.aghmed.fsnet.co.uk