[R] Problems with normality req. for ANOVA

[Bert Gunter]

My sympathies, but I don't think it's the business of list
contributors to facilitate stupidity.

"Confidence interval for the p-value" is nonsense. You could try
sensitivity analyses via simulation, though.

Cheers,

Bert Gunter
Genentech Nonclinical Biostatistics

On Mon, Aug 2, 2010 at 11:31 AM, wwreith <reith_william at bah.com> 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.
>
> 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
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> ________________________________
> 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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