
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

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________________________________
From: David Winsemius [via R] [ml-node+2310616-1859960724-371040@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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