[R] Problems with normality req. for ANOVA

[Frank Harrell]

In addition the poster did not tell us what is wrong with a 
nonparametric test.

Frank E Harrell Jr   Professor and Chairman        School of Medicine
                      Department of Biostatistics   Vanderbilt University

On Mon, 2 Aug 2010, Bert Gunter wrote:

> 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
>> 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
>>
>> ______________________________________________
>> [hidden email]<https://webmail.bah.com/OWA/UrlBlockedError.aspx> mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>> ________________________________
>> View message @ http://r.789695.n4.nabble.com/Problems-with-normality-req-for-ANOVA-tp2310275p2310616.html
>> To unsubscribe from Problems with normality req. for ANOVA, click here< (link removed) =>.
>>
>>
>> --
>> View this message in context: http://r.789695.n4.nabble.com/Problems-with-normality-req-for-ANOVA-tp2310275p2310738.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
>>        [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>