[R] Problems with normality req. for ANOVA

[Frank Harrell]

To add to David's note, the Kruskal-Wallis test is the nonparametric 
counterpart to one-way ANOVA.  You can get a series of K-W tests for 
several grouping or continuous independent variables (but note these 
are SEPARATE analyses) using the Hmisc package's spearman2 function. 
The generalization of K-W to the case of multiple independent 
variables is the proportional odds ordinal logistic model (see e.g. 
the rms package lrm function).

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

On Mon, 2 Aug 2010, David Winsemius wrote:

>
> 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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