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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