[R] Non-parametric four-way interactions?

[Paul Smith]

Dear All

I am trying to study four-way interactions in an ANOVA problem.
However, qqnorm+qqline result

(at http://phhs80.googlepages.com/qqnorm.png)

is not promising regarding the normality of data (960 observations).
The result of Shapiro-Wilk test is also not encouraging:

W = 0.9174, p-value < 2.2e-16

(I am aware of the fact that normality tests tend to reject normality
for large samples.)

By the way, the histogram is at:

http://phhs80.googlepages.com/hist.png

To circumvent the problem, I looked for non-parametric tests, but I
found nothing, but the article:

http://www.pgia.ac.lk/socs/asasl/journal_papers/PDFformat/g.bakeerathanpaper-2.pdf

Finally, my question is: has R got implemented functions to use
non-parametric tests to avoid the fulfillment of the normality
assumption required to study four-way interactions?

Thanks in advance,

Paul