[R] Orthogonal Polynomials

[Bliese, Paul D MAJ WRAIR-Wash DC]

Looking to the wonderful statistical advice that this group can offer.

In behavioral science applications of stats, we are often introduced to
coefficients for orthogonal polynomials that are nice integers.  For
instance, Kirk's experimental design book presents the following
coefficients for p=4:

Linear     -3 -1  1  3
Quadratic   1 -1 -1  1
Cubic      -1  3 -3  1

In R orthogonal polynomials are not integers. For instance, in R where p =4:

> poly(c(1:4),3)
              1    2          3
[1,] -0.6708204  0.5 -0.2236068
[2,] -0.2236068 -0.5  0.6708204
[3,]  0.2236068 -0.5 -0.6708204
[4,]  0.6708204  0.5  0.2236068

Where, of course, column 1 is linear, column 2 Quadratic and 3 cubic.

My experience is that the coding scheme used in R works "better" than the
integer scheme discussed in Kirk for many regression type analyses.

Can anyone enlighten me as to why?

Thanks,

Paul Bliese
Walter Reed Army Institute of Research
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