[R] interpret significance from the contr.poly() function

[Ista Zahn]

By fitting some kind of model. contr.poly doesn't fit a model or test
significance, it just sets contrasts. Here is an example

data(mtcars)
> mtcars$carb <- factor(mtcars$carb)
> contrasts(mtcars$carb) <- contr.poly(n=levels(mtcars$carb))
> contrasts(mtcars$carb)
          .L         .Q         .C         ^4          ^5
1 -0.5976143  0.5455447 -0.3726780  0.1889822 -0.06299408
2 -0.3585686 -0.1091089  0.5217492 -0.5669467  0.31497039
3 -0.1195229 -0.4364358  0.2981424  0.3779645 -0.62994079
4  0.1195229 -0.4364358 -0.2981424  0.3779645  0.62994079
6  0.3585686 -0.1091089 -0.5217492 -0.5669467 -0.31497039
8  0.5976143  0.5455447  0.3726780  0.1889822  0.06299408
> mt.mod <- lm(mpg ~ carb, data=mtcars)
> summary(mt.mod)

Call:
lm(formula = mpg ~ carb, data = mtcars)

Residuals:
   Min     1Q Median     3Q    Max
-7.243 -3.325  0.000  2.360  8.557

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  19.0888     1.3373  14.274 8.18e-14 ***
carb.L       -7.2101     3.6566  -1.972   0.0594 .
carb.Q        3.4101     3.2378   1.053   0.3019
carb.C       -2.2938     3.4567  -0.664   0.5128
carb^4       -4.1155     3.3132  -1.242   0.2253
carb^5       -0.1224     2.6213  -0.047   0.9631
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.905 on 26 degrees of freedom
Multiple R-squared: 0.4445,     Adjusted R-squared: 0.3377
F-statistic: 4.161 on 5 and 26 DF,  p-value: 0.006546


Best,
Ista

On Thu, Feb 3, 2011 at 8:36 AM, Asan Ramzan <asanramzan at yahoo.com> wrote:
> Hello R-help
> I don’t know how to interpret significance from the contr.poly() function . From
> the example below
> : how can I tell if data has a significant Linear/quadratic/cubic trend?
>> contr.poly(4, c(1,2,4,8))
>               .L         .Q          .C
> [1,] -0.51287764  0.5296271 -0.45436947
> [2,] -0.32637668 -0.1059254  0.79514657
> [3,]  0.04662524 -0.7679594 -0.39757328
> [4,]  0.79262909  0.3442576  0.05679618
>>
>> diff(contr.poly(4, c(1,2,4,8))[,1])
> [1] 0.1865010 0.3730019 0.7460038
> Thanks
>
>
>
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-- 
Ista Zahn
Graduate student
University of Rochester
Department of Clinical and Social Psychology
http://yourpsyche.org