> grain1
   density grain
1       10  12.2
2       10  11.4
3       10  12.4
4       20  16.0
5       20  15.5
6       20  16.5
7       30  18.6
8       30  20.2
9       30  18.2
10      40  17.6
11      40  19.3
12      40  17.1
13      50  18.0
14      50  16.4
15      50  16.6
> 
> tapply(grain,density,mean)
10 20 30 40 50 
12 16 19 18 17 
> tapply(grain,density,mean)
10 20 30 40 50 
12 16 19 18 17 
> 
> grain.mod <- aov(grain~densityf)
> summary.lm(grain.mod)

Call:
aov(formula = grain ~ densityf)

Residuals:
   Min     1Q Median     3Q    Max 
 -0.90  -0.55  -0.40   0.45   1.30 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  16.4000     0.2233  73.441 5.35e-15 ***
densityf.L    3.7947     0.4993   7.600 1.84e-05 ***
densityf.Q   -3.7417     0.4993  -7.493 2.08e-05 ***
densityf.C    0.3162     0.4993   0.633    0.541    
densityf^4    0.8367     0.4993   1.676    0.125    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.8649 on 10 degrees of freedom
Multiple R-squared: 0.9213,     Adjusted R-squared: 0.8899 
F-statistic: 29.28 on 4 and 10 DF,  p-value: 1.690e-05 

> 
> summary(grain.mod,split=list(densityf=list(linear=1, quadratic=2,
+ cubic=3, quartic=4)))
                      Df Sum Sq Mean Sq F value    Pr(>F)    
densityf               4  87.60  21.900 29.2781 1.690e-05 ***
  densityf: linear     1  43.20  43.200 57.7540 1.841e-05 ***
  densityf: quadratic  1  42.00  42.000 56.1497 2.079e-05 ***
  densityf: cubic      1   0.30   0.300  0.4011    0.5407    
  densityf: quartic    1   2.10   2.100  2.8075    0.1248    
Residuals             10   7.48   0.748                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1