> ## sec 2.8 Tire Exp't
> #
> data<-read.table("tire.dat", h=T, skip=2)  
> data
   Tire Compound Wear
1     1        A  238
2     1        B  238
3     1        C  279
4     2        A  196
5     2        B  213
6     2        D  308
7     3        A  254
8     3        C  334
9     3        D  367
10    4        B  312
11    4        C  421
12    4        D  412
> g<- lm(Wear ~ as.factor(Tire) + Compound, data = data)
> anova(g)  # table 2.25
Analysis of Variance Table

Response: Wear
                Df Sum Sq Mean Sq F value    Pr(>F)    
as.factor(Tire)  3  39123   13041  37.240 0.0007618 ***
Compound         3  20729    6910  19.732 0.0033516 ** 
Residuals        5   1751     350                      
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 
> summary(g) # part of table 2.26

Call:
lm(formula = Wear ~ as.factor(Tire) + Compound, data = data)

Residuals:
      1       2       3       4       5       6       7       8       9 
 13.208   8.833 -22.042  -7.917   4.708   3.208  -5.292  -1.542   6.833 
     10      11      12 
-13.542  23.583 -10.042 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       224.792     14.292  15.728 1.89e-05 ***
as.factor(Tire)2  -20.875     16.206  -1.288  0.25410    
as.factor(Tire)3   34.500     16.206   2.129  0.08653 .  
as.factor(Tire)4   96.375     16.206   5.947  0.00192 ** 
CompoundB           4.375     16.206   0.270  0.79798    
CompoundC          76.250     16.206   4.705  0.00531 ** 
CompoundD         100.875     16.206   6.225  0.00157 ** 
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

Residual standard error: 18.71 on 5 degrees of freedom
Multiple R-Squared: 0.9716,	Adjusted R-squared: 0.9375 
F-statistic: 28.49 on 6 and 5 DF,  p-value: 0.001029 

> 
> # For a BIBD, ANOVA depends on the order of the treatment and block factors entering the model.
> # E.g., the following ANOVA table is different from Table 2.25
> # the correct ANOVA is Table 2.25 (the treatment effects are adjusted for the block effects)
> g<- lm(Wear ~ Compound + as.factor(Tire) , data = data)
> anova(g)  
Analysis of Variance Table

Response: Wear
                Df Sum Sq Mean Sq F value    Pr(>F)    
Compound         3  38814   12938  36.946 0.0007763 ***
as.factor(Tire)  3  21038    7013  20.026 0.0032406 ** 
Residuals        5   1751     350                      
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1