> tapply(zinc,list(city,rate),mean)
     0.5     1    1.5
A 24.550 30.45 36.175
B 31.175 48.20 72.600
C 19.100 21.90 20.050
> 
> barley.mod1 <- aov(zinc ~ city + rate + city:rate)
> summary(barley.mod1)
            Df Sum Sq Mean Sq F value    Pr(>F)    
city         2 5720.7 2860.34 149.130 2.560e-15 ***
rate         2 1945.4  972.72  50.715 7.185e-10 ***
city:rate    4 1809.4  452.35  23.584 1.779e-08 ***
Residuals   27  517.9   19.18                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> summary(barley.mod1,split=list(rate=list(linear=1,quadratic=2)))
                       Df Sum Sq Mean Sq  F value    Pr(>F)    
city                    2 5720.7 2860.34 149.1297 2.560e-15 ***
rate                    2 1945.4  972.72  50.7150 7.185e-10 ***
  rate: linear          1 1944.0 1944.00 101.3546 1.229e-10 ***
  rate: quadratic       1    1.4    1.44   0.0753    0.7858    
city:rate               4 1809.4  452.35  23.5842 1.779e-08 ***
  city:rate: linear     2 1760.1  880.07  45.8845 2.065e-09 ***
  city:rate: quadratic  2   49.3   24.63   1.2839    0.2933    
Residuals              27  517.9   19.18                       
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
>