> 
> tapply(cases,package,sum)
  1   2   3   4 
 73  67  78 136 
> sum(cases)
[1] 354
> 
> tapply(cases,package,mean)
   1    2    3    4 
14.6 13.4 19.5 27.2 
> mean(cases)
[1] 18.63158
> 
> tapply(cases,package,length)
1 2 3 4 
5 5 4 5 
> length(cases)
[1] 19
> 
> 
> kenton.aov1 <- aov(cases ~ factor(package))
> summary(kenton.aov1)
                Df Sum Sq Mean Sq F value   Pr(>F)    
factor(package)  3  588.2  196.07   18.59 2.58e-05 ***
Residuals       15  158.2   10.55                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> summary.lm(kenton.aov1)

Call:
aov(formula = cases ~ factor(package))

Residuals:
   Min     1Q Median     3Q    Max 
 -5.20  -1.95  -0.20   1.50   5.80 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)        14.600      1.452  10.053 4.66e-08 ***
factor(package)2   -1.200      2.054  -0.584   0.5677    
factor(package)3    4.900      2.179   2.249   0.0399 *  
factor(package)4   12.600      2.054   6.135 1.91e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 3.248 on 15 degrees of freedom
Multiple R-squared: 0.7881,     Adjusted R-squared: 0.7457 
F-statistic: 18.59 on 3 and 15 DF,  p-value: 2.585e-05 

> 
> e <- resid(kenton.aov1)
> 
> tapply(e,package,sum)
            1             2             3             4 
 5.551115e-16  5.329071e-15  4.440892e-16 -1.665335e-15 
> sum(e)
[1] 4.662937e-15
>