#ANOVA in Splus

Data:  The Kenton Food Example in Chapter 16

New Splus functions:
    tapply: can be used to calculate summary statistics by group
    aov:  one of several ways to fit an ANOVA model in Splus
    multicomp:  do multiple comparisons in Splus (only available in
        Splus version 4 and later)
________________________________________________________________________


>kenton<-read.table("CH16TA01.DAT",header=T)
>kenton$design<-factor(kenton$design)
>kenton$store<-factor(kenton$store)

>kenton
   num.cases design store 
 1        11      1     1
 2        17      1     2
 3        16      1     3
 4        14      1     4
 5        15      1     5
 6        12      2     1
 7        10      2     2
 8        15      2     3
 9        19      2     4
10        11      2     5
11        23      3     1
12        20      3     2
13        18      3     3
14        17      3     4
15        27      4     1
16        33      4     2
17        22      4     3
18        26      4     4
19        28      4     5

#____________________________________________________________________________
#Some EDA

> summary(kenton)                   
    num.cases    design   store   
 Min.   :10.00   1:5      1:4    
 1st Qu.:14.50   2:5      2:4    
 Median :17.00   3:4      3:4    
 Mean   :18.63   4:5      4:4    
 3rd Qu.:22.50            5:3    
 Max.   :33.00                   

> tapply(kenton$num.cases,kenton$design,mean)
    1    2    3    4 
 14.6 13.4 19.5 27.2
> sqrt(tapply(kenton$num.cases,kenton$design,var))
        1        2        3        4 
 2.302173 3.646917 2.645751 3.962323

motif()
par(mfrow=c(2,2))
boxplot(split(kenton$num.cases,kenton$design),xlab="Design",
	 ylab="# of cases")
title("Figure 1")

NOTES:
1.  Why didn't I draw a boxplot split on store number?
2.  See also the command:  plot.factor

#__________________________________________________________
#ANOVA
#There are many ways to fit ANOVA models in Splus.  The command aov is
#one possibility: 

>ken.aov<-aov(num.cases~design,kenton)

> print(summary(ken.aov),digits=4)
          Df Sum of Sq Mean Sq F Value      Pr(F) 
   design  3     588.2   196.1   18.59 0.00002585
Residuals 15     158.2    10.5         


#The multicomp command computes simultaneous confidence intervals.
#This command is only available in Splus version 4 and later, so it is
#not currently available in our Unix version of Splus

> multicomp(ken.aov,plot=T)

95 % simultaneous confidence intervals for specified 
linear combinations, by the Tukey method 

critical point: 2.8822 
response variable: num.cases 

intervals excluding 0 are flagged by '****' 

    Estimate Std.Error Lower Bound Upper Bound      
1-2      1.2      2.05       -4.72       7.120     
1-3     -4.9      2.18      -11.20       1.380     
1-4    -12.6      2.05      -18.50      -6.680 ****
2-3     -6.1      2.18      -12.40       0.179     
2-4    -13.8      2.05      -19.70      -7.880 ****
3-4     -7.7      2.18      -14.00      -1.420 ****


#__________________________________________________________
#Some diagnostics

#see page 757 of NKNW (using semi-studentized residuals here)
e.star<-ken.aov$residual/sqrt(sum(ken.aov$residual^2)/ken.aov$df.residual)

plot(kenton$design,e.star)
abline(h=0)
title("Figure 2")

plot(unclass(kenton$design),e.star) 
abline(h=0)
title("Figure 3")

qqnorm(e.star)
title("Figure 4")

#__________________________________________________________