R version 3.2.1 (2015-06-18) -- "World-Famous Astronaut"
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> # Taken from Rosenkrantz, Probability and Statistics for Science, Engineering and Finance, CRC 2008
> # p. 470. (Source Wetherill (1967) Elementary Statistical methods)
> # Data lists arithmetic test scores for pupils divided randomly into five equal sized groups.
> # Groups 1 and 2 were taught by the current method. Group 4,5 and 6 were taught together.
> # On each day, group 3 students were praised publicly, group 4 students were criticized publicly
> # and group 5 students heard the praise and criticism of the other students but were otherwise ignored.
> # Is there a difference in the responses of the five groups?
> #
> # ENTER PUPIL TEST SCORES
> #
>
> Score=scan();
1: 17 14 24 20 24 23 16 15 24
10: 21 23 13 19 13 19 20 21 16
19: 28 30 29 24 27 30 28 28 23
28: 19 28 26 26 19 24 24 23 22
37: 21 14 13 19 15 15 10 18 20
46: 
Read 45 items
>
> # CHECK
>
> matrix(Score,ncol=9,byrow=T)
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
[1,]   17   14   24   20   24   23   16   15   24
[2,]   21   23   13   19   13   19   20   21   16
[3,]   28   30   29   24   27   30   28   28   23
[4,]   19   28   26   26   19   24   24   23   22
[5,]   21   14   13   19   15   15   10   18   20
> 
> # ENTER TEACHING METHOD. MAKE IT A FACTOR
>
> Meth=rep(c("Con1","Con2", "Praised","Criticized","Ignored"),each=9);Meth;
 [1] "Con1"       "Con1"       "Con1"       "Con1"       "Con1"       "Con1"       "Con1"       "Con1"      
 [9] "Con1"       "Con2"       "Con2"       "Con2"       "Con2"       "Con2"       "Con2"       "Con2"      
[17] "Con2"       "Con2"       "Praised"    "Praised"    "Praised"    "Praised"    "Praised"    "Praised"   
[25] "Praised"    "Praised"    "Praised"    "Criticized" "Criticized" "Criticized" "Criticized" "Criticized"
[33] "Criticized" "Criticized" "Criticized" "Criticized" "Ignored"    "Ignored"    "Ignored"    "Ignored"   
[41] "Ignored"    "Ignored"    "Ignored"    "Ignored"    "Ignored"   
> Method=factor(Meth);
> 
> # PRINT SUMMARY BY METHOD
>
> tapply(Score,Method,summary);
$Con1
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  14.00   16.00   20.00   19.67   24.00   24.00 

$Con2
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  13.00   16.00   19.00   18.33   21.00   23.00 

$Criticized
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  19.00   22.00   24.00   23.44   26.00   28.00 

$Ignored
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  10.00   14.00   15.00   16.11   19.00   21.00 

$Praised
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  23.00   27.00   28.00   27.44   29.00   30.00 
>
> # SIDE-BY-SIDE BOXPLOT BY METHOD
>
> plot(Score~Method)
>
> # RUN ONE-WAY ANALYSIS OF VARIANCE. PRINT ANOVA TABLE, SUM-SQUARES AND DEGREES OF FREEDOM
>
> p=aov(Score~Method);summary(p)
            Df Sum Sq Mean Sq F value   Pr(>F)    
Method       4  722.7  180.67   15.27 1.16e-07 ***
Residuals   40  473.3   11.83                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> print(p)
Call:
   aov(formula = Score ~ Method)

Terms:
                  Method Residuals
Sum of Squares  722.6667  473.3333
Deg. of Freedom        4        40

Residual standard error: 3.439961
Estimated effects may be unbalanced
>
> # ESTIMATES OF EFFECTS MU_i
>
> tapply(Score,Method,mean)
      Con1       Con2 Criticized    Ignored    Praised 
  19.66667   18.33333   23.44444   16.11111   27.44444 
>
> # DO ANOVA "BY HAND"
>
> MSTr=9*var(tapply(Score,Method,mean));MSTr
[1] 180.6667
> MSE=mean(tapply(Score,Method,var));MSE
[1] 11.83333
> f=MSTr/MSE;f
[1] 15.26761
> pf(f,4,40,lower.tail=F)
[1] 1.162741e-07
> qf(.001,4,40,lower.tail=F)
[1] 5.698134
>
> # PRINT ESTIMATED  MU_i'S = "FITTED VALUES"
>
> matrix(fitted(p),ncol=9,byrow=T)
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]     [,9]
[1,] 19.66667 19.66667 19.66667 19.66667 19.66667 19.66667 19.66667 19.66667 19.66667
[2,] 18.33333 18.33333 18.33333 18.33333 18.33333 18.33333 18.33333 18.33333 18.33333
[3,] 27.44444 27.44444 27.44444 27.44444 27.44444 27.44444 27.44444 27.44444 27.44444
[4,] 23.44444 23.44444 23.44444 23.44444 23.44444 23.44444 23.44444 23.44444 23.44444
[5,] 16.11111 16.11111 16.11111 16.11111 16.11111 16.11111 16.11111 16.11111 16.11111
>
> # PRINT RESIDUALS = OBSERVED - FITTED
>
> matrix(residuals(p),ncol=9,byrow=T)
           [,1]      [,2]      [,3]       [,4]       [,5]       [,6]       [,7]       [,8]      [,9]
[1,] -2.6666667 -5.666667  4.333333  0.3333333  4.3333333  3.3333333 -3.6666667 -4.6666667  4.333333
[2,]  2.6666667  4.666667 -5.333333  0.6666667 -5.3333333  0.6666667  1.6666667  2.6666667 -2.333333
[3,]  0.5555556  2.555556  1.555556 -3.4444444 -0.4444444  2.5555556  0.5555556  0.5555556 -4.444444
[4,] -4.4444444  4.555556  2.555556  2.5555556 -4.4444444  0.5555556  0.5555556 -0.4444444 -1.444444
[5,]  4.8888889 -2.111111 -3.111111  2.8888889 -1.1111111 -1.1111111 -6.1111111  1.8888889  3.888889
> 
> # CHECK ON MODEL TO SEE IF RESIDUALS ARE PLAUSIBLY NORMAL
>
> qqnorm(residuals(p),,ylab="Residuals");qqline(residuals(p))
>