Stat 141  Nov 10
Analysis of Variance continued: 
    randomized blocks, factorial designs

> # do randomixed block alfalfa (SW p.487 "alfalfa and acid rain")

> alf = read.table(file="D:\\stat141\\alfalfa.dat", header = T)
> attach(alf)
> interaction.plot(trt, block, height) # plot of cell means, here n=1
> tapply(height, list(trt,block), mean)  #table cell means
           a    b    c    d   e
control 2.47 2.15 1.46 2.36 1.0
high    1.10 1.05 0.50 1.00 1.5
low     1.58 1.15 1.27 1.25 1.0

> rndb = aov(height ~ trt + block) # two factor anova, no interaction
> summary(rndb)                                  #match Table 11.9
            Df  Sum Sq Mean Sq F value  Pr(>F)  
trt          2 1.98601 0.99301  5.4709 0.03182 *
block        4 0.83963 0.20991  1.1565 0.39740  
Residuals    8 1.45205 0.18151   

> TukeyHSD(rndb)
  Tukey multiple comparisons of means
    95% family-wise confidence level
Fit: aov(formula = height ~ trt + block)
$trt
               diff       lwr       upr
high-control -0.858 -1.627935 -0.088065
low-control  -0.638 -1.407935  0.131935
low-high      0.220 -0.549935  0.989935
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           factorial designs soybean data. (plus co2 toads, summary in text)

> soy = read.table(file="D:\\stat141\\soybean.dat", header = T)
> attach(soy); tapply(area, list(shaking,light), mean)  # Table 11.11 p.492
             low moderate
control 245.3077 304.0769
stress  212.9231 268.8462

> tapply(area, list(shaking,light), sd)
             low moderate
control 27.02278 26.92416
stress  29.74744 35.23220

> tapply(area, list(shaking,light), length)
        low moderate
control  13       13
stress   13       13

> interaction.plot(shaking, light, area)    # Fig 11.4 p.493

> soyaov = aov(area ~ shaking*light)
> summary(soyaov)                                #
              Df Sum Sq Mean Sq F value    Pr(>F)    
shaking        1  14858   14858 16.5954 0.0001725 ***
light          1  42752   42752 47.7490 1.010e-08 ***
shaking:light  1     26      26  0.0294 0.8645695    
Residuals     48  42976     895                      
---

> TukeyHSD(soyaov)  [single contrast, row and column]