# problem-11.16

problem-11.16 We need to compare the following

    > summary(lm(Speed ~ factor(Expt),data=morley))
    ...
    Coefficients:
                     Estimate Std. Error t value Pr(>|t|)
    (Intercept)         909.0       16.6   54.76  < 2e-16 ***
    factor(Expt)2    -53.0       23.5   -2.26  0.02625 *
    factor(Expt)3    -64.0       23.5   -2.73  0.00763 **
    factor(Expt)4    -88.5       23.5   -3.77  0.00028 ***
    factor(Expt)5    -77.5       23.5   -3.30  0.00136 **

To the output of TukeyHSD()

    > TukeyHSD(aov(Speed ~ factor(Expt), data=morley))
      Tukey multiple comparisons of means
        95% family-wise confidence level

    Fit: aov(formula = Speed ~ factor(Expt), data = morley)

    $"factor(Expt)"
         diff     lwr    upr
    2-1 -53.0 -118.28  12.28
    3-1 -64.0 -129.28   1.28
    4-1 -88.5 -153.78 -23.22
    5-1 -77.5 -142.78 -12.22
    3-2 -11.0  -76.28  54.28
    4-2 -35.5 -100.78  29.78
    5-2 -24.5  -89.78  40.78
    4-3 -24.5  -89.78  40.78
    5-3 -13.5  -78.78  51.78
    5-4  11.0  -54.28  76.28

The latter flags 4-1, 5-1 and 5-4. The marginal tests find that all the means are different from the reference level 1.