ST4241: Design and Analysis of Clinical Trials - The Department of ...

where the dummy variables b i ’s and t j ’s are defined conventionally.
The R code
lm.fit1=lm(x~s+a)
produces the following ANOVA table:
Df Sum Sq Mean Sq F value Pr(>F)
s 9 982.00 109.11 11.7558 2.615e-05 ***
a 5 35.44 7.09 0.7638 0.5898
Residuals 15 139.22 9.28
The F ratio for the examiner effect is 0.7638 with a p-value 0.5898. There is no significant
effect of the examiners.
(ii) By looking at the data, it seems that Examiner 5 and 6 have higher mean scores than the
other examiners. One would like to see whether the following contrasts are significant:
α 1 + α 2 + α 3 + α 4
4
α 1 + α 2 + α 3 + α 4
4
α 1 + α 2 + α 3 + α 4
4
− α 5 + α 6
,
2
− α 5 ,
− α 6 .
Using an appropriate multiple comparison criterion, test the significance of the above
contrasts by controlling the overall error rate at 0.05.
In terms of the parameters of the linear model, the contrasts are equivalent to the linear
forms:
a 2 + a 3 + a 4
4
a 2 + a 3 + a 4
4
a 2 + a 3 + a 4
4
− a 5 + a 6
,
2
− a 5 ,
− a 6 .
The estimated a j ’s and their variance matrix are as follows:
5