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Design and Analysis of Experiments

Question 1
A reduction in the number of airborne asbestos bres that occur when asbestos is being
removed from buildings makes such removal much safer. The treatment that was pro-
posed was to spray an aqueous saturating solution in the room as the asbestos was being
removed. The treatments were three di erent spraying times – 30, 50 and 90 minutes.
Ten buildings were available for the experiment and there were three rooms available in
each building. The response was the bre count. The results of the experiment appear
below. In each case the rst room corresponds to the 30 minutes, the second to 50 and
the third to 90.
Are the di erences between the spraying times statistically signi cant? Is the assumption
of normal errors warranted? What are your conclusions?
Building Room 1 Room 2 Room 3
1 14 12 8
2 12 10 6
3 11 8 9
4 15 13 10
5 11 10 9
6 9 8 7
7 10 12 7
8 12 10 7
9 12 9 10
10 12 12 9
Question 2
Three technicians in a chemical plant are given the task of investigating the chemical yield
of a raw material by applying one of ve experimental treatments. Three responses are
to be observed for each treatment. Design an appropriate experiment for this study. Is
there a blocking factor?
Question 3
The responses of ve pairs of monkeys to a certain kind of stimulus under ve di erent
conditions during 5 successive weeks were observed according to the Latin square design
given below. The numbers are the total number of responses and the letters are the
Are the di erences between the conditions statistically signi cant? Is the assumption of
normal errors warranted? What are your conclusions?
Animals 1 2 3 4 5
1 194 b 369 d 344 c 380 a 693 e
2 202 d 142 b 200 a 356 e 473 c
3 335 c 301 a 439 e 338 b 528 d
4 515 e 590 c 552 b 677 d 546 a
5 184 a 421 e 355 d 284 c 366 b
Question 4
Consider the linear model for the randomised complete block design with a = 3 and b = 4.
Give the normal equations for this model and show that the estimable function 1? 2 has
the same estimate when using the constraints given in class or 1 = 0 and 1 = 0. (Hint:
Find the normal equations without imposing the constraints
=1 i = 0 and
=1 j = 0
and then derive the estimate for 1? 2 using these constraints and the constraints 1 = 0
and 1 = 0)



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