Provide an example of an experimental situation where there is one factor of primary interest and where a suitable experimental design would be
randomised blocks,
a Latin square.
In each case, explain carefully why the design is suitable and why the other design would not be appropriate.
An industrial experiment to compare four treatments for increasing the tensile strength of steel is carried out according to a completely randomised design. For various reasons, it is not possible to use the same number of replicates for each treatment. The increases, in a suitable unit of tensile strength, are as follows.
Treatment
A
Treatment
B
Treatment
C
Treatment
D
10.1
21.1
9.2
22.6
21.2
20.3
8.8
17.4
11.6
16.0
15.2
23.1
13.6
15.0
19.2
[The sum of these data items is 256.8 and the sum of their squares is 4471.92 .]
Construct the usual one-way analysis of variance table. Carry out the appropriate test, using a \(5 \%\) significance level.
RECOGNISING ACHIEVEMENT