Describe, with the aid of a specific example, an experimental situation for which a Latin square design is appropriate, indicating carefully the features which show that a completely randomised or randomised blocks design would be inappropriate.
The model for the one-way analysis of variance may be written, in a customary notation, as
$$x _ { i j } = \mu + \alpha _ { i } + e _ { i j }$$
State the distributional assumptions underlying \(e _ { i j }\) in this model. What is the interpretation of the term \(\alpha _ { i }\) ?
An experiment for comparing 5 treatments is carried out, with a total of 20 observations. A partial one-way analysis of variance table for the analysis of the results is as follows.
Source of variation
Sums of squares
Degrees of freedom
Mean squares
Mean square ratio
Between treatments
Residual
68.76
Total
161.06
Copy and complete the table, and carry out the appropriate test using a \(1 \%\) significance level.