of Example a Latin Square Design. Four companies A, B, C, D supply a component for a motor vehicle. The component can be used in four different types of engine for four different models of car; all types of engines can be fitted to all models of car. A standard test is applied, and the lengths of time for which the components works satisfactorily in the test are recorded (the units in the table have been coded for simple analysis). Type of engine Model 1 2 3 4 Total 1 B: 25 A: 32 D: 24 C: 37 118 2 A: 31 C: 33 B: 30 D: 28 122 3 C: 40 D: 32 A: 36 B: 28 136 4 D: 26 B: 34 C: 41 A: 37 138 Total 122 131 131 130 514
Minitab c1 test data, c2 company, c3 type of engine and c4 model. Data
Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 c1 25 32 24 37 31 33 30 28 40 32 36 28 26 34 41 37 c2 2 1 4 3 1 3 2 4 3 4 1 2 4 2 3 1 c3 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 c4 1 2 3 4 1 2 3 4 2 1 3 4 1 2 3 4
The GLM (general linear model function) is used because the design/experiment is not balanced, that is not all combinations of company, type and model are have the same number of observations (here some of the combinations do not occur in the design). Each type of engine and model occur with only one company (A, B, C or D).
Minitab command and output:
MTB > GLM c1 = c2 c3 General Linear Model Factor C2 C3 C4 Levels Values 4 1 4 1 4 1 c4.
2 2 2
3 3 3
4 4 4
Analysis of Variance for C1 Source C2 C...