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Details of the FACTEX Procedure |
In many experiments, proper randomization is crucial to the validity of the conclusions. Randomization neutralizes the effects of systematic biases that may be involved in implementing the design and provides a basis for the assumptions underlying the analysis. Refer to Kempthorne (1975) for a discussion.
The way in which randomization is handled depends on whether the design involves blocking.
Thus, the effect of the randomization is to transform the original design, as follows:
Run | A | B | C |
1 | 0 | 0 | 0 |
2 | 0 | 0 | 1 |
3 | 0 | 1 | 0 |
4 | 0 | 1 | 1 |
5 | 1 | 0 | 0 |
6 | 1 | 0 | 1 |
7 | 1 | 1 | 0 |
8 | 1 | 1 | 1 |
Run | A | B | C |
3 | 1 | -1 | -1 |
8 | -1 | -1 | 1 |
1 | 1 | 1 | -1 |
2 | 1 | 1 | 1 |
4 | 1 | -1 | 1 |
7 | -1 | -1 | -1 |
6 | -1 | 1 | 1 |
5 | -1 | 1 | -1 |
The resulting transformation is shown in the following:
Run | Block | A | B | C |
1 | 1 | 0 | 0 | 0 |
2 | 1 | 0 | 1 | 1 |
3 | 1 | 1 | 0 | 1 |
4 | 1 | 1 | 1 | 0 |
5 | 2 | 0 | 0 | 1 |
6 | 2 | 0 | 1 | 0 |
7 | 2 | 1 | 0 | 0 |
8 | 2 | 1 | 1 | 1 |
Run | Block | A | B | C |
8 | 2 | -1 | -1 | 1 |
7 | 2 | -1 | 1 | -1 |
6 | 2 | 1 | -1 | -1 |
5 | 2 | 1 | 1 | 1 |
4 | 1 | -1 | -1 | -1 |
1 | 1 | 1 | 1 | -1 |
2 | 1 | 1 | -1 | 1 |
3 | 1 | -1 | 1 | 1 |
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