Complete factorial design
In sixteen runs it is possible to use a single replicate of a complete 24 factorial experiment.
Factor | |||||
---|---|---|---|---|---|
Run | A | B | C | D | Response |
1 | -1 | -1 | -1 | -1 | y-—- |
2 | -1 | -1 | -1 | +1 | y-—+ |
3 | -1 | -1 | +1 | -1 | y--+- |
4 | -1 | -1 | +1 | +1 | y--++ |
5 | -1 | +1 | -1 | -1 | y-+— |
6 | -1 | +1 | -1 | +1 | y-+-+ |
7 | -1 | +1 | +1 | -1 | y-++- |
8 | -1 | +1 | +1 | +1 | y-+++ |
9 | +1 | -1 | -1 | -1 | y+—- |
10 | +1 | -1 | -1 | +1 | y+—+ |
11 | +1 | -1 | +1 | -1 | y+-+- |
12 | +1 | -1 | +1 | +1 | y+-++ |
13 | +1 | +1 | -1 | -1 | y++— |
14 | +1 | +1 | -1 | +1 | y++-+ |
15 | +1 | +1 | +1 | -1 | y+++- |
16 | +1 | +1 | +1 | +1 | y++++ |
In such a design, all main effects and interactions can be estimated independently.
Testing
If it is assumed that the 3- and 4-factor interactions are zero, their sums of squares can be combined to form a residual sum of squares with 5 degrees of freedom so the significance of the main effects and 2-factor interactions can be tested.