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.