Factorial center points do little to increase power: Now what?
Original question from a PhD student of pharmaceutical technology:
“I would like to do an experiment with three factors at two levels with a signal-to-noise [S/N] ratio of 1.5, which only produces a power of 36.9%. However, even if I specify 6 center points to bring the total runs up to 14, the power increases only slightly to 48.3%. Is there something else I can do to improve the power?”
Answer from Stat-Ease Consultant Shari Kraber:
“Center points [CPs] do not help very much to increase the power to detect effects because they are in the middle of the design space with no leverage. A much better alternative will be to replicate the entire design from 8 runs to 16 runs. Then, if you want to check for curvature, add 3 or 4 center points.”
PS by Mark: I was curious to see the relative impacts of these options—easily assessed with Design-Expert®
software’s built-in power-calculator.
- Going with the 16-run option of the replicated 2^3 produces a power of 78.6% at 1.5 S/N—far more than the 48.3% the experimenter would have gained by investing runs in center points.
- Adding 4 CPs to increase the total runs to 20 pushes the power to 80.4%—over the top of the 80% guideline. Furthermore, this design element provides a pathway for augmenting to a central-composite design for response-surface-method optimization.
However, I do have a further suggestion. When replication of a full factorial becomes necessary for power, consider adding another factor instead (in this case going to a 2^4): It will be essentially free. Who knows, perhaps that next most likely factor might lead to a breakthrough discovery. – Mark