A three-level full factorial grows as three raised to the number of factors. Count all combinations, repetitions and practical preparation work before booking the trial.
The statistical question
A three-level full factorial uses every combination of three levels for each selected factor. For k factors, that gives 3 raised to k treatment combinations before replication or extra runs. Three levels and three repetitions are different design ideas. Numerical levels may support curvature study, while nominal categories have a different interpretation; the factor definitions determine the appropriate model.
An illustrative review example
With two fictional factors the full grid contains nine combinations; with three it contains 27. If each of the 27 combinations is genuinely repeated twice, the planned total is 54 runs before added checks or invalid-run replacements. Three readings collected during one run do not automatically create three independent replicates. These counts concern a design budget, not a recommended experiment or production capacity.
Prepare the evidence for discussion
Write each factor and its three physical levels, then enumerate the combinations before estimating elapsed trial time. Include setup changes, cleaning, sample preparation and measurement work in the schedule rather than multiplying only machine cycle time. Ask the analyst whether all requested conclusions need a full grid or another justified design. Retain any omitted combinations as explicit departures so the final report does not claim complete full-factorial coverage.
Count the grid before scheduling
This blank worksheet is for your own project. It contains no H M machine trial result.
| Question to resolve | Evidence to retain |
|---|---|
| Factor levels | Three physical values or categories |
| Combination count | Three raised to factor count |
| Replications | Genuinely repeated experimental units |
| Schedule | Preparation and measurement included |
Customer Questions
How many combinations do three three-level factors require?
The full design contains 3 times 3 times 3, or 27 combinations, before repetition.
Is a third level a third repeat run?
No. A level changes a factor setting; replication repeats the relevant experimental conditions.
Can omitted combinations retain a full-factorial claim?
An incomplete grid needs its actual scope and analysis consequences stated.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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