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Three-Level Factorial How-To

This walkthrough builds a full three-level factorial for two factors and shows what the third level buys that a two-level design cannot give you.

Nothing here needs data. A design is built before the experiment is run, so every number below is determined by the design itself and you can check each one against your own sheet.

Steps

  1. QXL DOE New > Create Design, choose 3 Level Factorial, press Next.

  2. On the factor page set Select number of factors: to 2. Each factor row carries a # Levels entry and a Categorical check box; leave Categorical clear on both and leave the levels at 3. Name them Temp and Press and give each one three settings.

  3. Name one output, Yield, press Next.

  4. Leave Select number of replicates: at 1 and the blocking list at No blocking. Press Finish.

What you get

Nine runs, every combination of three levels of two factors, with the first factor changing fastest:

Press Copy for Excel and paste the block into an empty part of the worksheet to compare it against your sheet.

Run Temp Press
1 level 1 level 1
2 level 2 level 1
3 level 3 level 1
4 level 1 level 2
5 level 2 level 2
6 level 3 level 2
7 level 1 level 3
8 level 2 level 3
9 level 3 level 3

Nine is 3 times 3, and the run count of a full factorial is always the product of the level counts. Three factors at three levels is 27 runs, four is 81.

What the third level buys

A squared term becomes estimable. Two levels can only fit a straight line through a factor, so a two-level design cannot tell a flat response from a curved one. Three levels give the middle point that makes the curvature visible.

The cost is the run count, and it grows faster than a two-level design: 3^k against 2^k. At five factors that is 243 runs against 32. When curvature matters on only two or three factors, a central composite or Box-Behnken design reaches the same curved model in far fewer runs.

Things to try next

  • Tick Categorical on one factor. Its three levels become names you type rather than numbers, and the model treats it as three unordered categories rather than a quantity with a middle.
  • Add a third factor. The run count goes from 9 to 27, which is the multiplication made visible.
  • Set Select number of replicates: to 2. 18 runs, and the regression gains a pure error estimate.

See Also