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N-Level Factorial How-To

This walkthrough builds a mixed-level factorial, where the factors do not all have the same number of levels. It is the design to reach for when one factor is a three-way choice and another is on or off.

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 N Level Factorial, press Next.

  2. On the factor page set Select number of factors: to 2. Set the first factor's # Levels to 3 and the second's to 2. Name them Supplier and Coating, tick Categorical on Supplier, and give it three level names.

  3. Name one output and press Next, then leave replicates and blocking alone and press Finish.

What you get

Six runs, which is 3 times 2, 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 Supplier Coating
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

The run count is the product of the level counts, so this design's size follows directly from what you asked for: 3 x 2 is 6, and a 4 x 3 x 2 design is 24.

A categorical factor's levels are names, not numbers. The model fits one term per level beyond the first, so a three-level categorical factor spends two degrees of freedom rather than one.

Things to try next

  • Set both factors to 2 levels. You get the four run design a two-level factorial would build, which shows this design type as the general case of that one.
  • Add a 4-level factor. 24 runs, and the arithmetic is still just the product.
  • Untick Categorical on Supplier. Its levels become quantitative settings and the model can fit a trend across them rather than a separate term for each.

See Also