Three Level Factorial Design Matrix

See link for 2^k factorial design matrix.

See also Montgomery section 6.3 for the 2^k design, and Hicks section 10.2 for the 3^k design.

Explanation of the subscripts:

• The "L" subscript indicates the "Linear" component of the term or interaction.

• The "Q" subscript indicates the "Quadratic" component of the term or interaction.

The rows in bold blue text are those that are also in a 2-level 2-factor study that incorporates centerpoints.

The rows in red text are those that make a 3-level study different from a 2-level study with centerpoints. They allow the experimenter to quantitatively explore the impact (size and the specific associated term or interaction) of quadratic terms in the model.