Example for Power and Sample Size for 2-Level Factorial Design

A quality engineer plans a designed experiment to study the transparency of a plastic part. Before conducting the experiment, the engineer wants to ensure that the experiment will have adequate power. The engineer plans to examine 5 numeric factors. For a base design, the engineer selects a design with 8 experimental runs and 3 center points. The engineer wants to be able to detect an effect of 5 transparency units with no more than 4 replicates. Previous experimentation indicates that 4.5 is an adequate estimate of the standard deviation. The engineer decides to calculate the power for a model with main effects and a term for center points.

  1. Choose Stat > Power and Sample Size > 2-Level Factorial Design.
  2. In Number of factors, enter 5.
  3. In Number of corner points, enter 8.
  4. In Replicates, enter 1 2 3 4.
  5. In Effects, enter 5.
  6. In Number of center points per block, enter 3.
  7. In Standard deviation, enter 4.5.
  8. Click Design.
  9. In Number of terms omitted from model, enter 2.
  10. Click OK in each dialog box.

Interpret the results

The unreplicated design has a power of approximately 23%. With 4 replicates and 35 total runs, the design has nearly an 86% chance to detect an important effect. The power curve displays a curve for each combination of replicates and center points. The symbols on the curves represent the effect size of 5 that the engineer specified. The engineer decides to use the 4 replicate design so that the power is as high as possible.

2-Level Factorial Design
α = 0.05  Assumed standard deviation = 4.5


Factors:5Base Design:5, 8
Number of terms omitted from model: 2
Including a term for center points in model.


EffectRepsTotal RunsPower