Calibration of the Lenth Test for Unreplicated Factorial Designs

Abstract

The Lenth test is a simple procedure to test for significant factorial effects in unreplicated 2^k factorial experiments. Estimated factorial effects are standardized and compared to critical values from a t distribution with (2^k − 1)/3 degrees of freedom. However, the procedure does not maintain its nominal Type I error rates in small experiments. This article presents a simulation study in which the Lenth procedure error rates are found for several common values of k under numerous specified nominal error rates. This procedure is then calibrated and critical values are revised to produce a variety of common Type I error rates.

• Fractional-Factorial
• Simulation

Additional information

Notes on contributors

Thomas M. Loughin

Dr. Loughin is an Assistant Professor in the Department of Statistics and Statistical Laboratory.