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Calibration of the Length Test for Unreplicated Factorial Designs

Summary: The Lenth test is a simple procedure to test for significant factorial effects in unreplicated 2k factorial experiments. Estimated factorial effects are standardized and compared to critical values from a t distribution with (2k - 1)/3 degrees of freedom. However, the procedure does not maintain its nomial 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 nomial error rates. This procedure is then calibrated and critical values are revised to produce a variety of common Type I error rates.

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  • Topics:
  • Keywords: Simulations,Fractional factorials
  • Author: Loughin, Thomas M.
  • Journal: Journal of Quality Technology