CALIBRATION OF THE LENTH TEST FOR UNREPLICATED FACTORIAL-DESIGNS

The Lenth test is a simple procedure to test for significant factorial effects in unreplicated 2(k) factorial experiments. Estimated factori al effects are standardized and compared to critical values from a t d istribution with (2(k) - 1)/3 degrees of freedom. However, the procedu re does not maintain its nominal Type I error rates in small experimen ts. This article presents a simulation study in which the Lenth proced ure error rates are found for several common values of k under numerou s specified nominal error rates. This procedure is then calibrated and critical values are revised to produce a variety of common Type I err or rates.