Critical values of the Lenth method for unreplicated factorial designs

The Lenth method is an objective method for testing effects from unreplicated factorial designs and eliminates the subjectivity in using a half-normal plot. The Lenth statistics are computed for the factorial effects and compared to corresponding critical values. Since the distribution of the Lenth statistics is not mathematically tractable, we propose a simple simulation method to estimate the critical values. Confidence intervals for the estimated critical values can also easily be obtained. Tables of critical values are provided for a large number of designs, and their use is demonstrated with data from three experiments. The proposed method can also be adapted to estimate critical values for other methods.