The Analysis of Unreplicated Factorial Experiments Using All Possible Comparisons

Abstract

This article proposes a new procedure for analyzing small unreplicated factorial experiments. This procedure is based on using likelihood ratio tests to compare competing models. An easy method of implementing the procedure is presented and then demonstrated on a real set of data. Results of a simulation study are presented that indicate that the new procedure compares favorably with Lenth's method. Tables of constants are supplied that allow the new procedure to be easily applied to the analysis of 8-run, 12-run, and 16-run experiments.

KEY WORDS :

• Active contrast
• Geometric approach
• Half-normal plot
• Lenth's method
• Likelihood ratio test
• Model selection