A Method for Analyzing Unreplicated Factorial Experiments

Abstract

The analysis of unreplicated two-level factorial and fractional factorial experiments presents a challenge because after estimation of the effects by contrasts, there are no degrees of freedom left to estimate the error variance. Consequently, standard t tests cannot be used to identify the "active" effects. In practice, the standard method for identifying active effects continues to be a probability plot of the contrasts. There is a subjective element in deciding what constitutes an "active" effect in using the probability plot. This subjective element has motivated the recent flurry of activity to provide objective methods. Presently we propose yet another method based on hypothesis testing. The ability of the proposed method to detect "active" effects is found to be satisfactory.