Detecting active effects in unreplicated designs

Unreplicated factorial designs pose a difficult problem in analysis because there are no degrees of freedom left to estimate the error. Daniel [Technometrics 1 (1959), pp. 311–341] proposed an ingenious graphical method that does not require σ to be estimated. Here we try to put Daniel’s method into a formal framework and lift the subjectiveness that carries.A simulation study has been conducted that shows that the proposed method behaves better than Lenth’s [Technometrics 31 (1989), pp. 469–473] popular method.