A new look at half-normal plots for assessing the significance of contrasts for unreplicated factorials

The visual inspection of a half-normal plot is a popular procedure for interpreting data from unreplicated factorial experiments. As this technique is somewhat subjective, the plot should preferably be supplemented with a more formal procedure. However, despite the improvements proposed by Zahn, the formal method using the half-normal plot suggested by Daniel seems to be rarely used. We investigate this procedure by using simulations and real data and suggest a modification to improve its acceptability. We also present corrected critical values for a procedure proposed by Lenth which was found to be miscalibrated.