Reference:

R.V. Lenth (1989). “Quick and Easy Analysis of Unreplicated Factorials,”

R.V. Lenth (1989). “Quick and Easy Analysis of Unreplicated Factorials,”

*Technometrics*, 31, 469-473.Lenth’s Method for the Analysis of Unreplicated Experiments

NIST Handbook, Half Normal Plot, http://www.itl.nist.gov/div898/handbook/pri/section5/pri598.htm

Daniel, C., “Use of Half-Normal Plots in Interpreting Factorial two-level experiments”, Technometrics, v1, No.4, Nov 1959, p311-341.

At this point, Lenth’s method (Lenth, 1989) identifies inactive effects from which it constructs an estimate of the residual standard error, known as the Lenth Pseudo Standard Error (PSE).

The value for Lenth’s PSE is shown at the bottom of the Screening report. From the PSE, t-ratios are obtained. To generatep-values, a Monte Carlo simulation of 10,000 runs of n – 1 purely random values is created and Lenth t-ratios are produced from each set. The p-value is the interpolated fractional position among these values in descending order. The simultaneousp-value is the interpolation along the max(|t|) of the n – 1 values across the runs. This technique is similar to that in Ye and Hamada (2000).