Improved Approximation Scales for Unreplicated Factorial Experiments

Assessing the sizes of active contrasts in un-replicated factorial and fractional factorial experiments by quick and powerful methods are required in analyzing the big data in various research areas of Human endeavors. One of the old methods based on Lenth (1989) is being used in some statistical and data analytical applications which is fast and less efficient. We propose a new class of tests which are simpler, faster, and more powerful using the location median-function (ψmedx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\psi }_{med}\left({\varvec{x}}\right)$$\end{document}) after being skipped one and/or two times. An empirical study of simulation experiments to compute the critical values, sizes and powers using various sample sizes demonstrate the superiority of our methods. The proposed methods are illustrated in examples which can be employed in various fields of research in conducting data analytics using high computing power and machine learning.