Critical Values and Some Properties of a New Test Statistic for Analyzing Unreplicated Factorial Experiments

Abstract

Critical values of the test statistic proposed by Al‐Shiha and Yang (1999) for analyzing unreplicated factorials are estimated by fitting an appropriate linear model. Some important properties of the test are also provided.

On the Exact Null Distribution of the Generalised Likelihood Ratio Test for Analysing Unreplicated Factorial Designs

“…The corresponding complete Mathematica programs are printed in the appendix. The 95% quantile of L 5;2 calculated by Mathematica is equal to 44.713, which is very close to the empirical quantile 44.250 given in Table 2.2 by Al-Shiha and Yang (2000).…”

“…The comparison presented in Table 1 shows that Al-Shiha and Yang's (2000) simulated results are closer to our computed results than to their own computed results. The reason may be that Al- Shiha and Yang's (2000) computed results are based on the tabulations of Cochran (1941) and the Statistical Research Group, Columbia University (1947), which have a lower accuracy.…”

“…The statistic L n; k was also used by Al-Shiha and Yang (2001) to detect multiple outliers in normal case. Because of the difficulty of determining the null distribution of L n; k analytically, the critical values of L n; k given by them were obtained via Monte-Carlo methods (Al-Shiha and Yang, 1999, 2000, 2001. In next section, we give the exact null distribution function of L n; k .…”

Order Statistics for a Two-Level, Eight-Run Saturated-Unreplicated Fractional-Factorial Screening

“…Several of the aforementioned methods have this assumption deeply rooted in their hypothesis testing. Recent nonsubjective rules for the unreplicated orthogonal design analysis have been considered by Aboukalam and Al-Shiha (2001) and Al-Shiha and Yang (2000). The need for posterior adjustment of probabilities in multifactorial testing was explained by Stephenson et al (1989).…”

A Distribution-Free Multi-Factorial Profiler for Harvesting Information from High-Density Screenings

“…As a result, experts scrutinizing different strategies to engineer optimal experimental plans have recognized long ago that ‘saturation’ may be a desirable condition for maximizing the performance of information harvesting with minimum cost [19]–[23]. Likewise, it was discovered that additional gains in cost and time could be anticipated by potentially eliminating data replication at all [24]–[30]. Unreplicated trials simply constitute a single execution of a specified set of recipes as dictated by a given plan.…”