Sequential Tests Based on F-Distribution for Detecting Active Effects in Unreplicated Two-Level Factorial Designs

This paper introduces a new methodology for detecting active effects in unreplicated two-level factorial experiments, which are of great importance in many scientific and practical fields. The proposed method aims to enhance the reliability and accuracy of detecting active effects compared to the popular method introduced by Lenth (1989). The new approach utilizes the F-distribution for significance testing, and it eliminates the needs of estimating the error variance or creating new critical value tables. A comprehensive simulation study was conducted using the Monte Carlo simulation method to evaluate the performance of the proposed method compared to Lenth's method in terms of the size and power of the test under different conditions. The results demonstrated the superiority of the proposed method. Additionally, three practical applications were analyzed using both methods to illustrate the practical effectiveness of the new approach. The simplicity and robustness of the proposed method make it a practical and effective method and a good choice for the analysis of unreplicated two-level factorial experiments.