Comparison of Re-sampling Methods to Generalized Linear Models and Transformations in Factorial and Fractional Factorial Designs

Abstract

the bootstrap (re-sampling) could be used to determine the active factors (factors that have an effect on the response) without any requirements on the type of data provided. This study shows that this method of determining active factors agrees with other methods, such as the halfnormal plots, in addition this study shows how this method can be used to obtain confidence intervals for responses after determining active factors. The bootstrap has been shown to provide better than normal estimates of distribution functions of studentized statistics (see Singh, 1981; Bickle & Freedman, 1980; Babu & Singh 1983; Babu and Singh 1984). Qumsiyeh (1994) demonstrated that bootstrap approximation for the distribution of the studentized least square estimate is asymptotically better, not only than the normal approximation, but also than the two-term Edgeworth expansion. Lahiri (1992) showed the superiority of the bootstrap for approximating the distribution of M-estimators. Bhattacharya and Qumsiyeh (1989) conducted an L p comparison between the bootstrap and Edgeworth expansions. Finally, Qumsiyeh and Shaughnessy (2010) showed that the bootstrap can be used to determine the active factors in two level designs with missing responses.