A Monte Carlo Investigation of Nonparametric One-Way Multivariate Analysis of Variance (Rank Transformation, Normal Scores, Manova Test, Robustness).
Date of Award
Doctor of Philosophy (PhD)
This research is concerned with the rank and normal score transform procedures in which the usual parametric procedures are applied to the ranks of the data and the normal scores based on the ranks instead of the original data in one-way multvariate analysis of variance (MANOVA). Four MANOVA test criteria were compared in terms of the parametric, rank and normal score procedures: (1) Roy's largest root, R, (2) Lawley-Hotelling trace, T, (3) Wilks's likelihood ratio, W and (4) Bartlett-Nanda-Pillai trace, V. A Monte Carlo investigation was designed to compare the procedures in terms of control of Type I error and power. Four factors were involved in the Type I error study for each of the four MANOVA criteria: the number of variates (p = 2, 3, 4, 5), the number of groups (k = 3, 4, 5), the equal group size (Ns = 5, 10, 20, 40) and the five distributions (normal, lognormal, uniform, Cauchy, exponential). Each of the variates in a sample was generated independently from a parent distribution. In the power study, p = 3, k = 4, Ns = 10 and 20 were selected. Five levels of location parameter for group 1 were used. The major results drawn from the investigation are as follows. The rank and normal score procedures compete well with the parametric procedure for the normal distribution and outperform it in other cases. The overall evaluation indicates that the normal scores are preferable in terms of Type I error control, closely followed by the rank procedure. However, the overall power evaluation favors the rank procedure, followed by normal scores. The nonparametric procedures are rather robust and consistent throughout the considered distributions and four MANOVA test criteria. Even though normal scores appear to be slightly better than the ranks in terms of Type I error control, the advantage of the normal scores over the ranks is not significant enough to offset the complicated nature of the normal score transform. Consequently, the use of the rank transform can be recommended when the data do not meet the normality assumption.
Myung, Geon Seek, "A Monte Carlo Investigation of Nonparametric One-Way Multivariate Analysis of Variance (Rank Transformation, Normal Scores, Manova Test, Robustness)." (1986). LSU Historical Dissertations and Theses. 4198.