Abstract
Differences among treatment groups in terms of which variable or linear combination of variables causes a significant multivariate analysis of variance (MANOVA) are often difficult to determine. This study is an attempt to develop a means by which a significant MANOVA can be followed by a discriminant analysis for the purpose of finding a significant contrast which can determine which variable or linear combination of variables is causing differences in which treatment groups.
Significance of the contrast was tested using Roy-Bose simultaneous confidence intervals. These intervals traditionally have been considered conservative as a hypothesis-testing procedure. Of concern in any hypothesis-testing procedure is type I error and power. This study investigated type I error and power of the procedure in numerous situations which used many combinations of number of groups, number of variables, nominal alpha, and group size. Included are situations which involved no violation of MANOVA assumptions, as well as situations involving a violation of normality or a violation of the assumption of a homogeneous covariance structure.
Results show that the proposed procedure needs great improvement when the assumptions of MANOVA are not met. When the assumptions are met, the procedure works fairly well in terms of power and type I error for a small number of groups or variables. As the number of groups or variables reaches six, the procedure begins to lose power, but type I error is acceptable.
Recommended Citation
Elliott, Ronald S. and Barcikowski, Robert S.
(1994)
"Investigation of Power Using F Approximations for the Hotelling-Lawley Trace and Pillai's Trace,"
Mid-Western Educational Researcher: Vol. 7:
Iss.
4, Article 2.
Available at:
https://scholarworks.bgsu.edu/mwer/vol7/iss4/2
