Multivariate analysis of variance, Advanced Statistics

Multivariate analysis of variance is the procedure for testing equality of the mean vectors of more than two populations for the multivariate response variable. The method is directly analogous to the analysis of the variance of univariate data except that the groups are compared on q response variables at the same time. In the univariate case, F-tests are used to assess hypotheses of interest. In the multivariate case, though, no single test statistic can be constructed which is optimal in all situations. The most extensively used of the available test statistics is Wilk' slambda (L) which is based on the three matrices W(the within groups matrix of the sums of squares and products), T (the total matrix of sums of the squares and cross-products)and B (the among groups matrix of sums of squares and the cross-products), can be defined as follows: 
966_multivariate analysis.png 
These matrices satisfy the following written equation
125_multivariate analysis1.png 

Wilk's lambda is given by ratio of the determinants of the W and T, that is

1917_multivariate analysis2.png 

The statistic, L, can be transformed to provide a F-test to assess null hypothesis of the equality of the population of the mean vectors. Additionally to L a number of other test statistics are available.

Posted Date: 7/30/2012 5:58:35 AM | Location : United States







Related Discussions:- Multivariate analysis of variance, Assignment Help, Ask Question on Multivariate analysis of variance, Get Answer, Expert's Help, Multivariate analysis of variance Discussions

Write discussion on Multivariate analysis of variance
Your posts are moderated
Related Questions
i need help for my assignment and the deadline is Friday

Resentful demoralization is the possible phenomenon in the clinical trials and intervention studies in which comparison groups not attaining a perceived desirable treatment become

historigrams and histogram

Multiple comparison tests : Procedures for detailed examination of the differences between a set of means, generally after a general hypothesis that they are all equal has been rej

Lancaster models : The means of representing the joint distribution of the set of variables in terms of the marginal distributions, supposing all the interactions higher than a par

Bubble plot : A method or technique for displaying the observations which involve three variable values. Two of the variables are used to make a scatter diagram and values of the t

what are tests for residual with nonconstant variance in regression diagnostic checking?

Regression discontinuity design is the quasi-experimental design in which participants in, for instance, an intervention study, are assigned to the treatment and control groups on

Economic Interpretation of the Optimum Simplex solution

This term sometimes is applied to the model for explaining the differences found between naturally happening groups which are greater than those observed on some previous occasion;