Multivariate analysis of variance, Advanced Statistics

Assignment Help:

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.


Related Discussions:- Multivariate analysis of variance

Doubly multivariate data, This term is sometimes used for the data collecte...

This term is sometimes used for the data collected in those longitudinal studies in which more than the single response variable is recorded for each subject on each occasion. For

Continual reassessment method, Continual reassessment method: An approach ...

Continual reassessment method: An approach which applies Bayesian inference for determining the maximum tolerated dose in a phase I trial. The method starts by assuming a logistic

Explain initial data analysis (ida), Initial data analysis (IDA): The firs...

Initial data analysis (IDA): The first phase in the examination of the data set which comprises  number of informal steps including the following steps * checking the quality o

Compound symmetry, Compound symmetry : The property possessed by the varian...

Compound symmetry : The property possessed by the variance-covariance matrix of the set of multivariate data when its chief diagonal elements are equal to each other, and in additi

Resentful demoralization, Resentful demoralization is the possible phenome...

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

Integrated Economic Statistics, Advantages and disadvantages of Integrated ...

Advantages and disadvantages of Integrated Economic Statistics

Factorial designs, Designs which permits two or more questions to be addres...

Designs which permits two or more questions to be addressed in the investigation. The easiest factorial design is one in which each of the two treatments or interventions are p

Non-identified response, Non-identified response is a term used to signify...

Non-identified response is a term used to signify censored observations in survival data, which are not independent of the endpoint of the interest. Such observations can happen f

Explain johnson-neyman technique, Johnson-Neyman technique:  The technique ...

Johnson-Neyman technique:  The technique which can be used in the situations where analysis of the covariance is not valid because of the heterogeneity of slopes. With this method

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd