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

Quantitative, How has quantitative analysis changed the current scenario in...

How has quantitative analysis changed the current scenario in the management world today?

Expected monetary value, Ask quesoil company is considering whether or not ...

Ask quesoil company is considering whether or not to bid for an offshore drilling contract. If they bid, the value would be $600m with a 65% chance of gaining the contract. The com

Projection pursuit, Projection pursuit is a procedure for attaning a low-d...

Projection pursuit is a procedure for attaning a low-dimensional (usually two-dimensional) representation of the multivariate data, which will be particularly useful in revealing

Interior analysis, Interior analysis is the  term now and again applied to...

Interior analysis is the  term now and again applied to analysis carried out on the fitted model in regression problem. The basic target of such analyses is the identification of

Probability weighting, Probability weighting is the procedure of attaching...

Probability weighting is the procedure of attaching weights equal to inverse of the probability of being selected, to each respondent's record in the sample survey. These weights

Cointegration, Cointegration : The vector of not motionless time sequence i...

Cointegration : The vector of not motionless time sequence is said to be cointegrated if the linear combination of the individual series is stationary. Facilitates suitable testing

Gaussian markov random field, It is the multivariate normal random vector w...

It is the multivariate normal random vector which satisfies certain conditional independence suppositions. This can be viewed as a model framework which contains a wide range of st

Times series plots, There is high level of fluctuation in a zigzag pattern ...

There is high level of fluctuation in a zigzag pattern in the time series for RESI1 which indicates that there is possibly negative autocorrelation present. Column C11 show

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