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

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

Multilevel models, Multilevel models are the regression models for the mul...

Multilevel models are the regression models for the multilevel or clustered data where units i are nested in the clusters j, for example a cross-sectional study where students are

Develop the equations to calculate the flow rates, A two-step distillation ...

A two-step distillation and mixing process is shown in the figure. The system operates at steady-state conditions and there are no chemical reactions. The known flow rates and comp

G, sfdgfdg

sfdgfdg

Rational –experiential inventory, Demographic data: Age: continuous vari...

Demographic data: Age: continuous variable Gender: categorical variable with males coded 1, females coded 2. Relationship status: categorical variable 1 to 5. Rational

Evidence-based medicine (ebm), Described by the leading proponent as 'the c...

Described by the leading proponent as 'the conscientious, explicit, and judicious uses of present best evidence in making the decisions about the care of individual patients, and

Explanatory analysis, This term is sometimes used for the analysis of data ...

This term is sometimes used for the analysis of data from the clinical trial in which treatments A and B are to be compared under the suppositions that the patients remain on their

Balanced incomplete repeated measures design (birmd), Balanced incomplete r...

Balanced incomplete repeated measures design (BIRMD): An arrangement of the N randomly selected experimental units and k treatments in which each and every unit receives k1 treatm

EM, What is the EM?

What is the EM?

Egret, This is acronym for the Epidemiological, Graphics, Estimation and Te...

This is acronym for the Epidemiological, Graphics, Estimation and Testing of the program developed for the analysis of the data from studies in epidemiology. It can be made in use

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