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

Hypothesis testing paper, Prepare a 1,400- to 1,750-word paper in which you...

Prepare a 1,400- to 1,750-word paper in which you formulate a hypothesis based on your selected research issue, problem, or opportunity. Address the following: •Describe your sele

Mixture experiment, Mixture experiment is an experiment in which the two o...

Mixture experiment is an experiment in which the two or more ingredients are blended together to form an end product. The measurements are taken on the several blends of the ingre

Captures recapture sampling, Captures recapture sampling : Another approach...

Captures recapture sampling : Another approach to a census for estimating the size of population, which operates by sampling the population number of times, identifying the individ

Explain interim analyses, Interim analyses : An analysis made before the pl...

Interim analyses : An analysis made before the planned end of a clinical trial, typically with the aim of detecting the treatment differences at the early stage and thus preventing

Define non linear mapping (nlm), Non linear mapping (NLM ) is a technique f...

Non linear mapping (NLM ) is a technique for obtaining a low-dimensional representation of the set of multivariate data, which operates by minimizing a function of the differences

Markov chains.., a shop is selling laptops at regular price and at half pri...

a shop is selling laptops at regular price and at half price.If the laptops are regular price a day they will be at regular price tha day after with proba 2/3, if the laptops are a

Bayesian network, Bayesian network : It is essentially an expert system in ...

Bayesian network : It is essentially an expert system in which the uncertainty is dealt with using the conditional probabilities and Bayes' Theorem. Formally such type of network c

Collective risk models, Collective risk models : The models applied to insu...

Collective risk models : The models applied to insurance portfolios which do not create direct reference to the risk characteristics of individual members of the portfolio when des

Barnard, Barnard, George Alfred (1915^2002) : Born in Walthamstow in the ea...

Barnard, George Alfred (1915^2002) : Born in Walthamstow in the east of London, Barnard achieved a scholarship to St. John's College, Cambridge, from where he graduated in the math

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

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