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

Rejection Region (graded), How is the rejection region defined and how is t...

How is the rejection region defined and how is that related to the z-score and the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians

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

Probability, Modern hotels and certain establishments make use of an electr...

Modern hotels and certain establishments make use of an electronic door lock system. To open a door an electronic card is inserted into a slot. A green light indicates that the doo

Public network, This is given by common network e.g. Phone Company. The pub...

This is given by common network e.g. Phone Company. The public networks are those networks, which are given by common carriers. It can be a telephone company or an other organizati

Dummy variables, The variables resulting from the recoding categorical vari...

The variables resulting from the recoding categorical variables with more than two categories into the sequence of binary variables. Marital status, for instance, if originally lab

Describe length-biased sampling, Length-biased sampling : The bias which ar...

Length-biased sampling : The bias which arises in the sampling scheme based on the visits of patient, when some individuals are more likely to be chosen than others simply because

Describe Generalized principal components analysis, Generalized principal c...

Generalized principal components analysis: The non-linear version of the principal components analysis in which the goal is to determine the non-linear coordinate system which is

Funnel plot, It is an informal method of assessing the effect of the public...

It is an informal method of assessing the effect of the publication bias, generally in the context of the meta-analysis. The effect measures from each of the reported study are plo

Descriptive statistics, how to describe association between quantitative an...

how to describe association between quantitative and categorical variables

Link functions, Link functions: The link function relates the linear p...

Link functions: The link function relates the linear predictor ηi to the expected value of the data. In classical linear models the mean and the linear predictor are identical

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