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

Omitted covariates, Omitted covariates is a term generally found in the co...

Omitted covariates is a term generally found in the connection with regression modelling, where the model has been incompletely specified by not including significant covariates.

Describe meta-analysis, Meta-analysis is the collection of techniques wher...

Meta-analysis is the collection of techniques whereby the results of two or more independent studies are statistically combined to yield the overall answer to a question of intere

Correlation matrix, Correlation matrix : A square, symmetric matrix with th...

Correlation matrix : A square, symmetric matrix with the rows and columns corresponding to the variables, in which the non diagonal elements are correlations between the pairs of t

Conditional logistic regression, Conditional logistic regression : The form...

Conditional logistic regression : The form of logistic regression designed to work with the clustered data, such as data including matched pairs of the subjects, in which subject-s

Mareg, MAREG is the software package for the analysis of the marginal regr...

MAREG is the software package for the analysis of the marginal regression models. The package permits the application of generalized estimating equations and the maximum likelihoo

Determinant, A value related with the square matrix which represents sums a...

A value related with the square matrix which represents sums and products of its elements. For instance, if the matrix is   then the determinant of A (conventionally written as

Explain yate s'' continuity correction, Yate s' continuity correction : Whe...

Yate s' continuity correction : When the testing for independence in contingency table, a continuous probability distribution, known as chi-squared distribution, is used as the app

Define lagging indicators, Lagging indicators: The part of a collection of...

Lagging indicators: The part of a collection of the economic time series designed to give information about the broad swings in measures of the aggregate economic activity known a

Staitistics project, I need a statistics project done. How much will it cos...

I need a statistics project done. How much will it cost?

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