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

Linear regression, regression line drawn as Y=C+1075x, when x was 2, and y ...

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Explain Genstat, Genstat: The basic purpose piece of statistical software ...

Genstat: The basic purpose piece of statistical software for the management and the analysis of data. The package incorporates the wide variety of data handling events and a wi

Spreading function and scattering function, 1)  Consider an antenna with a ...

1)  Consider an antenna with a pattern: G(θ,φ) = sinn(θ/θ0) cos(θ/θ0)   where θ0 = Π/1.5 (a) What is the 3-dB bandwidth? (b) What is the 10-dB beam width? (c) What is t

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

Profile plots, Profile plots  is a technique of representing the multivaria...

Profile plots  is a technique of representing the multivariate data graphically. Each of the observation is represented by a diagram comprising of a sequence of equispaced vertical

Decision Models., An oil company thinks that there is a 60% chance that the...

An oil company thinks that there is a 60% chance that there is oil in the land they own. Before drilling they run a soil test. When there is oil in the ground, the soil test comes

Central tendency, explain the graphical method of measure of central tenden...

explain the graphical method of measure of central tendency

Infant mortality rate, Infant mortality rate is the ratio of the number of...

Infant mortality rate is the ratio of the number of deaths during the calendar year among the infants under one year of age to the total number of live births during that particul

Explain healthy worker effect, Healthy worker effect : The occurrence where...

Healthy worker effect : The occurrence whereby employed individuals tend to have lower mortality rates than those who are unemployed. The effect, which can pose the serious problem

Efficiency, This term applied in the context of comparing the different met...

This term applied in the context of comparing the different methods and techniques of estimating the same parameter; the estimate with the lowest variance being regarded as the mos

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