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

Uncertainty analysis, Uncertainty analysis is the process for assessing th...

Uncertainty analysis is the process for assessing the variability in the outcome variable that is due to the uncertainty in estimating the values of input parameters. A sensitivit

Describe jonckheere terpstra test, Jonckheere Terpstra test  is the test fo...

Jonckheere Terpstra test  is the test for detecting particular types of departures from the independence in a contingency table in which both the row and column categories contain

Quincunx, Quincunx  is the device used by Galton to illustrate his lecture...

Quincunx  is the device used by Galton to illustrate his lectures, which is shown in the Figure. It had a glass face and a funnel at its top. The shot was passed through funnel an

Implementation of huffman coding, Input to the compress is a text le with a...

Input to the compress is a text le with arbitrary size, but for this assignment we will assume that the data structure of the file fits in the main memory of a computer. Output of

Bimodal distribution, Bimodal distribution : The probability distribution, ...

Bimodal distribution : The probability distribution, or we can simply say the frequency distribution, with two modes. Figure 15 shows the example of each of them

Explain multiple comparison tests, Multiple comparison tests : Procedures f...

Multiple comparison tests : Procedures for detailed examination of the differences between a set of means, generally after a general hypothesis that they are all equal has been rej

Buffon''s needle problem, Buffon's needle problem : A problem proposed and ...

Buffon's needle problem : A problem proposed and solved by the scientist Comte de Buffon in 1777 which includes determining the probability, p, which a needle of length l will inte

Explain lancaster models., Lancaster models : The means of representing the...

Lancaster models : The means of representing the joint distribution of the set of variables in terms of the marginal distributions, supposing all the interactions higher than a par

Fibonacci distribution, The probability distribution of the various observa...

The probability distribution of the various observations is required to obtain the run of two successes in the series of Bernoulli trials with the probability of success equal to a

Explain information theory., Information theory: This is the branch of app...

Information theory: This is the branch of applied probability theory applicable to various communication and signal processing problems in the field of engineering and biology. In

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