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

Explain intervention analysis in time series, Intervention analysis in time...

Intervention analysis in time series : The extension of the autoregressive integrated moving average models applied to time series permitting for the study of the magnitude and str

Dummy variable, Discuss the use of dummy variables in both multiple linear ...

Discuss the use of dummy variables in both multiple linear regression and non-linear regression. Give examples if possible

Catastrophe theory, Catastrophe theory : A theory of how little is the cont...

Catastrophe theory : A theory of how little is the continuous changes in the independent variables which can have unexpected, discontinuous effects on the dependent variables. Exam

Probabilistic matching, Probabilistic matching is a method developed to ma...

Probabilistic matching is a method developed to maximize the accuracy of the linkage decisions based on the level of agreement and disagreement among the identifiers on different

Combine standard deviation, what is the combine standard deviation height f...

what is the combine standard deviation height from the follwing

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

Prepare a report using regression analysis, Paul Jordan has just been hired...

Paul Jordan has just been hired as a management analyst at Digital Cell Phone Inc. Digital Cell manufactures a broad line of phones for the consumer market. Paul's boss, John Smith

Change point problems, Change point problems : Problems with chronologicall...

Change point problems : Problems with chronologically ordered data collected over the period during which there is known to have been a change in the underlying data generation cou

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