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

Line-intersect sampling, Line-intersect sampling is a technique of unequal...

Line-intersect sampling is a technique of unequal probability sampling for selecting the sampling units in the geographical area. A sample of lines is drawn in a study area and, w

Describe nuisance parameter, Nuisance parameter : The parameter of the mode...

Nuisance parameter : The parameter of the model in which there is no scienti?c interest but whose values are generally required (but in usual are unknown) to make inferences about

Develop an algebraic linear programming model, Duck Lovers Unlimited (DLU) ...

Duck Lovers Unlimited (DLU) Inc. assembles specially configured light jet aircrafts for airborne duck hunting. The quarterly demand forecasts for the upcoming fiscal year are:

Fiducial inference, The problematic and enigmatic theory of an inference in...

The problematic and enigmatic theory of an inference introduced by the Fisher, which extracts a probability distribution for the parameter on the basis of the data without having f

Treatment allocation ratio, Treatment allocation ratio is the ratio of the...

Treatment allocation ratio is the ratio of the number of subjects allocated to the two treatments in a clinical trial. The equal allocation is most usual in practice, but it might

Linked micro map plot, Linked micro map plot is a plot which provides the ...

Linked micro map plot is a plot which provides the graphical overview and the details for spatially indexed statistical summaries. The plot shows the spatial patterns and statisti

Fuzzy set theory, A radically different approach of dealing with the uncert...

A radically different approach of dealing with the uncertainty than the traditional probabilistic and the statistical methods. The necessary feature of the fuzzy set is a membershi

Math, A statewide survey of 1,706 California adults’ residents include the ...

A statewide survey of 1,706 California adults’ residents include the following question: would you favor or oppose providing a path to citizenship for illegal immigrants in the U.S

Develop the equations to calculate the flow rates, A two-step distillation ...

A two-step distillation and mixing process is shown in the figure. The system operates at steady-state conditions and there are no chemical reactions. The known flow rates and comp

Data reduction, The method of summarizing the large amounts of data by form...

The method of summarizing the large amounts of data by forming the frequency distributions, scatter diagrams, histograms, etc., and calculating statistics like means variances and

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