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

Identifying the necessary and sufficient conditions, You have probably noti...

You have probably noticed by now that some of the statements of necessary and sufficient conditions sound more natural than others. For example it seems more natural to express "We

Zero sumgame, Zero sumgame is a game played by the number of persons in wh...

Zero sumgame is a game played by the number of persons in which the winner takes all stakes given by the losers so that the algebraic sum of gains at any stage is zero. Number of

Doane''s rule, A rule for computing the number of classes to use while cons...

A rule for computing the number of classes to use while constructing a histogram and  can be given by   here n is the sample size and ^ γ is the estimate of kurtosis.

Centile reference charts, Centile reference charts : Charts which are used ...

Centile reference charts : Charts which are used inmedicine to observe the clinical measurements on individual patients in the context of the population values. If the population i

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:

Describe monty hall problem, Monty Hall problem : A apparently counter-intu...

Monty Hall problem : A apparently counter-intuitive problem in the probability which gets its name from the TV game show, 'Let's Make a Deal' hosted by the Monty Hall. On show a pa

Partial autocorrelation function, The graph for Partial Autocorrelation Fun...

The graph for Partial Autocorrelation Function for RES1 shows that there is no autocorrelation even though there are alternating spikes because they fall inside the 5% significance

Forecast, The particular projection which an investigator believes is most ...

The particular projection which an investigator believes is most likely to give an accurate prediction of the future value of some process. Commonly used in the context of the anal

Define probability judgements, Probability judgements : Human beings often ...

Probability judgements : Human beings often require assessing the probability which some event will occur and accuracy of these probability judgements often determines success of o

Coplot, This is the powerful visualization tool for studying how the respon...

This is the powerful visualization tool for studying how the response relies on an explanatory variable given the values of other explanatory variables. The plot comprises of a num

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