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

Multilevel models, Multilevel models are the regression models for the mul...

Multilevel models are the regression models for the multilevel or clustered data where units i are nested in the clusters j, for example a cross-sectional study where students are

Explain johnson-neyman technique, Johnson-Neyman technique:  The technique ...

Johnson-Neyman technique:  The technique which can be used in the situations where analysis of the covariance is not valid because of the heterogeneity of slopes. With this method

Describe hurdle model, Hurdle Model:  The model for count data which postul...

Hurdle Model:  The model for count data which postulates two processes, one generating the zeros in the data and one generating positive values. The binomial model decides the bina

Quittingill effect, Quittingill effect is a  problem which occurs most fre...

Quittingill effect is a  problem which occurs most frequently in studies of the smoker cessation where smokers frequently quit smoking following the onset of the disease symptoms

Gaussian markov random field, It is the multivariate normal random vector w...

It is the multivariate normal random vector which satisfies certain conditional independence suppositions. This can be viewed as a model framework which contains a wide range of st

Explain multicentre study, Multicentre study : The clinical trial conducte...

Multicentre study : The clinical trial conducted simultaneously in the number of participating hospitals, with all centres following an agreed-upon study of the protocol and with

Define hazard function, Hazard function : The risk which an individual expe...

Hazard function : The risk which an individual experiences an event in a small time interval, given that the individual has survived up to the starting of the interval. It is th

Scatter plots - non-linear relationship, The scatter plots of SRES1, RESI1 ...

The scatter plots of SRES1, RESI1 versus totexp demonstrates that there is non-linear relationship that exists as most of the points are below and above zero. The scatter plots sho

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