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

Frailty, A term usually used for unobserved individual heterogeneity. Such ...

A term usually used for unobserved individual heterogeneity. Such variation is of main concern in the medical statistics particularly in the analysis of the survival times where ha

Obuchowski and rockette method, Obuchowski and Rockette method  is an alter...

Obuchowski and Rockette method  is an alternative to the Dorfman-Berbaum-Metz technique for analyzing multiple reader receiver operating curve data. Instead of the modelling the ja

Lexis diagram, Lexis diagram  is the diagram for displaying the simultaneou...

Lexis diagram  is the diagram for displaying the simultaneous effects of the two time scales (generally age and calendar time) on a rate. For instance, mortality rates from cancer

Epidemic, The rapid development or growth of the disease in a community or ...

The rapid development or growth of the disease in a community or region. Statistical thinking has made very much significant contributions to the understanding of such type of phen

Data smoothing algorithms, The procedures for extracting the pattern in a s...

The procedures for extracting the pattern in a series of observations when this is obscured by the noise. Basically any such technique or method separates the original series into

Cartogram, Cartogram : It is the diagram in which descriptive statistical i...

Cartogram : It is the diagram in which descriptive statistical information is displayed on the geographical map by the means of shading, different symbols or in some other possibly

Pasture trials, Pasture trials is the study in which the pastures are subj...

Pasture trials is the study in which the pastures are subjected to number of treatments (types of forage, animal management systems, agronomic treatments, and many more)The grazin

Explain yate s'' continuity correction, Yate s' continuity correction : Whe...

Yate s' continuity correction : When the testing for independence in contingency table, a continuous probability distribution, known as chi-squared distribution, is used as the app

Explain interim analyses, Interim analyses : An analysis made before the pl...

Interim analyses : An analysis made before the planned end of a clinical trial, typically with the aim of detecting the treatment differences at the early stage and thus preventing

Factorial moment generating function, The function of a variable t which, w...

The function of a variable t which, when extended formally as a power series in t, yields factorial moments as the coefficients of the respective powers. If the P(t) is probability

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