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

K-means cluster analysis, K-means cluster analysis is the method of cluste...

K-means cluster analysis is the method of cluster analysis in which from an initial partition of observations into K clusters, each observation in turn is analysed and reassigned,

Incubation period, Incubation period is the time elapsing amongs the receip...

Incubation period is the time elapsing amongs the receipt of infection and the appearance of the symptoms. The length of the incubation time period depends on the disease, ranging

Case Study, ACC – A pioneer in the Indian cement industry Associated Cemen...

ACC – A pioneer in the Indian cement industry Associated Cement Companies Ltd. (ACC) came into existence in 1936, after the merger of 10 companies belonging to four important bus

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

Statistics, cholscores Treatment income ($000) Patient ID low Income? ...

cholscores Treatment income ($000) Patient ID low Income? 0.6 Old 21.3 2 Yes 0.17 Old 27.2 13 Yes 0.69 New 27.1 16 Yes 1.09 Old 94.8

Link functions, Link functions: The link function relates the linear p...

Link functions: The link function relates the linear predictor ηi to the expected value of the data. In classical linear models the mean and the linear predictor are identical

Minimization, Minimization is the method or technique for allocating patie...

Minimization is the method or technique for allocating patients to the treatments in clinical trials which is usually the acceptable alternative to random allocation. The procedur

Bubble plot, Bubble plot : A method or technique for displaying the observa...

Bubble plot : A method or technique for displaying the observations which involve three variable values. Two of the variables are used to make a scatter diagram and values of the t

Cumulative frequency distribution, The tabulation of a sample of observatio...

The tabulation of a sample of observations in terms of numbers falling below particular values. The empirical equivalent of the growing probability distribution. An example of such

Explain labour force survey, Labour force survey : This survey carried out ...

Labour force survey : This survey carried out in the UK on the quarterly basis since the spring of year 1992. It covers 60 000 households and gives labour force and other detail

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