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

Multiple correlation coefficient, Multiple correlation coefficient is th...

Multiple correlation coefficient is the correlation among the observed values of dependent variable in the multiple regression, and the values predicted by estimated regression

Chi-squared distribution, Chi-squared distribution : It is the probability ...

Chi-squared distribution : It is the probability distribution, f (x), of the random variable de?ned as the sum of squares of the number (v) of independent standard normal variables

Individual differences, Individual differences scaling is a form of multid...

Individual differences scaling is a form of multidimensional scaling applicable to the data comprising of a number of proximity matrices from the different sources that is differe

Mosaic displays, Mosaic displays  is the graphical display of the standardi...

Mosaic displays  is the graphical display of the standardized residuals from the fitting a log-linear model to a contingency table in which the colour and outline of the mosaic's '

Effect sparsity, The term which is used in the industrial experimentation, ...

The term which is used in the industrial experimentation, where there is commonly a large set of candidate factors believed to have the possible significant influence on the respon

Relative risk, Relative risk is the measure of the association between the...

Relative risk is the measure of the association between the exposure to a particular factor and the risk or probability of a convinced outcome, calculated as follows     therefor

Quasi-experiment, Quasi-experiment is a term taken in use for studies whic...

Quasi-experiment is a term taken in use for studies which resemble experiments but are weak on some of the characteristics, particularly that allocation of the subjects to groups

Rates of return, An investor with a stock portfolio sued his broker, claimi...

An investor with a stock portfolio sued his broker, claiming that a lack of diversification in his portfolio had led to poor performance. The data, shown below, are the rates of re

Quality-adjusted survival analysis, Quality-adjusted survival analysis is ...

Quality-adjusted survival analysis is a method for evaluating the effects of treatment on survival which allows the consideration of quality of life as well as the quantity of lif

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