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

Scatter plots, The scatter plot of SRES1 versus totexp demonstrates that th...

The scatter plot of SRES1 versus totexp demonstrates that there is non-linear relationship that exists as most of the points are below and above zero. The scatter plot show that th

Degenerate distributions, The special cases of the probability distribution...

The special cases of the probability distributions in which the random variable's distribution is concentrated at one point only. For instance, a discrete uniform distribution when

Graphical deception, Graphical deception : Statistical graphics which are n...

Graphical deception : Statistical graphics which are not as honest as they should be. It is relatively simple. To mislead the unwary with the graphical material. For instance, c

Business Statistic HW., Hello , I have a business statistic HW that is due ...

Hello , I have a business statistic HW that is due after 23 hours exactly for now . I need full and details answers please , plus they must be in a done and typed in a word or exce

Times series plots, There is high level of fluctuation in a zigzag pattern ...

There is high level of fluctuation in a zigzag pattern in the time series for RESI1 which indicates that there is possibly negative autocorrelation present. Column C11 show

Mixture experiment, Mixture experiment is an experiment in which the two o...

Mixture experiment is an experiment in which the two or more ingredients are blended together to form an end product. The measurements are taken on the several blends of the ingre

Chebyshev''s inequality, Chebyshev's inequality: A statement about the pro...

Chebyshev's inequality: A statement about the proportion of the observations which fall within some number of the standard deviations of the mean for any of the probability distri

NULL HYPOTHESES, Ask questT-TEST? ion #Minimum 100 words accepted#

Ask questT-TEST? ion #Minimum 100 words accepted#

Regression discontinuity design, Regression discontinuity design is the qu...

Regression discontinuity design is the quasi-experimental design in which participants in, for instance, an intervention study, are assigned to the treatment and control groups on

Residual calculation, Regression line drawn as y= c+ 1075x ,when x was2, an...

Regression line drawn as y= c+ 1075x ,when x was2, and y was 239,given that y intercept was 11. Calculate the residual ?

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