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

Hirap, #q A paper mill products two grade of paper viz., X & Y. Because of ...

#q A paper mill products two grade of paper viz., X & Y. Because of raw material restriction, it cannot produce more than 400 tons of grade X paper & 300 tons of grade Y paper in a

Homework help, Q1: The growth in bad debt expense for Aptara Pvt. Ltd. Comp...

Q1: The growth in bad debt expense for Aptara Pvt. Ltd. Company over the last 20 years is as follows. 1997 0.11 1998 0.09 1999 0.08 2000 0.08 2001 0.1 2002 0.11 2003 0.12 2004 0.1

Estimating functions, The functions of the data and the parameters of inter...

The functions of the data and the parameters of interest which can be brought in use to conduct inference about the parameters when full distribution of the observations is unknown

Confidence interval, Confidence interval : A range of the values, calculate...

Confidence interval : A range of the values, calculated from the sample observations which is believed, with the particular probability, to posses the true parameter value. A 95% c

Case-cohort study, Case-cohort study : The research design in epidemiology ...

Case-cohort study : The research design in epidemiology which involves the sampling of controls at the outset of the study that is to be compared with the cases from the cohort. Th

Explain prevalence, Prevalence : The measure of the number of people in a p...

Prevalence : The measure of the number of people in a population who have a certain disease at a given point in time. It c an be measured by two methods, as point prevalence and p

Fibonacci distribution, The probability distribution of the various observa...

The probability distribution of the various observations is required to obtain the run of two successes in the series of Bernoulli trials with the probability of success equal to a

Cellular proliferation models, Cellular proliferation models : Models are u...

Cellular proliferation models : Models are used to describe the growth of the  cell populations. One of the example is the deterministic model   where N(t) is the number of cel

Factorization theorem, The theorem relating structure of the likelihood to ...

The theorem relating structure of the likelihood to the concept of the sufficient statistic. Officially the necessary and sufficient condition which a statistic S be sufficient for

Explain perturbation theory, Perturbation theory : The theory useful in ass...

Perturbation theory : The theory useful in assessing how well a specific algorithm or the statistical model performs when the observations suffer less random changes. In very commo

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