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

Describe hello-goodbye effect., Hello-goodbye effect : The phenomenon initi...

Hello-goodbye effect : The phenomenon initially described in psychotherapy research, but one which might arise whenever a subject is assessed on two occasions, with some interventi

Concordant mutations test, Concordant mutations test : A statistical test u...

Concordant mutations test : A statistical test used in the cancer studies to determine whether or not a diagnosed second primary tumour is biologically independent of the original

Homework and Assignment assistance for RES610 Course, Interested in 10 hour...

Interested in 10 hour program with twice a week tutoring for 1 hour each. Need tutor to assist with answering the assignment questions for the next 5 weeks.

L''abbe ´ plot, L'Abbe ´ plot is often used in the meta-analysis of the cl...

L'Abbe ´ plot is often used in the meta-analysis of the clinical trials where the result is the binary response of it. The event risk (number of events/number of the patients in a

Response feature analysis, Response feature analysis is the approach to th...

Response feature analysis is the approach to the analysis of longitudinal data including the calculation of the suitable summary measures from the set of repeated measures on each

Data mining, The non-trivial extraction of implicit, earlier unknown and po...

The non-trivial extraction of implicit, earlier unknown and potentially useful information from data, specifically high-dimensional data, using pattern recognition, artificial inte

Current status data, The Current status data arise in the survival analysis...

The Current status data arise in the survival analysis if the observations are limited to the indicators of whether or not the event of interest has happened at the time the sample

Gauss markov theorem, This is the theorem which states that if the error te...

This is the theorem which states that if the error terms in a multiple regression have the same variance and are not corrected, then the estimators of the parameters in the model p

Descriptive statistics, how to describe association between quantitative an...

how to describe association between quantitative and categorical variables

What is harris and stevens forecasting, Harris and Stevens forecasting is ...

Harris and Stevens forecasting is the method of making short term forecasts in the time series which is subject to abrupt changes in pattern and the transient effects. Instances o

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