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

Chapter 7&8, Chapter 7 2. Describe the distribution of sample means (shape...

Chapter 7 2. Describe the distribution of sample means (shape, expected value, and standard error) for samples of n =36 selected from a population with a mean of µ = 100 and a sta

Explanatory variables, The variables appearing on the right-hand side of eq...

The variables appearing on the right-hand side of equations defining, for instance, multiple regressions or the logistic regression, and which seek to predict or 'explain' response

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

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

#title.Statistics for management, The growth in bad debt expense for Johnst...

The growth in bad debt expense for Johnston office supply Company over this time period.If this rate continues,estimate the percentage increase in bad debts for 1997,relative to 19

Dot plot, The more effective display than a number of other methods or tech...

The more effective display than a number of other methods or techniques, for instance, pie charts and bar charts, for displaying the quantitative data which are labeled. An instanc

Quota sample, Quota sample is the sample in which the units are not select...

Quota sample is the sample in which the units are not selected at the random, but in terms of a particular number of units in each of a number of categories; for instance, 10 men

Mobile Marketing statistics., 1) Has smartphones affected the consumer beh...

1) Has smartphones affected the consumer behavior? If so How ? And how is it going to change in future? 2) Forecasting of Mobile market (Time series analysis) 3) Comparison of fou

Barnard, Barnard, George Alfred (1915^2002) : Born in Walthamstow in the ea...

Barnard, George Alfred (1915^2002) : Born in Walthamstow in the east of London, Barnard achieved a scholarship to St. John's College, Cambridge, from where he graduated in the math

Change point problems, Change point problems : Problems with chronologicall...

Change point problems : Problems with chronologically ordered data collected over the period during which there is known to have been a change in the underlying data generation cou

Hill-climbing algorithm, Hill-climbing algorithm is  an algorithm which is ...

Hill-climbing algorithm is  an algorithm which is made in use in those techniques of cluster analysis which seek to find the partition of n individuals into g clusters by optimizin

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