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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: These matrices satisfy the following written equation Wilk's lambda is given by ratio of the determinants of the W and T, that is 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.
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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 dire
4-13. Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previou
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The type of longitudinal study in which the subjects receive different treatments on the various occasions. Random allocation is required to determine the order in which the treatm
Longitudinal data : The data arising when each of the number of subjects or patients give rise to the vector of measurements representing same variable observed at the number of di
Band matrix: A matrix which has its non zero elements arranged uniformly near to the diagonal, so that aij = 0 if (i - j)> ml or (j - i)> mu where aij are the elements of matrix a
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