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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.
Balanced incomplete block design : A design in which all the treatments are not used in all blocks. Such designs have the below stated properties: * each block comprises the
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Multi dimensional unfolding is the form of multidimensional scaling applicable to both the rectangular proximity matrices where the rows and columns refer to the different sets of
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An approach to investigations designed to recognize a particular medical condition in the large population, usually by means of a blood test, which might result in the considerable
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Least significant difference test is an approach to comparing a set of means which controls the family wise error rate at some specific level, let's assume it to be α. The hypothe
A term usually used for unobserved individual heterogeneity. Such variation is of main concern in the medical statistics particularly in the analysis of the survival times where ha
Confounding: A procedure observed in some factorial designs in which it is impossible to differentiate between some main effects or interactions, on the basis of the particular d
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