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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.
Ordination is the procedure of reducing the dimensionality (that is the number of variables) of multivariate data by deriving the small number of new variables which contain much
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Weathervane plot is the graphical display of the multivariate data based on bubble plot. The latter is enhanced by the addiction of the lines whose lengths and directions code the
Suppose that $4 million is available for investment in three projects. The probability distribution of the net present value earned from each project depends on how much is invest
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stationary time series
Missing Data - Reasons for screening data In case of any missing data, the researcher needs to conduct tests to ascertain that the pattern of these missing cases is random.
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Linked micro map plot is a plot which provides the graphical overview and the details for spatially indexed statistical summaries. The plot shows the spatial patterns and statisti
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