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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.
Length-biased data is a data which arise when the probability that an item is sampled is proportional to its own length. A main example of this situation occurs in the renewal the
The problematic and enigmatic theory of an inference introduced by the Fisher, which extracts a probability distribution for the parameter on the basis of the data without having f
The graph for Partial Autocorrelation Function for RES1 shows that there is no autocorrelation even though there are alternating spikes because they fall inside the 5% significance
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Martingale: In the gambling context the term at first referred to a system for recouping losses by doubling the stake after each loss has occured. The modern mathematical concept
A rule for computing the number of classes to use while constructing a histogram and can be given by here n is the sample size and ^ γ is the estimate of kurtosis.
The process of providing the numerical value for the population parameter on the basis of information gathered from a sample. If a single ?gure is computed for the unknown paramete
Biplots: It is the multivariate analogue of the scatter plots, which estimates the multivariate distribution of the sample in a few dimensions, typically two and superimpose on th
Case series : It is the series of reports on the condition of the individual patients made by treating physician. Such reports might be helpful and informative for the rare disease
Wilcoxon's ranksum test is the distribution free method or technique used as an alternative to the Student's t-test for assessing whether two populations have the same location. G
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