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In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used when there are two or more dependent variables , [ 1 ] and is often followed by significance tests involving individual dependent variables separately.
Inspired by ANOVA, MANOVA is based on a generalization of sum of squares explained by the model and the inverse of the sum of squares unexplained by the model . The most common [ 6 ] [ 7 ] statistics are summaries based on the roots (or eigenvalues ) λ p {\textstyle \lambda _{p}} of the matrix A := S model S res − 1 {\textstyle A:=S_{\text ...
The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of multiple linear regression to the case of more than one dependent variable.
In statistics, Wilks' lambda distribution (named for Samuel S. Wilks), is a probability distribution used in multivariate hypothesis testing, especially with regard to the likelihood-ratio test and multivariate analysis of variance (MANOVA).
Additionally, the power of MANOVA is contingent upon the correlations between the dependent variables, so the relationship between the different conditions must also be considered. [2] SPSS provides an F-ratio from four different methods: Pillai's trace, Wilks’ lambda, Hotelling's trace, and Roy's largest root.
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables.
In statistics, path analysis is used to describe the directed dependencies among a set of variables. This includes models equivalent to any form of multiple regression analysis, factor analysis, canonical correlation analysis, discriminant analysis, as well as more general families of models in the multivariate analysis of variance and covariance analyses (MANOVA, ANOVA, ANCOVA).
Growth curve model: [2] Let X be a p×n random matrix corresponding to the observations, A a p×q within design matrix with q ≤ p, B a q×k parameter matrix, C a k×n between individual design matrix with rank(C) + p ≤ n and let Σ be a positive-definite p×p matrix.