Көпөлшемді үлгілердің орташа мәндерін салыстыру процедурасы

Procedure for comparing multivariate sample means

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, and is often followed by significance tests involving individual dependent variables separately. Without relation to the image, the dependent variables may be k life satisfactions scores measured at sequential time points and p job satisfaction scores measured at sequential time points. In this case there are k+p dependent variables whose linear combination follows a multivariate normal distribution, multivariate variance covariance matrix homogeneity, and linear relationship, no multicollinearity, and each without outliers.

Assume dimensional observations, where the ’th observation is assigned to the group and is distributed around the group center with multivariate Gaussian noise: where is the covariance matrix. Then we formulate our null hypothesis as

One can also test if there is a group effect after adjusting for covariates. For this, follow the procedure above but substitute with the predictions of the general linear model, containing the group and the covariates, and substitute with the predictions of the general linear model containing only the covariates (and an intercept). Then are the additional sum of squares explained by adding the grouping information and is the residual sum of squares of the model containing the grouping and the covariates.