Usually discriminant analysis is presented conceptually in an upside down sort of way, where what you would traditionally think of as dependent variables are actually the predictor variables, and group membership rather than being the levels of the IV are groups whose membership is being predicted In the case where there are more than two groups, DA permits you to test the hypothesis that there is more than one significant way of describing how the groups differ on a weighted linear combination of the discriminating variables, and you can think of these combinations, called canonical variables, as “dimensions” of difference. These variables will be uncorrelated with each other.This way of using DA is called descriptive discriminant analysis. In such a situations, we are not so interested in how the variables perform individually per se, but how well as a set they classify cases according to the groups.ĭiscriminant Analysis permits a multivariate analysis of variance hypothesis of the test that two or more groups (conditions, levels) differ significantly on a linear combination of discriminating variables. Another way to put this is: how well can the levels of the grouping variable be discriminated by scores on the discriminating variables? In general it’s good to use naturally occurring groups that are mutually exclusive groups that are exhaustive of the domain, rather than median splits or arbitrary divisions. Classification is a separate procedure in which the discriminating variables (or functions) are used to predict group membership. Discriminant Analysis is usually concerned with actually putting people into groups (classification) and testing how well (or how poorly) subjects are classified and to answer the question of how can the continuous variables be linearly combined to best classify a subject into a group? The primary goal in DFA may be geared more towards classification. MANOVA and discriminant function analysis are mathematically identical but are different in terms of emphasis. One can think of it as MANOVA in reverse -with MANOVA we asked if groups are significantly different on a set of linearly combined dependent variables. If this is true, then those same dependent variables can be used to predict group membership. One may also perform planned comparison or post hoc comparisons to see which values of a factor contribute most to the explanation of the dependents.ĭiscriminant Analysis is used primarily to predict group membership from a set of continuous predictors. Where ANOVA tests the differences in means of the interval dependent for various categories of the independent(s), MANOVA tests the differences in the centroid (vector) of means of the multiple interval dependents, for various categories of the independent(s). MANOVA uses one or more categorical independents as predictors, like ANOVA, but unlike ANOVA, there is more than one dependent variable. Multiple analysis of variance (MANOVA) is used to see the main and interaction effects of categorical variables on multiple dependent interval variables. Multivariate GLM, MANOVA, and MANCOVA all deal with the situation where there is more than one dependent variable and one or more independents. Multivariate GLM is the version of the general linear model now often used to implement two long-established statistical procedures - MANOVA and MANCOVA.
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