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Using multivariate statistics
1 Multivariate Statistics: Why?
Multivariate statistics are increasingly popular techniques used for analyzing complicated data sets. They provide analysis when there are many independent variables (IVs) and/or many dependent variables (DVs), all correlated with one another to varying degrees. Because of the difficulty in addressing complicated research questions with univariate analyses and because of the availability of canned software for performing multivariate analyses, multivariate statistics have become widely used. Indeed, a standard univariate statistics course only begins to prepare a student to read research literature or a researcher to produce it.
But how much harder are the multivariate techniques? Compared with the multivariate meth¬ods, univariate statistical methods are so straightforward and neatly structured that it is hard to believe they once took so much effort to master. Yet many researchers apply and correctly interpret results of intricate analysis of variance before the grand structure is apparent to them. The same can be true of multivariate statistical methods. Although we are delighted if you gain insights into the full multivariate general linear model, we have accomplished our goal if you feel comfortable selecting and setting up multivariate analyses and interpreting the computer output.
Multivariate methods are more complex than univariate by at least an order of magnitude. However, for the most part, the greater complexity requires few conceptual leaps. Familiar concepts such as sampling distributions and homogeneity of variance simply become more elaborate.
Multivariate models have not gained popularity by accident—or even by sinister design. Their growing popularity parallels the greater complexity of contemporary research. In psychology, for example, we are less and less enamored of the simple, clean, laboratory study, in which pliant, first-year college students each provides us with a single behavioral measure on cue.
The Domain of Multivariate Statistics:
Numbers of IVs and DVs
Multivariate statistical methods are an extension of univariate and bivariate statistics. Multivariate statistics are the complete or general case, whereas univariate and bivariate statistics are special cases of the multivariate model. If your design has many variables, multivariate techniques often let you perform a single analysis instead of a series of univariate or bivariate analyses.
Variables are roughly dichotomized into two major types—independent and dependent. Independent variables (IVs) are the differing conditions (treatment vs. placebo) to which you ex¬pose your subjects, or the characteristics (tall or short) that the subjects themselves bring into the
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