I am entering my 19th year on the faculty at Texas Tech, yet this is the first time I've taught multivariate. However, I've taught two other graduate stat courses in the department, QM I/Intro and QM IV/SEM, many times. Further, I've published articles using many of the techniques we'll cover in QM III, so I think I'll do OK.
What do we mean by "multivariate statistics"? I think it's most useful to contrast the term with other related ones.
If we're looking at just one variable at a time, then we're dealing with univariate analyses. Here are some examples.
If we're looking at the relationship of two variables, then we're dealing with bivariate analyses. For example, we might want to know how, among adults, age correlates with annual earnings. Or, using a chi-square for nominal variables, we can test whether self-identification with Democratic, Republican, or other political parties differs in parents vs. non-parents.
Finally, we have multivariate analysis. The word "multiple" would suggest a multivariate analysis is anything using three or more variables. Thus, a multiple-regression analysis featuring one dependent variable and six predictor variables (seven variables total) would count as multivariate. However, some authors confine the term "multivariate" to multiple dependent variables. Multivariate Analysis of Variance (MANOVA) would be one example of this restricted definition of multivariate. In this course, I plan to be more inclusive in deciding what is a multivariate analysis.
