A population may include just one thing about every member of a group, or it may include two or more things about every member. In either case there will be one observation for each group member. Univariate statistics are concerned with making inferences about one variable populations, like "what is the mean shoe size of business students?" Multivariate statistics is concerned with making inferences about the way that two or more variables are connected in the population like, "do students with high grade point averages usually have big feet?" What's important about multivariate statistics is that it allows you to make better predictions. If you had to predict the shoe size of a business student and you had found out that students with high grade point averages usually have big feet, knowing the student's grade point average might help. Multivariate statistics are powerful and find applications in economics, finance, and cost accounting.
Ann Howard and Kevin Schmidt might use multivariate statistics if Mr. McGrath asked them to study the effects of radio advertising on sock sales. They could collect a multivariate sample by collecting two variables from each of a number of cities—recent changes in sales and the amount spent on radio ads. By using multivariate techniques you will learn in later chapters, Ann and Kevin can see if more radio advertising means more sock sales.
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