The modern world is full of complexity. Data that describe it too often must mirror that complexity. Statistical problems with only one independent variable and a single dependent variable are usually only found in textbooks. The real world is hopelessly multivariate and filled with interconnected variables. Any data display that fails to represent those complexities risks misleading us. Einstein's advice that “everything should be as simple as possible, but no simpler” looms prescient.

If we couple Einstein's advice with Tukey's (1977) observation (discussed in the introduction to this section) that the best way to find what we are not expecting is with a well-designed graphic display, we have an immediate problem. Most of our data displays must be represented on a two-dimensional plane. Yet trying to show three or four or more dimensions on a two-dimensional surface requires something different than the usual metaphor of representing the data spatially, for example, bigger numbers are represented by a bigger bar, a larger pie segment, a line that reaches higher, or any of the other Cartesian representations.

Happily there have been large numbers of ingenious methods developed to display multivariate data on a two-dimensional surface.

Forty years ago Yale's John Hartigan proposed a simple approach for looking at some kinds of multivariate data. This is now called the “Inside Out Plot.” Most data begin as a table, and so it is logical that we use a semigraphic display to help us look at such tabular data. The construction of an inside out plot builds on the idea that sometimes a well-constructed table can be an effective display, giving us hope that a mutated table can help us look at high-dimensional data within the limitations of a two-dimensional plotting surface.

As in most instances on the topic of display, explanation is best done through the use of an example. The popularity of the movie Moneyball provides the topic.

A Multivariate Example: Joe Mauer vs. Some Immortals

In the February 17, 2010 issue of USA Today there was an article about the Minnesota Twins all-star catcher Joe Mauer. Mauer's first six years in the major leagues have been remarkable by any measure, but especially from an offensive perspective (during that time he won three batting titles).