"The bulk of commonly used contemporary statistical methods is based on a relatively simple application of the mathematics of Euclidean n-dimensional space. Unfortunately this fact is rarely acknowledged in elementary or medium-level statistics courses." This statement, from Saville and Wood (TAS v40(3), 1986), seems incomprehensible to most statistics educators. Why would anyone use n-dimensional space to teach introductory statistics?

In the seminar, I will describe how geometry is used in introductory statistics at Macalester College. Our introductory course covers so-called "advanced" methods --- e.g. analysis of covariance --- methods that can provide insight into the complex situations that students study in other courses and hear about in current events. Modern computation makes the advanced methods easily available even to introductory students; the challenge is to help students develop judgment and conceptual understanding. Conventionally, the theory behind the methods is based in linear algebra, a topic very few introductory students have mastered. But many of the techniques of statistics can be understood in 2- or 3-dimensional space using concepts that students find easy: angles, lengths, projections, the Pythagorean theorem. Even people who already have considerable statistical skills often gain more insight by looking at things geometrically.