The Sphere as a Tool for Teaching Statistics

The use of statistics is commonplace in the geosciences, so teaching statistics is important; however, abstract statistical concepts are difficult for teachers to communicate and formidable for students to grasp. A physical model can be very effective in communicating certain abstract ideas. The surface of a sphere makes a good physical analogue for the universe of equi-probable results (sample space) required for formulating a null hypothesis. If data can be plotted on a sphere and if the observations can be modeled as a coin toss (even with an unfair coin), then a combination of spherical geometry and the binomial distribution can be used for testing hypotheses about the data set. A spherical surface provides a tangible model for abstract concepts such as null and alternate hypotheses and probability. I provide a geometrically simple example that requires the use of binomial tables and a more geometrically challenging example using the normal approximation of the binomial distribution and paleomagnetic data from the Peninsular Ranges terrane.