Current research interests: Statistical measures of ordinal data.We've all filled out surveys on which questions appear of the form "On a scale from 1 to 5, ...." Though incorrect, it is common for people analyzing data collected in this way to use means and standard deviations. My goal is to gauge the amount of error and the types of errors that result from such use. Statistical measures on bipartite graphs. The "High School Prom Theorem" was popularized recently by the late mathematician and economist David Gale. In terms of graph theory, it states that the means of the degree sequence on either vertex class of a balanced bipartite graph must agree. My goal is to develop similar theorems for other statistical measures. Geometric Visualization. There are many interesting geometries other than Euclidean plane geometry, but they can be hard to imagine. My goal is to create new ways of visualizing geometric surfaces and spaces. |