Using Simulations to Teach Statistical Concepts

Abstract

Many fundamental concepts in applied Statistics rely upon large sample or asymptotic results. In teaching statistics, instructors refer to the Central Limit Theorem (CLT) and/or other Normal approximations to legitimize a long list of techniques and approaches that play essential roles in statistical inference. To appreciate the validity of such concepts the students need to have enough exposure to the underlying themes of theoretical statistics and a thorough understanding of calculus, which undergraduate Statistics students usually do not have. Instructors may choose to use simulation as a simple way to explore asymptotic normality. Computers can be used to generate large numbers of random observations from hypothetical (yet known) population distributions to show that the results of large sample theory hold. In this talk, we demonstrate how we use the statistical free-ware R to teach the Central Limit Theorem and Confidence Intervals estimation in an elementary statistics course.