Using Simulation to Improve Students' Understanding in Statistical Theory

• Activity Number: 387
• Type: Roundtables
• Date/Time: Tuesday, August 6, 2013 : 12:30 PM to 1:50 PM
• Sponsor: Section on Statistical Education
• Author(s): Elena G. Rantou (Randou)*+
• Companies: George Mason University
• Keywords: Mathematical statistics ; Probability ; Simulation ; Statistic behavior ; R ; Observation

Abstract

In an attempt to effectively communicate important results from statistical theory, the professor can introduce simulation studies. Prior experience has indicated that such studies not only enhance students' understanding, but also boost their self-confidence in statistics. Important results from probability and statistical theory such as transforming and combining random variables, the Central Limit Theorem, the normal approximation to the binomial distribution, and the Cramer-Rao lower bound for minimum variance appear to be highly comprehensible and well justified through simulation. Such attempts have been used, in combination with the R-language, in various courses ranging from undergraduate probability to graduate mathematical statistics and have been proven effective in significantly improving the understanding and perception of statistics. Students are asked to generate and observe the behavior of a statistic, and are consequently led to the results through this observation. The positive effect from the use of these techniques is measured by using different tests and ultimately from the students' improved performance in the course.