# P2-15: Evaluating the Effectiveness of Using Simulations to Teach the Central Limit Theorem and the Sampling Distribution of a Mean

### Saturday, May 18th11:00 am – 12:00 pm ET

By Veronica Hupper, University of New Hampshire

### Information

There are several papers declaring that the use of simulations to demonstrate the use of probability distributions in statistics courses is superior to traditional approaches of presenting material. However, very few of these papers provide actual statistical evidence to support this claim. In most cases, anecdotal and testimonial support is provided. Although it has become common that instructors use simulation to demonstrate the idea of sampling distributions and the Central Limit Theorem, “few instructors explore just what students actually learn from these activities” (Garfield & Gal, 1999). Simulations provide an attractive alternative to mathematical methods and probability for demonstrating the central limit theorem because “they are ‘mathematical experiments’ that can be performed and understood by most students regardless of their mathematical ability” (Blume & Royall, 2003), making these methods particularly appealing to students with little mathematical background such as those who would be studying introductory statistics as a discovery or quantitative reasoning course.

In the GAISE report (Guidelines for Assessment and Instruction in Statistics Education) published in 2007 by the American Statistical Association, it is recommended that students not only recognize that variability is essential to the study of statistics and that they experience this first-hand, but also that students take “into consideration randomness and distribution, patterns and deviations, mathematical models for patterns, and model –data dialogue” (Gabrosek et. al., 2008). Although some have come to think that teaching the Central Limit Theorem and the sampling distribution of the mean is obsolete, another key element of the GAISE report is the importance of understanding the concept of sampling distributions in relation to statistical inference (Gabrosek, et. al., 2008). In addition, students in introductory statistics courses who do not have a strong mathematics background and are not mathematics, statistics, or engineering majors, tend to grasp concepts such as statistical inference better if they are presented with a hands-on approach to support the ideas presented such as would be included in a simulation exercise.

Although the literature supports the use of simulations and computer assisted instruction (CAI) in general, few studies have specifically investigated the effectiveness of these in teaching statistics at an introductory level (Basturk, 2005). In addition, little of the research that has been done in the area involves students at a college (post-secondary) level (Garfield & Ben-Zvi, 2007).

This poster presentation outlines a study being done in the University of New Hampshire’s course “Statistical Discovery for Everyone.” This course is designed to give a broad overview of the main topics in probability and statistics for non-majors. All student participants will take both a pretest prior to covering material relating to the central limit theorem and the sampling distribution of the mean and an identical posttest after completion of one of two activities - a homework assignment on the topics consistent with the type of homework they have done over the course of the semester and a simulation exercise using Jmp. The pretest/posttest contains 5 concepts questions of varying types with each question being followed by a ranking of how confident the student feels in their response.  This is intended to determine if there is not only a significant gain in knowledge in students who did the simulation activity, but also to determine if students who worked on the simulation had a more significant increase in their confidence to apply what they had learned.

Since only one section of this course runs each semester, students from the same class will be randomly assigned to either the control group (doing the homework exercises) or the experimental group (doing the simulation exercise) using a random number generator. Both graphical and inferential methods will be used to assess whether students demonstrate a significantly greater gain in knowledge and confidence after completing the simulation exercise as compared to when a more traditional homework assignment is completed.

Conference participants will be provided a view of the research process including the research questions, the student learning objectives, and the research objectives and how they are interrelated. Samples of the pretest/posttest questions will be on display along with the relevant scoring rubrics which are modeled on rubrics typically used for course level assessment. A map of how these questions directly relate to the student learning outcomes, the research questions, and the research objectives will also be presented. This will essentially outline the process used to establish the methodology for this project and that can be applied to similar research. In addition, a summary of how this simulation exercise was created and the important components of any simulation activity will be presented. Sample materials such as the pretest/posttest, scoring rubrics, and the simulation exercise for the CLT and sampling distribution of the mean will be made available via email to anyone who is interested.