Chris Malone – Winona State University
One’s success in a course is often determined by his or her desire and motivation to learn. Unfortunately, desire and motivation are often lacking in an introductory statistics course. I have learned some tricks over my years of teaching to enhance motivation — leverage their existing knowledge whenever possible and require students to repeatedly consider the phrase “What would happen if … .”[pullquote]Modern technologies and the recent advances in the use of simulation-based methods in teaching introductory statistics have allowed students to easily consider a variety of “What would happen if …” scenarios. [/pullquote]
Consider the difficult topic of getting students to conceptualize the sampling distribution of a sample proportion. Modern technologies and the recent advances in the use of simulation-based methods in teaching introductory statistics have allowed students to easily consider a variety of “What would happen if …” scenarios. For example, students can quickly obtain a simulated sampling distribution under Ho: p = 0.50 and compare it against a simulated distribution under Ho: p = 0.90 to understand that the variation in these distributions depends on p. To be honest, I’ve come to accept that fact that very few of my introductory students will ever come to appreciate this as much as I do. Instead, their concern tends to be centered on their ability to get their p-value below 0.05 so they can achieve the desirable outcome of rejecting Ho. But in my opinion, these ‘What would happen if …” investigations do indeed invoke curiosity and in turn motivate students to learn statistics.
I should not advocate for the use of these “What would happen if …” investigations without communicating some of the adverse consequences. Consider again the investigation of the sampling distribution of a sample proportion under Ho. I find that students tend to gravitate toward the more natural situation of creating the sampling distribution using instead of generating the distribution under Ho. Obviously, in a testing situation the sampling distribution using is not considered as we evaluate evidence against the null hypothesis. However, generating the sampling distribution using is completely valid in other situations, such as obtaining an estimate of the margin-of-error. Generating a sampling distribution using (or under any highly-specified model) can be thought of as a parametric bootstrap approach which differs from the typical non-parametric approach of taking several repeated samples with replacement from your data.
Statistics is a discipline in a constant state of change. It is no wonder that instructors often feel overwhelmed when considering how to best to teach statistics. Instructors should carefully consider their motives in using the bootstrap or other simulation-based approaches in teaching introductory statistics. Our motives and goals in using the bootstrap are not often matched by the students. [pullquote]Instructors should carefully consider their motives in using the bootstrap or other simulation-based approaches in teaching introductory statistics. Our motives and goals in using the bootstrap are not often matched by the students.[/pullquote]From our perspective, the purpose of generating a sampling distribution under Ho (to obtain a p-value), is very different than the purpose of generating a sampling distribution using (to obtain an estimated for the margin-of-error). From a student’s perspective, the “What would happen if …” approach to teaching along with the bootstrap provides a way for him or her to freely explore distributions without some pre-determined motive. The bootstrap does not make teaching easier, students still need to understand that the p-value is to be computed under Ho and that the margin-of-error is computed when the sampling distribution is obtained using the observed statistic. The bootstrap does however require less in the way of formulas and theoretical assumptions which often needlessly complicate the teaching of introductory statistics.