By Megan Heyman (Rose-Hulman Institute of Technology)
Information
Statistical inference techniques like bootstrapping, randomization tests, and traditional named distributions that build the null (or sampling) distribution have underlying conditions. As students quickly learn, multiple techniques could be used to answer the same question. Students tend to ask, “What if you select a correct model but then conduct inference under an incorrect condition?” For example, consider a hypothesis test for a single population mean using the t-distribution. What if it is not reasonable to assume that the population distribution is normal, but instead, it is heavily skewed? Or, what if the population distribution is symmetrical but has heavy (or light) tails, relative to a normal distribution?
An R Shiny applet that allows students to explore questions like this, via simulation, can demonstrate the need for multiple statistical inference approaches. We provide an activity that helps students explore how inference conditions are related to long-run error rates and confidence interval length in the simple case of modeling one population mean. This activity helps reinforce underlying concepts and definitions that students may be struggling with. We use this activity asynchronously in our introductory statistics course, with several sections of ~25 students each, to help review before a summative assessment.