|
Abstract:
|
This presentation describes a simulation-based approach to an applied statistics course, intended to build intuition for what happens when assumptions are not true. As they learn R, students first investigate how well the Central Limit Theorem works for various population distributions, sample sizes, and population sizes. We simulate distributions of p-values - not only rejection rates - from t-tests after breaking each of the assumptions. We use the same technique to show when non-parametric alternatives are most useful. By simulation, we highlight the difference between power and validity and explore the relative power of parametric and non-parametric tests. Later, we simulate interval coverage to understand the robustness of regression to its assumptions. The goal is for students to gain the ability to run simulations to check robustness in future scenarios that they encounter. One group ran a simulation to test the robustness of an F-test to its assumptions upon realizing that assumptions weren't met for their final project data. Another group designed simulations to break combinations of multiple regression assumptions simultaneously.
|
