By Xiaochen Xian (Georgia Tech)
Information
This poster will showcase a series of low-cost, high-impact, in-class demonstrations and analogies designed to teach core statistical concepts to a diverse cohort of graduate engineering students. The primary method is "active learning through relatable application," where each complex topic is introduced not only with its equation, but with a tangible, real-world problem that the students implicitly understand. Each chapter of this course is associated with one relatable example according to the students' background. Here are a few examples of the series of demonstrations: (i) Random Variables (The "Mechanical Engineering" Example): To introduce discrete and continuous random variables, an experiment of Galton boards is used to mimic steel bearings moving on a conveyor, linking discrete and continuous distributions as well as their distribution functions. (ii) Normal Distributions (The "Nuclear" Example): To explore the complex relationship between two variables, we use an interactive online applet that visualizes a bivariate normal distribution. Students can manipulate the correlation coefficient in real-time, watching the 3D bell curve transform from a slender ridge to a squat, round mound to another slender ridge in the opposite direction. This provides an immediate, intuitive grasp of covariance and dependence before any matrix algebra is introduced. (iii) Statistical Estimation (The "Business" Example): The core challenge of inferential statistics estimating a population parameter from a sample is introduced with a literal "black box." A box containing an unknown number of colored balls is shown to the class. Students draw from the box, compile the samples to create a sampling distribution, and estimate the true proportion inside the box. The other five examples will be shown in the poster. These demonstrations are integrated throughout each chapter from the introduction to homework exercises and was implemented at Georgia Tech, School of Industrial and Systems Engineering in the "Statistical Methods and Applications" core graduate-level service course for potentially all master's and PhD students in the university. Thus, the students are a highly diverse cohort of 30-40 students per semester. Not all of them have a formal statistics background. Surveys and reflection statements in assignments were used to capture informal feedback.