PANEL: Rethinking the First Statistics Course for Math Majors Joint Statistical Meetings, 8/11/04 Allan Rossman Beth Chance Cal Poly – San Luis Obispo

Course/Program/Students Dickinson College: Two course sequence in prob and math stat, not required for math major but could count as elective, calc prereq  Developed new introductory course in data analysis for math majors UOP: One semester course for math and engineering majors, probability with applications to statistics, calc prereq  Changed textbook and focus of course

Course/Program/Students Cal Poly: Two course sequence (probability then statistics) for math, statistics, CS, and engineering majors (only first quarter required), calc prereq  Infusion of activities, data, and applications to statistics into both courses  New statistics course emphasizing the statistical process and introducing probability “just in time” New curricular materials, instructional technology Experimental courses for prospective math teachers, science majors

Why Metamorphosis? First course, not “math stat” course Need complete overhaul, not “tweaking”  Goals are fundamentally different  New course consistent with Ginger’s points Including successful features from “Stat 101”  Focus on process of statistical investigations Not separate pieces Students investigate entire process over and over in new situations

Example 1: Friendly Observers Psychology experiment  Butler and Baumeister (1998) studied the effect of observer with vested interest on skilled performance A: vested interest B: no vested interest Total Beat threshold 3811 Do not beat threshold 9413 Total12 24 How often would such an extreme experimental difference occur by chance, if there was no vested interest effect?

Example 1: Friendly Observers Students investigate this question through  Hands-on simulation (playing cards)  Computer simulation (Java applet)  Mathematical model counting techniques

Example 1: Friendly Observers Focus on statistical process  Data collection, descriptive statistics, inferential analysis Arising from genuine research study  Connection between the randomization in the design and the inference procedure used Scope of conclusions depends on study design  Cause/effect inference is valid Use of simulation motivates the derivation of the mathematical probability model  Investigate/answer real research questions in first two weeks

Example 2: Sleep Deprivation Physiology Experiment  Stickgold, James, and Hobson (2000) studied the long-term effects of sleep deprivation on a visual discrimination task sleep condition n Mean StDev Median IQR deprived unrestricted How often would such an extreme experimental difference occur by chance, if there was no sleep deprivation effect? (3 days later!)

Example 2: Sleep Deprivation Students investigate this question through  Hands-on simulation (index cards)  Computer simulation (Minitab)  Mathematical model p-value= p-value .002

Example 2: Sleep Deprivation Experience the entire statistical process again  Develop deeper understanding of key ideas (randomization, significance, p-value) Tools change, but reasoning remains same  Tools based on research study, question – not for their own sake Simulation as a problem solving tool  Empirical vs. exact p-values

Example 3: Sleepless Drivers Sociology case-control study  Connor et al (2002) investigated whether those in recent car accidents had been more sleep deprived than a control group of drivers No full night’s sleep in past week At least one full night’s sleep in past week Sample sizes “case” drivers (crash) “control” drivers (no crash)

Example 3: Sleepless Drivers Sample proportion that were in a car crash Sleep deprived:.581 Not sleep deprived:.484 Odds ratio: 1.48 How often would such an extreme observed odds ratio occur by chance, if there was no sleep deprivation effect?

Example 3: Sleepless Drivers Students investigate this question through  Computer simulation (Minitab) Empirical sampling distribution of odds-ratio Empirical p-value  Approximate mathematical model 1.48

Example 3: Sleepless Drivers SE(log-odds) = Confidence interval for population log odds:  sample log-odds + z* SE(log-odds)  Back-transformation 90% CI for odds ratio: 1.05 – 2.08

Example 3: Sleepless Drivers Students understand process through which they can investigate statistical ideas Students piece together powerful statistical tools learned throughout the course to derive new (to them) procedures  Concepts, applications, methods, theory

Reference Investigating Statistical Concepts, Applications, and Methods Preliminary Edition Duxbury Press Slides at

Table of Contents 1: Comparisons and Conclusions 2: Comparisons with Quantitative Variables 3: Sampling from Populations 4: Models and Sampling Distributions 5: Comparing Two Populations 6: Comparing Several Populations, Exploring Relationships