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PANEL: Rethinking the First Statistics Course for Math Majors

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.

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PANEL: Rethinking the First Statistics Course for Math Majors

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

  2. 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

  3. 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

  4. 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

  5. Example 1: Friendly Observers • Psychology experiment • Butler and Baumeister (1998) studied the effect of observer with vested interest on skilled performance • How often would such an extreme experimental difference occur by chance, if there was no vested interest effect?

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

  7. 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

  8. Example 2: Sleep Deprivation • Physiology Experiment • Stickgold, James, and Hobson (2000) studied the long-term effects of sleep deprivation on a visual discrimination task (3 days later!) sleep condition n Mean StDev Median IQR deprived 11 3.90 12.17 4.50 20.7 unrestricted 10 19.82 14.73 16.55 19.53 • How often would such an extreme experimental difference occur by chance, if there was no sleep deprivation effect?

  9. 15.92 Example 2: Sleep Deprivation • Students investigate this question through • Hands-on simulation (index cards) • Computer simulation (Minitab) • Mathematical model p-value=.0072 p-value .002

  10. 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

  11. 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

  12. 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?

  13. 1.48 Example 3: Sleepless Drivers • Students investigate this question through • Computer simulation (Minitab) • Empirical sampling distribution of odds-ratio • Empirical p-value • Approximate mathematical model

  14. 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

  15. 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

  16. Reference • Investigating Statistical Concepts, Applications, and Methods Preliminary Edition Duxbury Press www.rossmanchance.com/iscam/ • Slides at www.rossmanchance.com/jsm04/ • arossman@calpoly.edu, bchance@calpoly.edu

  17. 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

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