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Some Controversies of Statistics Education and Practice

Some Controversies of Statistics Education and Practice. Do we teach the right stuff? . Larry Weldon. Does it matter what we teach?. Just mental exercise? Content not so crucial? But modern statistics is a new subject Need new tools, concepts, culture . Overview of talk.

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Some Controversies of Statistics Education and Practice

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  1. Some Controversies of Statistics Education and Practice • Do we teach the right stuff? Larry Weldon

  2. Does it matter what we teach? • Just mental exercise? • Content not so crucial? • But modern statistics is a new subject • Need new tools, concepts, culture

  3. Overview of talk • The role of parametric inference • Is it declining in favor of data analysis? • The practice of statistics • Are we serving practitioners? • Problems of pedagogy • Do our students learn what we intend?

  4. Part I: Focus on Parametrics Is it still appropriate? More Parametric Modeling? Less Parametric Inference?

  5. Ex 1: A time series

  6. Something we should do? Teach more smoothing and time series at an early stage

  7. Ex 2: Modeling Variability

  8. Ex 3: Regression Setting: Approximation Model EG: Predict House Price ($,000) from Square Feet And Lot Size In South Delta, Price = -200 + 0.1*LTSZ + 0.1*SQFT In North Delta Price = -350 + 0.067*LTSZ + 0.067*SQFT

  9. Linear Model Useful?

  10. Why do we focus on parametric inference? Before Computers for Graphics and Simulation Need for Data Reduction Pre-computer: Intense Interest in “best” methods for estimating parameters …. e.g. unbiasedness criterion

  11. Ex 4. Unbiasedness • Being exactly right, on average! • Better to be a close often? • E.G. Estimation of 2 MMSE estimator?

  12. Normal Model

  13. Expo Model

  14. MMSE Estimator? • Does MSE really tell us what we want to know about our estimator of VARiance? • What is distribution of signed error of estimate of VAR?

  15. Typical Error or Whole Dist’n? • MSE measures typical error. • Distribution of error is more informative & easy to report. • Whole distributions often do not need parametric summary! Use Graph.

  16. Ex 6. Does Variance measure Variation? • E.g. Variance of Yield in Bushels Squared?

  17. Analysis of Variance: SST=SSR+SSE How does it compare with Analysis of SD ? Is R-squared a ratio of useful units? Is “64% of variance” as useful as “80% of SD”?

  18. Anova Table • DF Sum Sq Mean Sq F value Pr(>F) • block 5 343.29 68.66 4.4467 0.015939 * • N 1 189.28 189.28 12.2587 0.004372 ** • P 1 8.40 8.40 0.5441 0.474904 • K 1 95.20 95.20 6.1657 0.028795 * • N:P 1 21.28 21.28 1.3783 0.263165 • N:K 1 33.14 33.14 2.1460 0.168648 • P:K 1 0.48 0.48 0.0312 0.862752 • Residuals 12 185.29 15.44

  19. Variance? • Students need to know squared units are weird!

  20. Role of Simulation • Exploring intractable strategies • Exploring model estimates • Calibrating complex models to match outcome data One use of parametric models is to do simulations. But this is Different than “inference” as we usually teach it.

  21. Traffic Demo • Accordion Effect in heavy highway traffic • Thanks to Andrej Blejec for teaching me R

  22. Ex 7: Traffic Accordion • Simple Rule Adjust speed to allow 2.5 seconds gap (and add a little noise) Uses only simple models. Go to R …

  23. Use of Parametric Models For simulation! One reason why applied prob’y modeling is so useful.

  24. Part II: Needs of Stats Practice Students prepared for practice? Preparation for fast learning of applied stats?

  25. Target Students? Student populations in stats • 1000 in first course • 250 in second course • 100 in third course • 50 in fourth course Most students take only 1-2 courses!What goals for the 1000 + 250? = 90% What goals for the 100 + 50? = 10%

  26. Quote from Cleveland(1993) A very limited view of statistics is that it is practiced by statisticians. … The wide view has far greater promise of a widespread influence of the intellectual content of the field of data science.

  27. Service vs Mainstream • Service = anyone more interested in applications than developing new techniques (90 %?) • Mainstream = enabling development of new techniques (10 %?) • Various Levels for each ….

  28. First Year Course Either • “stat appreciation” (service) or • “stat strategies” (mainstream)

  29. Second Year Course Either (Service) • How to read data-based research papers Or (Mainstream) • Regression, Data Analysis, and some Experiment Design

  30. Third Year Course • Mainstream and Service • Design of Experiments • Probability Models and Parametric Inference • Sampling Surveys • Software Options • Multivariate

  31. Fourth Year Course Mainstream only: • Linear Models • Bayesian Methods & inference options • Math-Stat • Advanced Graphical Methods

  32. Changes? • The courses we have do allow these things • Most radical suggestions are at lower division • Some minor (?) suggestions for LD and UD …

  33. Gripe 1: Decision Making vs Statistical Significance • Significance = (In-)Credibility of NullNot really decision-making machineryyet “Type I and Type II errors” suggests decisions are being made. • Decision making requires Loss Fcn Priors

  34. Gripe 2: Data: By Design or Serendipity? Purpose of Analysis = Purpose of Data Collection? e.g. Designed Expts, Some Observational Studies Purpose of Analysis ≠ Purpose of Data Collection e.g. Serendipity -> Data Mining Inference Sample->Population ?

  35. Gripe 3: Role of Graphics • Preliminary Data Analysis and Screening • Model Analysis • Model Testing (via Residual Plot) • Model Fit Result (Data + Fit) (Graph enhances other methods) • What if no model? • As in non-par smooth fit • As in simulation relationship(Graph is only way to show result)Enhanced Role of Graph as Result Report

  36. Gripe 4: SPC • Our STAT 340/440 used to teach some ideas that are basic stats • Management by exception &response costs • Incremental improvement (QC, EVOP ideas) • Alternative variability measures • Role of industrial experiments (robust design)

  37. Part III: Pedagogy • Logical Sequence vs Case Studies • Logical 1 var, 2 var, 3 var, … • 0-1 data, categorical, ordinal, interval, … • Case study approach • Spatial patterns, time series variability, smoothing, biological diversity, …

  38. Tests and Exams • Determines what students learn • What do we want students to learn? • How and What? or Why and When?Do we ask students to • Explain to a Prof & TA, or to a Peer or Lay? • Hand Calculation or Software Output interpretation? • Memorize (Closed Book) or Understand (Open Book)?

  39. Common Sense • How does it fit with stat culture? • Stat as the tool of Inference Police. • Never assume something is simple • Never jump to conclusions • Never assume naive thinking will help • Are students afraid to use their own “common sense”? • Maybe Stat as Discovery Tools

  40. Changes? • More conceptual approach? • More simulation? • More graphics? • More admission of parametric limitations? • More options for inference? • More creativity? • More data analysis? • More time series, and decision tools?

  41. What Less? • Math-Stat, optimization, lin. models • Parametric Inference (but more modeling) • Least Squares • Unbiasedness • Hand reproduction of stat package results (even at lower division)

  42. Summary • More context-specific data analysis • Less focus on parametric inference • Better use of simulation and graphics

  43. “The question I wish to raise is whether the 21st century statistics discipline should be equated so strongly to the traditional core topics and activities as they are now. Personally I prefer a more inclusive interpretation of statistics that reflects its strong interdisciplinary character.” Kettenring (1997) Former ASA President

  44. Thank you for listening!Your Comments Please!

  45. Normal Model

  46. Expo Model

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