Teaching Statistical Concepts with Simulated Data

1. Teaching Statistical Concepts with Simulated Data Andrej Blejec National Institute of Biology andUniversity of Ljubljana Ljubljana, Slovenia andrej.blejec@nib.si

2. Kinds of data • real life data • invented data • simulated data Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

3. Real life data • interesting for students • need subject matter knowledge to interpret statistical results • oversimplified problems • complex problems • unclear relevance of statistical results Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

4. Invented data • a collection of data, no story • useful mostly for calculation drill • no possible interpretation of results • uninteresting for students Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

5. Simulated data • sampled from known distribution • composed according to prespecified modele.g. Y = a + b * X + e, with known distribution of X and e • known statistical propertiese.g. mean, variance, regression coefficient • analysis results can be compared to true values Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

6. Goals of teaching statistics • interest for statistics • understanding of statistical methods • skills in use of statistics • experiences in analyzing data • other ( insert your own :) ___________ Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

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8. Sun Absorption spectrum Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

9. Hydrogen Sun Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

10. Hydrogen Sun Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

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22. Least squares estimate of the mean

23. Mean squared deviations Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

24. Mean squared deviations Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

25. Mean squared deviations Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

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47. Mean squared deviations Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

48. True mean value μ LS estimate Mean squared deviations Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011

49. Maximum likelihood estimation of the mean

50. Workshop in Methodology of Teaching Statistics / Novi Sad, December 13, 2011