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### 25 fin

1. 1. Stat310 Fin Hadley Wickham Saturday, 24 April 2010
2. 2. Thank you! To those of you who bought your textbooks from my amazon link. To the textbook publishers who generously sent me free copies of books. To Kensey for suggesting chik-ﬁl-a Saturday, 24 April 2010
3. 3. 1. Eat! 2. Final & help sessions 3. Finish off hypothesis testing 4. Other statistics opportunities 5. Feedback (TA & me) Saturday, 24 April 2010
4. 4. Final Saturday, 24 April 2010
5. 5. Final Take home. Two hours long. Three (double-sided) pages of notes. Available Wednesday April 28 9am. Due Wednesday May 5, 5pm, under my door. Ten small questions of approximately equal weight. Similar to questions from the homework/book. Saturday, 24 April 2010
6. 6. Common themes Probability of an event. Independence & conditioning. Distributions: pdf/pmf, cdf, mgf, named. Transformations. Sampling distribution of mean and variance. Estimation and testing. Philosophy of grading Saturday, 24 April 2010
7. 7. Help sessions Mon, Tue, Wed, Thurs, Fri, Sat, Sun? Morning or afternoon? One-on-one help, plus brief revision of topics of particular interest. Suggest and vote at http://goo.gl/mod/joIx Saturday, 24 April 2010
8. 8. Honour code Remember to pledge your exam, and note the time at which you started and ended. You may refer only to your note sheets, not to the text book or old homeworks etc. Saturday, 24 April 2010
9. 9. Hypothesis testing Saturday, 24 April 2010
10. 10. Course grades Assume I took a random sample of 20 students from each years, and that course grades are normally distributed by variance 80. What is the distribution of difference of the two group means? Saturday, 24 April 2010
11. 11. Your turn The average grade from 2009 was 85 and the average grade from 2010 was 90. What is the p-value? (The probability that you’d see a difference this large or large if there really was no difference in the population means) Saturday, 24 April 2010
12. 12. 1. Write down Ho and Ha (positions of defence and prosecution) 2. Figure out good test statistic (what numeric summary?) 3. Work out null distribution (distribution of innocents) 4. Calculate p-value by comparing actual value to null distribution (what proportion of true innocents look more guilty than the suspect) 5. Reject Ho if p-value smaller than cutoff Saturday, 24 April 2010
13. 13. Say is Say is guilty innocent False Is guilty Correct acquittal False Is innocent Correct conviction Saturday, 24 April 2010
14. 14. Your turn Which type of error is more expensive/ more costly/worse in the criminal justice system? Saturday, 24 April 2010
15. 15. Reject HO Accept HO Type II HO false Correct error Type I HO true Correct error Saturday, 24 April 2010
16. 16. Rates For a given test, P(false conviction) = α = signiﬁcance level P(false acquittal) = 1 - β β = power What do think happens to β if you try to make α smaller? Saturday, 24 April 2010
17. 17. α↑ β↓ α↓ β↑ Saturday, 24 April 2010
18. 18. Cut off Choose cut-off based on rate of false convictions. If you want a 5% rate of false convictions, reject Ho if the p-value is less than 0.05. (This is the industry standard rate) Can work out power. Saturday, 24 April 2010
19. 19. μx=80, μy=85 90 y y y y 88 y y yy y y y y y y y y y y y y y y y yy y 86 y y y y y x y y y y y y y y y y y y y yy y y y y y y y y y y y yy y y y y 84 y y x y y y yxx yy y y y y y x y x y y x y y x yy xy x yx y y x x x yx x x yyx x yy 82 y x x x y x xx x y y y x x y x x x x x x y x x 80 x x x x x x x x x x xx xxx x x x x x x x xxxx x xx x y x x x x x x x x x x x x x x x xx x x xx x 78 x x x xx x x x x x 76 x x 20 40 60 80 100 Saturday, 24 April 2010
20. 20. μx=80, μy=85 10 8 6 Difference 4 2 0 −2 20 40 60 80 100 Saturday, 24 April 2010
21. 21. μx=80, μy=85 10 8 |Difference| 6 4 2 0 20 40 60 80 100 Saturday, 24 April 2010
22. 22. μx=80, μy=85 3.5 3.0 2.5 z−score 2.0 1.5 1.0 0.5 0.0 20 40 60 80 100 Saturday, 24 April 2010
23. 23. μx=80, μy=85 0.8 0.6 p−value 0.4 0.2 0.0 20 40 60 80 100 Correctly reject null 39% of the time Saturday, 24 April 2010
24. 24. μx=μy=80 x x 84 y x y x x y y x x x x y y y y x y x xy xy y x x y y 82 y yy y y y x yxx x y y x y y y y xx x y x y x y y y x x y y y x y x y yy y x x x y y x yx y x y y x yy y x 80 x y y xx x yy y y yxxx x x y y x yy x x y x x x yx y y x yy y xx x x y y xy x xxxyy xy x x x y x x y xxy x x x yy y y y x x y x x 78 x x x y y xx y x x y y x x y y y y x y y y xx x y x xx x x y y x 76 y x y y x x 20 40 60 80 100 Saturday, 24 April 2010
25. 25. μx=μy=80 5 difference 0 −5 20 40 60 80 100 Saturday, 24 April 2010
26. 26. μx=μy=80 3.0 2.5 2.0 z−score 1.5 1.0 0.5 0.0 20 40 60 80 100 Saturday, 24 April 2010
27. 27. μx=μy=80 8 6 |difference| 4 2 0 20 40 60 80 100 Saturday, 24 April 2010
28. 28. μx=μy=80 0.8 0.6 p−value 0.4 0.2 0.0 20 40 60 80 100 Incorrectly reject null 6% of the time Saturday, 24 April 2010
29. 29. Your turn The average grade from 2009 was 85 and the average grade from 2010 was 90. Would you reject the null hypothesis that the average grade was the same? Saturday, 24 April 2010
30. 30. Connection to conﬁdence intervals If you construct a 90% conﬁdence interval, and it doesn’t include the parameter until the null, then the p-value must be > 1 - 0.9 = 0.1. If the p-value is 0.08, then a 92% or greater conﬁdence interval would include the null parameter, and a smaller conﬁdence interval would not. Saturday, 24 April 2010
31. 31. Statistics Saturday, 24 April 2010
32. 32. Majoring 3 required stat classes (Stat310, Stat405, Stat410) + 6 stat electives + calc, linear algebra, computing + design project Makes for a great double major. Particularly useful if you’re thinking about grad school. (Appealing to employers too) http://statistics.rice.edu/ShowInterior.aspx?id=58 Saturday, 24 April 2010
33. 33. Minoring From next year Three required: Track A: stat310, stat405, stat400/410 Track B: stat100, stat280, stat385 Three elective: 300 level+, one outside stat if it has strong statistical component Saturday, 24 April 2010
34. 34. Stat410 Introduction to linear models Powerful and general statistical tool. Theory and data. Offered in Fall. Saturday, 24 April 2010
35. 35. Stat405 Project based introduction to data analysis. Lots of computing and hardly any maths. http://had.co.nz/stat405 Offered in Fall, and next year in Spring. Saturday, 24 April 2010
36. 36. Electives SOCI 436 (Houston area survey), 313 (demography) ECON 340/440 (game theory), 400 (econometrics), 475 (optimisation), 477 (math of economics), 479 (modelling) STAT 385, 431 (more theory), 420 (process control), 421 (time series), 422 (Bayesian data analysis), 423 (bioinformatics), 453 (biostatistics), 485 (environmental) Saturday, 24 April 2010
37. 37. Feedback One form for me. One form Xin Zhao, who most of you never met but was the TA in charge of your grading. No form for Garrett. Saturday, 24 April 2010