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Stat310               Fin


                          Hadley Wickham
Saturday, 24 April 2010
Thank you!

                     To those of you who bought your
                     textbooks from my amazon link.
     ...
1. Eat!
                 2. Final & help sessions
                 3. Finish off hypothesis testing
                 4. Ot...
Final



Saturday, 24 April 2010
Final
                     Take home. Two hours long.
                     Three (double-sided) pages of notes.
          ...
Common themes
                          Probability of an event.
                          Independence & conditioning.
  ...
Help sessions

                     Mon, Tue, Wed, Thurs, Fri, Sat, Sun?
                     Morning or afternoon?
      ...
Honour code

                     Remember to pledge your exam, and
                     note the time at which you starte...
Hypothesis testing



Saturday, 24 April 2010
Course grades

                     Assume I took a random sample of 20
                     students from each years, and...
Your turn

                     The average grade from 2009 was 85 and
                     the average grade from 2010 wa...
1. Write down Ho and Ha
                    (positions of defence and prosecution)
                 2. Figure out good tes...
Say is      Say is
                                      guilty    innocent

                                             ...
Your turn


                     Which type of error is more expensive/
                     more costly/worse in the crim...
Reject HO Accept HO


                                                Type II
                          HO false    Correc...
Rates
                     For a given test,
                     P(false conviction) = α = significance level
            ...
α↑ β↓
                          α↓ β↑
Saturday, 24 April 2010
Cut off
                     Choose cut-off based on rate of false
                     convictions.
                     ...
μx=80, μy=85



   90                                                                                                     ...
μx=80, μy=85




              10

               8

               6
 Difference




               4

               2

...
μx=80, μy=85




                10

                8
 |Difference|




                6

                4

           ...
μx=80, μy=85




           3.5

           3.0

           2.5
 z−score




           2.0

           1.5

           1....
μx=80, μy=85




           0.8


           0.6
 p−value




           0.4


           0.2


           0.0
           ...
μx=μy=80



                                              x                                                               ...
μx=μy=80




               5
 difference




               0



              −5




                          20   40  ...
μx=μy=80




           3.0

           2.5

           2.0
 z−score




           1.5

           1.0

           0.5

 ...
μx=μy=80




                8


                6
 |difference|




                4


                2


             ...
μx=μy=80




           0.8


           0.6
 p−value




           0.4


           0.2


           0.0
               ...
Your turn

                     The average grade from 2009 was 85 and
                     the average grade from 2010 wa...
Connection to
                          confidence intervals
                     If you construct a 90% confidence
        ...
Statistics



Saturday, 24 April 2010
Majoring
                     3 required stat classes (Stat310, Stat405, Stat410)
                     + 6 stat electives
...
Minoring
                     From next year
                     Three required:
                     Track A: stat310, s...
Stat410

                     Introduction to linear models
                     Powerful and general statistical tool.
  ...
Stat405

                     Project based introduction to data
                     analysis. Lots of computing and hard...
Electives
                     SOCI 436 (Houston area survey), 313
                     (demography)
                     ...
Feedback

                     One form for me.
                     One form Xin Zhao, who most of you
                  ...
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  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
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