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Inference after ANOVA, Multiple Comparisons 3/21/12

Inference after ANOVA, Multiple Comparisons 3/21/12. Inference after ANOVA The problem of multiple comparisons Bonferroni’s Correction. Section 8.2. Professor Kari Lock Morgan Duke University. Midterm Evaluation. Clicker: overwhelmingly positive Textbook: positive

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Inference after ANOVA, Multiple Comparisons 3/21/12

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  1. Inference after ANOVA, Multiple Comparisons • 3/21/12 • Inference after ANOVA • The problem of multiple comparisons • Bonferroni’s Correction • Section 8.2 • Professor Kari Lock Morgan • Duke University

  2. Midterm Evaluation • Clicker: overwhelmingly positive • Textbook: positive • Homework: surprisingly positive • Lecture: mostly positive, some complaints • most common complaint: too fast • not always open to questions • full lecture slides not posted in advance • Lab: less positive, varied complaints • TA too busy, TA not helpful • can do at home • too long

  3. Midterm Evaluation

  4. To Do • Project 1 (due TOMORROW, 5pm) • Homework 7 (due Monday, 3/26) • NO LATE HOMEWORK ACCEPTED! • Turn in by Friday, 3/23, 5pm to get it graded before Exam 2. • Start preparing for Exam 2 (next Wednesday and Thursday)

  5. Project 1 Comments • Conclusion: What have you learned? Make sure to answer the research question posed in your introduction. • This is a paper, there should be text. Do not just give R output, formulas, and numbers.

  6. Exam 2 • Exam 2: • In-class portion: Wednesday, 3/28 • Lab portion: Thursday, 3/29 • In-class portion: (75%) • Open only to a calculator and two double sided pages of notes prepared by you • Lab portion: (25%) • Open to everything except communication of any form with other humans

  7. Exam 2 • The emphasis will be on material we have learned since the first exam, although you are still responsible for everything we learned prior to the first exam

  8. Practice • On the course website, under documents: • Last semester’s in-class exam, and solutions • Last semester’s labs exam, and solutions • Full solutions to all essential synthesis problems from Unit 3 • Full solutions to all review problems from Unit 3 • Full solutions to all odd problems from Chapters 7 and 8 • Doing problems is the key to success!!!

  9. Keys to In-Class Exam Success • Work lots of practice problems! • Take last year’s exams under realistic conditions (time yourself, do it all before looking at the solutions, etc.) • Prepare a good cheat sheet and use it when working problems • Read the corresponding sections in the book if there are concepts you are still confused about

  10. Keys to Lab Exam Success • Primarily, make sure you know how to summarize, visualize, create an interval, and conduct a test for any one variable or relationship between two variables • For practice, try doing both intervals and tests for any one or two variables in our class survey • Beyond that, make sure you are comfortable with the content from the labs • Open-book does NOT mean you don’t have to study. You will not have time to look up every command you need during the exam.

  11. Office Hours before Exam • You have LOTS of opportunities for help! • Today, 3 – 5pm (Prof Morgan) • Today, 6 – 8 pm (Michael) • Friday, 1:30 – 3 pm (Prof Morgan) • Sunday, 5 – 7 pm (Jessica) • Sunday, 7 – 9 pm (Michael) • Monday, 3 – 4 pm (Prof Morgan) • Monday, 4 – 6 pm (Christine) • Tuesday, 3 – 6 pm (Prof Morgan) • Tuesday, 6 – 8 pm (Yue)

  12. Cuckoo Birds • Cuckoo birds lay their eggs in the nests of other birds (typically small birds). • When the cuckoo baby hatches, it kicks out all the original eggs/babies • If the cuckoo is lucky, the mother will raise the cuckoo as if it were her own • Do cuckoo birds found in nests of different species differ? http://opinionator.blogs.nytimes.com/2010/06/01/cuckoo-cuckoo/

  13. Length of Cuckoo Eggs

  14. Length of Cuckoo Eggs Is there a significant difference between the groups? Yes No

  15. ANOVA Table • Equal variability • Normal(ish) data We have very strong evidence that average length of cuckoo eggs differs for nests of different species

  16. Cuckoo Birds • How long are cuckoo bird eggs found in robins’ nests? • Is there a significant difference between the average length of eggs found in robins’ nests and the average length of eggs found in sparrows’ nests? • While we could proceed with formulas from Chapter 6 or simulation methods from Chapters 3 and 4, there are special ways of doing inference after ANOVA…

  17. Inferences after ANOVA • If the ANOVA assumption of equal variability across groups is satisfied, we can use the data from all groups to estimate variability:

  18. Cuckoo Birds • How long are cuckoo bird eggs found in robins’ nests? Give a 90% confidence interval. • Is there a significant difference between the average length of eggs found in robins’ nests and the average length of eggs found in sparrows’ nests? • Yes • No (22.19, 22.97)

  19. Cuckoo Birds • How long are cuckoo bird eggs found in robins’ nests? Give a 90% confidence interval. t* We are 90% confident that the average length of Cuckoo eggs found in Robins’ nests is between 22.19 and 22.97 mm.

  20. Cuckoo Birds • Is there a significant difference between the average length of eggs found in robins’ nests and the average length of eggs found in sparrows’ nests? This study does not provide evidence for a difference in average mean length of Cuckoo eggs between those found in Robins and Sparrows nests.

  21. Pairwise Comparisons • Pairwise comparisons test for a difference in means between each pair of groups • Only do pairwise comparisons if the overall ANOVA is significant • If there are lots of categories, the number of possible pairwise comparisons grows quickly • Automate the process with RStudio

  22. Cuckoo Birds

  23. Length of Cuckoo Eggs

  24. Extrasensory Perception • Is there such a thing as extrasensory perception (ESP), or a “sixth sense”? • Do you believe in ESP or a sixth sense? • (a) Yes • (b) No • (c) Not sure

  25. Extrasensory Perception

  26. Extrasensory Perception • How would you test whether American belief in ESP differs between current Duke students who take STAT 101 and all Americans in 2001? • z-test • t-test • Chi-square test • ANOVA

  27. Extrasensory Perception • Based on the available data, how would you test whether belief in ESP differs between 1990 and 2001? • z-test • t-test • Chi-square test • ANOVA

  28. Summary • When performing inference after ANOVA, use √MSE as an estimate for standard deviation within groups, and use n – k as the degrees of freedom for the t-distribution

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