1. Stat 301 – Day 9 Fisher’s Exact Test Quantitative Variables

2. Recap In analyzing two-way tables, the p-value tells us whether the difference in the group proportions/relative risk could have happened by the random assignment process alone Simulated the random assignment process to see whether our observed result was extreme “Fisher’s Exact Test”: Use counting methods to determine the exact probability

3. Investigation 1.6.2 (p. 72) Only 6 of 21 minorities coached at third 24 nonminorities coached at third and 15 at first How set up two-way table? How define random variable?

4. Investigation 1.7.2 Two-way table successes Group A p-value = P(X < 6) If we let X represent the number of minorities at third, want to find P(X < 6) Hypergeometric with N = 60, M = 30, n = 21 = C(30,6)C(30,15) + … =.0146 C(60, 21) failures

5. Investigation 1.7.2 Two-way table successes Group A p-value = P(X < 6) If we let X represent the number of minorities at third, want to find P(X < 6) Hypergeometric with N = 60, M = 21, n = 30 = C(21,6)C(39,24) + … =.0146 C(60,30)

6. Quiz 6

7. Big Picture Comparing two groups on a categorical response variable  Appropriate graphical summary (seg bar graph)  Appropriate numerical summaries (conditional proportions, relative risk, odds ratio)  Is the difference statistically significant? Fisher’s Exact Test: How often get a difference at least this large by the random assignment process alone  Scope of conclusions Cause and effect? Generalize beyond those in study? Compare results Randomized?

8. Big Picture Do it all again! Compare groups on a quantitative response variable  Graphical summaries  Numerical summaries  Statistical significance  Scope of conclusions

9. Investigation 2.1.1 (p. 102) Match the histogram with the variable (“Probability and Statistics for Engineers and Scientists”) Most important – your justifications

10. Stat 301 data

11. The moral: Try to anticipate variable behavior/explain patterns and deviations from patterns

12. Investigation 2.1.2

13. Aside: History of Statistics and Agriculture  www.nass.usda.gov/About_NASS/History_of_Ag_Statistics/

14. Investigation 2.1.2 (a) Experiment or observational study? Imposed seeding/unseeded Experimental units? clouds (b) Explanatory and response variable?

15. Investigation 2.1.2 Center Spread Shape Unusual observations Always label!!!

16. Skip to Minitab detour (p. 110) Course Materials > ISCAM Data Page  Minitab: Chapter 2, Minitab Files, Cloud Seeding.mtw Instructions in text  R: Chapter 2, TXT files, Cloud Seeding.txt Handout Boxplots Dotplots Descriptive statistics

17. Graphical and numerical summaries Five number summary Median = (41.1+47.3)/2 = 44.2

18. Five number summary Unseeded Min=1.0 Q 1 = 24.4 median=44.2 Q 3 =163 Max=1202.6 Seeded Min=4.1 Q 1 =92.4 median=221.6 Q 3 =430 max=2745.6

19. Boxplots 936.4 IQR1.5IQR

20. Boxplots 164.6 442 23% of data lie above mean

21. For Wednesday Mini-project 1 proposal Finish Investigation 2.1.2 through part (n)  See online solutions, bring questions to class PP 2.1.1 (p. 113)  Combine parts (b) and (g) together  (c)-(f) in Blackboard as multiple choice Investigation 2.1.4 parts (a)-(d) (p. 119-120)