1. Stat 512 Day 4: Quantitative Data

2. Last Time p-values and statistical significance  What p-values tell us (and do not tell us) For now, approximating the p-value through simulating the randomization process  How small p-values provide evidence that the difference we observed did not occur “just by chance” (randomization) Assume there is no treatment effect…  If a randomized experiment, then can also draw cause and effect conclusions

4. Practice Problem In (a), “controlling variables”  Specify the explanatory variable In (d), if no association…  If no relationship, same “success proportion” in each group  Not 1/2 since not equal group sizes (“significant”)  No inference here Role of randomization test  Don’t have to have equal sample sizes In (f), Causal vs. relationship Don’t panic, sorry for my biased comments

5. Statistical Methods Design: Planning and carrying out research studies  Observational units, Number and types of variables Descriptive: Summarizing and exploration data Inference: Making predictions or generalizing about phenomena represented by data What conclusions can we draw based on each of these three steps?

6. Repeat the Process – Quantitative Data Consider data collection issues Consider appropriate numerical and graphical summaries  Several measures, what does each tell you?  How do we get Minitab to do all the work? Simulation of p-values to determine statistical significance  Interpretation of p-values

7. Example 1: Cloud Seeding “A Bayesian analysis of a multiplicative treatment effect in weather modification”  Simpson, Alsen, Eden  Technometrics, 17, 161-166 (1975)

8. Example 1 (a) Type of study, observational units? Experiment since randomly assigned the clouds (b) EV and RV seeding Cloudscompare rainfall no seeding randomized

9. Example 1 With a quantitative response variable, can compare the groups through parallel dotplots

10. What to look for Center Spread Shape Unusual observations

11. Numerical Summaries Five number summary Variable treatment Minimum Q1 Median Q3 Maximum rainfall seeded 4 79 222 445 2746 unseeded 1.0 23.7 44.2 183.3 1202.6

12. Numerical Summaries Five number summary Min, Q1, median, Q3,outliers

13. Mean vs. Median

14. Properties The University of North Carolina took a survey of the students who had graduated as geology majors. In 1998, the average annual salary of geology majors who graduated from UNC was more than $500,000. The next year it was less than $100,000.

15. Summary Comparing the distribution of a quantitative variable between two or more groups  Graphical summaries: (parallel) dotplots, boxplots, side by side stemplots Center, spread, shape (skewed?), outliers  Numerical summaries Center: mean, median (five-number summary)  Mean = average of all values (not “resistant”)  Median = “typical” value Outliers: 1.5IQR criterion

16. Old Faithful

17. Histograms

19. Geyser Eruptions  1978 Range = 95-42 = 53 minutes  2003 Range = 110-56 = 54 minutes Without outliers:  110-70 = 40 minutes 95 42 110 5670

20. Geyser Eruptions  1978 IQR = 81-58 = 23 minutes  2003 IQR = 98-87 = 11 minutes Without outliers IQR = 98-87 = 11 minutes

21. Standard Deviation Want to compare the distance of the observations from the mean  Deviation from mean: y i -  Absolute deviations  Squared deviations

22. Old Faithful  1978 SD = 13 minutes  2003 SD = 8.5 minutes Without outliers SD=6.9 (  SD is not resistant!)

23. Example 3 What do we mean by variability?

24. Notes on histograms Left-hand endpoint rule Choice of interval widths Also watch use of “even” in describing shape (flat vs. symmetric)

25. Notes on Using Minitab Worksheets vs. Projects Saving graph windows Stacked vs. unstacked data

26. To Do For Tuesday: PP 4 For Thursday: PP 5 and reading HW 3 by Friday  Heavy Minitab component  Favor Upcoming: Project proposal