Stat 31, Section 1, Last Time

1. Stat 31, Section 1, Last Time • Producing Data • Observational Study • Experiment • How to Sample? • History of Presidential Polls • Random Sampling

2. Midterm I Coming up: Tuesday, Feb. 15 Material: HW Assignments 1 – 4 Extra Office Hours: Mon. Feb. 14, 8:30 – 12:00, 2:00 – 3:30 (Instead of Review Session) Bring Along: 1 8.5” x 11” sheet of paper with formulas

3. More about Sampling The “simple random sample” (recall “each equally likely”) can be expensive (e.g. nationwide political poll, collected by personal interview) So there are many cheaper variations: • Stratified Sampling • Multi Stage Sampling • See text • And there are others as well

4. Sampling for Experiments • Experiments (Recall I was Observational Studies, Now take similar look at II) Terminology: “treatments” are applied to “individuals” i.e. to “subjects” i.e. to “experimental units”

5. Sampling for Experiments A “treatment” is: a combination of “levels”, of explanatory variables (quantities), called “factors”. E.g. Medicine, Agriculture, …

6. Sampling for Experiments Agriculture Example: Study how plant growth depends on: fertilizer and water So plants = “experiment’l units”, i.e. “subjects” “Factors” are fertilizer and water, Each plant gets some “level” of each.

7. HW on Sampling Terminology HW: 3.9 3.11

8. Design of Experiments The “design” of an experiment is the assignment of levels and treatments to experimental units (just as “choice of sample” was critical for sampling, this is too. There is a huge literature on this, including current research)

9. Design of Experiments Key Design Issues: • Control Idea: Eliminate “lurking variable” effects, by comparing treatments on groups of similar experimental units.

10. Controlled Experiments Common Type: compare “treatment” with “placebo”, a “sham treatment” that controls for psychological effects (think you are better, so you are better…) Further Refinement: “Double Blind” experiment means neither patient, nor doctor knows is real or not Eliminates possible doctor bias

11. Design of Experiments 2. Randomization Useful method for choosing groups above (e.g. Treatment and Control) Recall: Different from “just choose some”, instead means “make each equally likely”

12. Design of Experiments 2. Randomization Big Plus: Eliminates biases, i.e. effects of “lurking variables” (same as random choice of samples, again pay price of added variability, but well worth it)

13. Design of Experiments • Replication Idea: Reduce chance variation by applying same treatment to several (even many?) experimental units. How many replications are needed? (depends on context: tradeoff between cost and reduction of variation) Will build tools to study (based on probability)

14. Design of Experiments Fancier Designs (there are many, some in text) • Blocks • Matched Pairs • Balanced Designs

15. Example of an Experiment (to tie above ideas together) Gastric Freezing: Treatment for stomach ulcers • Anesthetize patient • Put balloon in stomach • Fill with freezing coolant

16. Gastric Freezing Initial Experiment, 1958 24 patients, all cured Became popular, and better than surgery But there were some skeptics…. Was it a Placebo Effect??? I.e. was fact of “some type of treatment” enough for “cure”

17. Gastric Freezing Approach, 1963: • Controlled Experiment (some treated others not, shows who gets better with no treatment) • Randomize: Eliminates other sources of bias, i.e. lurking variables (randomly choose: treated or not)

18. Gastric Freezing • “Blind” Patient doesn’t know if treated (Got a balloon in stomach of not? Both groups got that, but only Treatment group got freezing coolant) (iv) “Double Blind”: Doctor doesn’t know if treated or not. (somebody else controls freezing coolant) Important: since doctor decides if “cured”

19. Gastric Freezing Results: Treatment Group: 82 Control Group: 78 Initially: Treatment Control No Symptoms: 29% 29% Improved: 47% 39% After 24 Months: Relapse: 45% 39%

20. Gastric Freezing Results: No strong effect of treatment over control is apparent. All placebo effect? Analysis: Will build tools to show: “Difference within natural variation, assuming there is no difference”

21. Gastric Freezing Historical Notes: • Famous case for eliminating “ineffective treatments” • Showed importance of double blind controlled experiments • That are commonly used today • Stomach ulcers currently very effectively treated with drugs

22. Class Experiment Pepsi Challenge Try “double blind approach” • Taste test Pepsi vs. Coke • Where “taster” doesn’t know which is which (“blind” part of experiment) • And same for “giver” (“double blind” part)

23. Pepsi Challenge Approach: Groups of 3 Each does each job once: • Pourer (put your name and others on slip) • Giver (again put names on slip, does all outside of room) • Taster (always outside room) • Giver: record results on their slip

24. Pepsi Challenge Ideas: • Create “double blind”, i.e. “no knowledge of doctor” by pourer filling cups in room, so that giver does not see • Avoid “color association” by randomizing • Pourer does not watch tasting (no telegraphing with big grin….) • After tasting: compare notes, check forms • Will report, and analyze results later