1. Feb. 2 Statistic for the day: Assignment: Exercise #1, p. 63; Exercise #11, p. 124; Exercise #4, p. 136 These slides were created by Tom Hettmansperger and in some cases modified by David Hunter Percent of the time, since 1887, that Punxsutawney Phil has correctly predicted the length of winter: 39 Source: http://www.stormfax.com/ghogday.htm

2. Research question: Does a chemical QS when added to sun tan lotion enhance tanning when mixed with Coppertone? Response: Tanning index Explanatory Variable: QS or not. What sort of study? Randomized Experiment? Observational Study? Randomized Experiment.

3. W/O QS QS 8.08.8 8.39.3 8.49.1 8.79.6 9.210.0 9.310.4 9.710.6 10.811.6 10.911.7 11.012.0

4. There is a lot of overlap between the boxplots. This suggests that there is NOT a significant difference between QS and W/O QS.

5. The problem: Too much variability within the two groups due to variation in tanning ability. We need to eliminate some of the within variability. Then we may be able to detect the difference across the two groups.

6. The answer is to let each subject be his/her own control. RANDOMLY assign QS or not to left or right side of the body. The experimental design is called PAIRED DATA DESIGN. Tan for 3 hours. Measure the tanning index. Record the difference between QS and W/O QS

7. QS – W/O QS 0.8 1.0 0.7 0.9 0.8 0.9 0.9 0.8 0.8 1.0 Notice that the treatments are only compared within a subject.

8. Boxplot of 10 differences within subjects. Note that the entire data set is above 0. This means QS had higher index than W/O QS for all subjects.

9. W/O Quaker State Quaker State 8.08.8 8.39.3 8.49.1 8.79.6 9.210.0 9.310.4 9.710.6 10.811.6 10.911.7 11.012.0 QS – W/O QS 0.8 1.0 0.7 0.9 0.8 0.9 0.9 0.8 0.8 1.0

10. Unpaired Paired

11. Research question: How prevalent is cheating at PSU? Imagine the following study: Individual students taking an exam in a particular course are filmed and observed closely by a team of extra observers, who then record the number of instances of cheating they observe. Any problems with this? Hawthorne Effect!

12. What sort of a study could be used to answer this? Observational Study? Randomized Experiment? Observational Study If we cannot establish cause and effect, can we establish an association between cell phones and cancer? Research question: Do cell phones cause cancer?

13. Observational Study: Response Variable: whether or not a subject gets cancer. Explanatory Variable: whether or not the subject uses a cell phone. Randomly select people who use cell phones and record the % who get cancer. Randomly select people who never use cell phones and record the % who get cancer. This may require a very long time.

14. A special kind of observational study: SWITCH RESPONSE AND EXPLANATORY VARIABLES Response Variable: whether a subject uses a cell phone or not Explanatory Variable: whether a subject has cancer or not. 1.Select a sample of cancer patients (Cancer Case) 2.Develop a group of people who match the cancer patients but do not have cancer. (Control) 3.Compute the % who use cell phones in each group. Called a Case-Control Study

15. Also Called: Retrospective Case-Control Study Retrospective because we asked subjects if they have been using cell phones in the past. Note that since we only look for an association it does not matter which variable is the response and which is the explanatory. Suppose we take 100 cancer patients and then take 200 non-cancer patients in the same hospital as controls.

16. Yes Cell Phone NoCellPhone Cancer30------------30%ME=10%70-----------70%ME=10%100 NoCancer50------------25%ME=7%150-----------75%ME=7%200 Data:

17. Plot with Margins of Error We would probably conclude that there is little or no association between using cell phones and cancer.

18. Research question: How does putting a smiley face on the bill influence a waitperson’s tip? Interacting variable: Sex of waitperson Interacting variable: Sex of waitperson Female waitress: Drawing a smiley face increased tip significantly Female waitress: Drawing a smiley face increased tip significantly Male waiter: Drawing a smiley face decreased tip, though not significantly Male waiter: Drawing a smiley face decreased tip, though not significantly Source: Journ. Appl. Soc. Psych, 1996

19. Interaction plot: Smiley-face experiment