1. Stat 217 – Day 6 Two-way Tables (Topic 6) Preliminary Questions 1-3 Calculators!

2. Last Time (Wrap Up p. 84) An experiment deliberately imposes the explanatory variable on the subjects, rather than passively observing and recording information A randomized comparative experiment can establish a cause-and-effect relationship between two variables by guarding against confounding  Should be no other systematic differences between the groups Random assignment vs. random sampling

3. Activity 5-5 (p. 80) (a) An experiment? This study is experimental because the experimenter actively imposed the explanatory variable (the sequence of letters) on the subjects.  Identify what was controlled/imposed (context)  Therefore can draw cause-and-effect (b) EV/RV? EV = which sequence (categorical) RV = number of letters memorized (quantitative)  Don’t confuse with research question JFK-CIA-FBI-USA-SAT-GPA-GRE-IBM-NBA-CPR JFKC-IAF-BIU-SASA-TGP-AGR-EIB-MN-BAC-PR

4. Activity 5-5 (p. 80) (c) How and Why random assignment? Random assignment was implemented by randomly distributing the sheets without choose who received which number sequence  Shuffled and dealt out blindly It is important because different people have different memorizing abilities. Random assignment cancels out this factor (and others)  Allows us to draw cause and effect conclusions

5. Activity 5-4 Def: Placebo Often give fake or empty treatment to equate psychological effects Ideally study will be double-blind

6. Three main issues in drawing conclusions Issue #1: Do I believe the sample I have is representative of the population that I am interested in for this issue (generalizable)?  Yes, if have a random sample Issue #2: Can I draw a cause and effect conclusion when comparing groups (causation)?  Yes, if have a randomized comparative experiment Issue #3: Is the result statistically significant?  Yes, if p-value is small

7. Uses of randomness

8. Scope of Conclusions Allocation of units to groups By random assignment No random assignment Selection of units Random sampling A random sample is selected from one population; units are then randomly assigned to different treatment groups Random samples are selected from existing distinct populations Inferences to populations can be drawn Not random sampling A groups of study units is found; units are then randomly assigned to treatment groups Collections of available units from distinct groups are examined Cause and effect conclusions can be drawn In its statement, Merck said that both it and some of its consultants were also concerned that, because patients with acute coronary syndrome in the Vioxx study would also be taking low doses of aspirin to prevent heart attack and stroke, their experiences might not be representative of patients who were not taking aspirin.

9. Next Step Now that we can properly design a study and collect data, what are the best ways to analyze the data, especially to compare groups  Topic 6: Categorical variables  For example: Do males and females feel differently about choice of lifetime achievement? Activity 6-3 (p. 100)

10. Activity 6-3 (p. 100) Blackboard Survey: If you could choose one of the following accomplishments for your life, which would you choose:  To win an Olympic gold medal  To win a Nobel Prize  To win an Academy Award Research question: Do men and women respond differently to this question?

11. Activity 6-3 (p. 100) (a) Classify variables Gender: categorical Preferred lifetime achievement: categorical (b) Explanatory: gender Response: preferred lifetime achievement (c) Determine the marginal distribution of preferred lifetime achievement

12. Marginal distribution

13. Does this answer our research question? Gender Two-way table

14. Descriptive Statistics Segmented bar graph 57% of women chose Nobel prize; 78% of men chose Olympic gold medal

15. “Independence” There is an association between gender and choice There is no association between gender and choice

16. Caution Most choosing the Olympic gold medal were men?

17. Lab 2: Is Yawning Contagious Anecdotal evidence? Experiment?  Mythbusters  Pre-lab on video posted soon!

18. To turn in with partner  Activity 6-2 (p. 99-100) (a)-(g) skip (e) For Thursday  Remember to meet in computer lab, bring USB  Turn in Lab 1  Pre-lab for Lab 2 in Blackboard No class Monday! For Tuesday  Activity 6-1, 6-5, and (optional) 6-4  Be working on HW 2

19. Analyzing Two Categorical Variables Activity 6-1 (p. 94)  Two-way table Explanatory variable as the columns  Marginal distribution = just one variable Too little: 398/646 .616 About right:.307, too much:.077 Tendency to think government spends too little on the environment

20. Activity 6-1 Conditional Distribution LiberalModerateConservative Too Little127158113 About Right278091 Too Much11732 Total155255236

21. Activity 6-1 Conditional Distribution  Of 155 liberals, 127 or about.819 said “too little”  “About right” = 27/155 .174  “Too much” = 1/155 .006 LiberalModerateConservative Too Little127158113 About Right278091 Too Much11732 Total155255236

22. Activity 6-1 (p. 94) Marginal distribution Conditional distributions Environmental Spending Tendency to think government spends too little on the environment Liberals are more likely to think govt spends too little, conservatives less so

23. Activity 6-1 Environmental Spending Space Spending The differences between the political parties are smaller when asked about space spending. Opinion is closer to independent of party with space. 35%

24. Perfect independence…

25. Activity 6-1 Conditional Distribution  127/398 =.319  31.9% of “too little” group classified as liberal  127/155 => 81.9% of liberals think “too little” LiberalModerateConservative Too Little127158113 About Right278091 Too Much11732 Total155255236

26. Activity 5-4 (p. 79) (a) Need something to compare to, maybe most people experience pain relief just over time (b) comparison group, random assignment (c) Confounding variable = knowledge that drug receiving should reduce their pain

27. Activity 5-4 (p. 79) (a) Need something to compare to, maybe most people experience pain relief just over time (b) comparison group, random assignment (c) Confounding variable = knowledge that drug receiving should reduce their pain What about? Extent of pain Cause of pain Pain tolerance Exercise Other health issues Back pain could have subsided on own Not “confounding” if don’t differ between EV groups (“lurking”)

28. Activity 5-4 (p. 79) (a) Need something to compare to, maybe most people experience pain relief just over time (b) comparison group, random assignment (c) Confounding variable = knowledge that drug receiving should reduce their pain (d) Both groups believe they could be receiving the helpful treatment