2. Lecturer’s desk INTEGRATED LEARNING CENTER ILC 120 Screen 11 10 2 1 98 7 6 5 13 12 15 14 17 16 19 18 4 3 Row A Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Computer Storage Cabinet Cabinet Table 20 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 27 26 4 3 28 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 26 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 26 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 27 26 4 3 28 13 12 14 16 15 17 18 19 29 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 27 26 4 3 28 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 27 26 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 26 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 25 24 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 24 4 3 13 12 14 16 15 17 18 19 11 10 2 1 9 8 7 6 5 21 20 23 22 4 3 13 12 14 16 15 17 18 19 11 10 9 8 7 6 5 4 3 13 12 14 16 15 17 18 19 broken desk

3. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2014 Room 120 Integrated Learning Center (ILC) 10:00 - 10:50 Mondays, Wednesdays & Fridays. http://www.youtube.com/watch?v=oSQJP40PcGI

4. Reminder A note on doodling

5. Schedule of readings Before next exam (November 21 st ) Please read chapters 7 – 11 in Ha & Ha Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

6. No homework due – Wednesday (November 19 th ) Just work on ANOVA projects Complete the two-way ANOVA worksheet Prepare for Exam 3

7. Labs continue this week with exam 3 review

8. By the end of lecture today 11/14/14 Use this as your study guide Two-way Analysis of Variance (ANOVA) Interpreting patterns of results Main effects Interactions

9. Extra Credit - Due November 24 th - There are five parts 1. A one page report of your design (includes all of the information from the writing assignment) Describe your experiment: what is your question / what is your prediction? State your Independent Variable (IV), how many levels there are, and the operational definition State your Dependent Variable (DV), and operational definition How many participants did you measure, and how did you recruit (sample) them Was this a between or within participant design (why?) 2. Gather the data Try to get at least 10 people (or data points) per level If you are working with other students in the class you should have 10 data points per level for each member of your group 3. Input data into Excel (hand in data) 4. Complete ANOVA analysis hand in ANOVA table 5. Statement of results (see next slide for example) and include a graph of your means (just like we did in the homework)

10. One way analysis of variance Variance is divided Total variability Within group variability (error variance) Between group variability (only one factor) Remember, 1 factor = 1 independent variable (this will be our numerator – like difference between means) Remember, error variance = random error (this will be our denominator – like within group variability Remember, one-way = one IV

11. Five steps to hypothesis testing Step 1: Identify the research problem (hypothesis) Describe the null and alternative hypotheses Step 2: Decision rule Alpha level? ( α =.05 or.01)? Step 3: Calculations Step 4: Make decision whether or not to reject null hypothesis If observed t (or F) is bigger then critical t (or F) then reject null Step 5: Conclusion - tie findings back in to research problem Critical statistic (e.g. z or t or F or r) value? MS Within MS Between F = Still, difference between means Still, variability of curve(s)

12. The average number of cookies sold for three different incentives were compared. The mean number of cookie boxes sold for the “Hawaii” incentive was 14, the mean number of cookies boxes sold for the “Bicycle” incentive was 12, and the mean number of cookies sold for the “No” incentive was 10. An ANOVA was conducted and there appears to be no significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 12) = 2.73; n.s. How to report the findings for an ANOVA One paragraph summary of this study. Describe the IV & DV, and present the means, which type of test was conducted, and the statistical results. Start summary with two means (based on DV) for two levels of the IV Describe type of test (t-test versus anova) with brief overview of results Type of test with degrees of freedom Value of observed statistic p<0.05 = “significant”

13. Remember, factor = independent variable Two-way analysis of variance Variance is divided further Total variability Within group variability Between group variability Factor A Variability Factor B Variability Interaction Variability Remember, within group variability = error variability = random error Remember, two-way = two IV Number of cookies sold NoneBikeHawaii trip Elementary College

14. What if we add an independent variable? Does “age” make a difference? Does the age and the type of incentive interact? We have two main effects and an interaction Number of cookies sold Incentives NoneBikeHawaii trip Number of cookies sold Age ElementaryCollege No incentive Number of cookies sold Age ElementaryCollege Bike Hawaii trip Number of cookies sold Incentives NoneBikeHawaii trip Elementary College Two-way gives info on “interactions” One-way ANOVA gives info on “Main effects” Two-way gives info “Main effects” &“Interactions”

15. Main effects and interactions We have two main effects and an interaction Number of cookies sold Incentives NoneBikeHawaii trip Number of cookies sold Age ElementaryCollege No incentive Number of cookies sold Age ElementaryCollege Bike Hawaii trip Number of cookies sold Incentives NoneBikeHawaii trip Elementary College Does incentive have an effect? Does age have an effect? Do age and the type of incentive interact? Rule for interactions: No interaction: If lines are parallel Yes interaction: If lines are (in any way) NOT parallel

16. What if there were no interactions? Does the age and the type of incentive interact? We have no interaction Number of cookies sold Incentives NoneBikeHawaii trip Number of cookies sold Age ElementaryCollege Incentives Number of cookies sold NoneBikeHawaii trip Elementary College Number of cookies sold Age ElementaryCollege No incentive Bike Hawaii trip Rule for interactions: No interaction: If lines are parallel Yes interaction: If lines are (in any way) NOT parallel Does incentive have an effect? Does age have an effect? Do age and the type of incentive interact?

17. Two-way ANOVA with one factor having two levels, and the other factor having three levels 2 x 3 design Incentive Type None Bike Hawaii mean = 1 mean = 5 mean = 6 39 4.55.5 0.5 1.5 Age ElementaryCollege mean=2.67mean=5.33 Number of cookies sold Incentives NoneBikeHawaii trip Number of cookies sold Age Elementary College What would this 2 x 3 design look like?

18. None Bike Hawaii mean = 1 mean = 5 mean = 6 39 4.55.5 0.5 1.5 Age ElementaryCollege mean=2.67mean=5.33 Incentive Type Number of cookies sold NoneBikeHawaii trip Elementary College Number of cookies sold Incentives NoneBikeHawaii trip Number of cookies sold Age ElementaryCollege

19. What would this 2 x 3 design look like? None Bike Hawaii mean = 1 mean = 5 mean = 6 39 4.55.5 0.5 1.5 Age ElementaryCollege mean=2.67mean=5.33 Incentive Type Number of cookies sold NoneBikeHawaii trip Elementary College Number of cookies sold Incentives NoneBikeHawaii trip Number of cookies sold Age ElementaryCollege Main effect of incentive

20. What would this 2 x 3 design look like? None Bike Hawaii mean = 1 mean = 5 mean = 6 39 4.55.5 0.5 1.5 Age ElementaryCollege mean=2.67mean=5.33 Incentive Type Number of cookies sold NoneBikeHawaii trip Elementary College Number of cookies sold Incentives NoneBikeHawaii trip Number of cookies sold Age ElementaryCollege Main effect of age

21. What would this 2 x 3 design look like? None Bike Hawaii mean = 1 mean = 5 mean = 6 39 4.55.5 0.5 1.5 Age ElementaryCollege mean=2.67mean=5.33 Incentive Type Number of cookies sold NoneBikeHawaii trip Elementary College Number of cookies sold Incentives NoneBikeHawaii trip Number of cookies sold Age ElementaryCollege Interaction

22. Examples of two-way ANOVA Effect of Adderall in subjects who have ADHD and who don’t on activity level Q: What is dependent variable? A: Activity level of subjects (like a measure of hyperactivity) Q: What is independent variable? A: Whether the subjects received Adderall or not Q: What are the levels of this independent variable? A: Yes received Adderall vs no, did not receive Adderall Q: What is other independent variable? A: Type of subject Q: What are the levels of this independent variable? A: Yes have ADHD versus no, do not have ADHD

23. 2x2 ANOVA Independent Variable? Effect of Adderall and subject type on activity level Type of subject (ADHD vs no ADHD) Amount of Activity Adderall NoYes No Adderall versus yes Adderall Independent Variable? Dependent Variable? Amount of activity Why even do a 2-way ANOVA??! What if we had done just a one-way ANOVA?. ADHD Control

24. Main effect: Whether there was a significant finding for one of the independent variables, ignoring the others When understanding a main effect it may be helpful to pretend we don’t know anything about the other variable, what would the results be if this had been a one-way ANOVA The effect of a single factor when any other factor is ignored NoYes Amount of Activity Adderall 2x2 ANOVA

25. Interactions Q: Does Adderall increase or decrease activity level? A: Depends on who is using it Whether levels of one independent variable respond differently to different levels of the other independent variable The joint effect of two (or more) factors on the dependent variable, independent of the separate effects of either factor. Interaction occurs whenever the effects of one factor are not consistent for all values (or levels) of the second factor Interaction

26. Interactions Whether levels of one independent variable respond differently to different levels of the other independent variable The joint effect of two (or more) factors on the dependent variable, independent of the separate effects of either factor. Interaction occurs whenever the effects of one factor are not consistent for all values (or levels) of the second factor Interaction Amount of Activity Adderall NoYes ADHD Control

27. Interactions Whether levels of one independent variable respond differently to different levels of the other independent variable The joint effect of two (or more) factors on the dependent variable, independent of the separate effects of either factor. Interaction Amount of Activity Adderall NoYes ADHD Control Interaction occurs whenever the effects of one factor are not consistent for all values (or levels) of the second factor

28. Main effect of Adderall? – Comparing “Yes” Adderall to “No” Adderall Adderall Yes ADHD Control Amount of Activity No Adderall ADHD Control Amount of Activity NoYes We have two “Yes Adderall” means Average would be about here We have two “No Adderall” means Average would be about here Main Effect of Adderall: Is there a difference between “Yes” Adderall and “No” Adderall? Main effect of Adderall? No, no difference in activity level in “yes” vs “no” Adderall groups YES NO

29. Main effect of Subject? – Comparing “Control” to “ADHD” Subjects Adderall Yes ADHD Control Amount of Activity No We have two “Contol” means Average would be about here Main Effect of Subject Type: Is there a difference between “Control” and “ADHD”? Adderall Yes ADHD Control Amount of Activity No We have two “ADHD” means Average would be about here Main effect of Subject Type? No, no difference in activity level in “control” vs “ADHD” groups Control ADHD

30. Interaction? Main effect of Adderall? Effect of Adderall and subject type on activity level Main effect of type of subject? No, no difference in activity level in “yes” vs “no” Adderall groups No, no difference in activity level of two groups Yes, the lines are not parallel – and it depends on who is using it Amount of Activity Adderall NoYes ADHD Control Amount of Activity Adderall NoYes ADHD Control 2x2 ANOVA

31. Interaction? Yes, the lines are not parallel – and it depends on who is using it Amount of Activity Adderall NoYes ADHD Control Amount of Activity Adderall NoYes ADHD Control Interaction occurs whenever the effects of one factor (Adderall) are not consistent for all values (or levels) of the second factor (who is using it – or type of subject)

32. Examples of two-way ANOVA Effect of exercise and calorie intake on weight Q: What is dependent variable? A: Amount each person weighs Q: What is independent variable? A: Amount of exercise Q: What are the levels of this independent variable? A: A lot versus a little exercise Q: What is other independent variable? A: Amount of calorie intake Q: What are the levels of this independent variable? A: More than 3000 versus less than 1000 per day

33. Interaction? Main effect of calorie intake? Weight Calorie Intake LowHigh High Exercise Low Exercise Effect of exercise and calorie intake on weight Main effect of exercise? Yes, lower calorie intake: lower weight Yes, higher exercise: lower weight No, the lines are parallel 2x2 ANOVA

34. Weight Calorie Intake LowHigh High Exercise Low Exercise Main effect of Calorie Intake? – Comparing “High” to “Low” We have two “High Intake” means Average would be about here We have two “Low Intake” means Average would be about here Main Effect of Calorie Intake: Is there a difference between “High Intake” and “Low Intake”? Yes there is a difference in Weight Depending on calorie intake. There is a difference between High and Low levels of calorie intake High Low Weight Calorie Intake LowHigh High Exercise Low Exercise High

35. Weight Calorie Intake LowHigh High Exercise Low Exercise Main effect of Exercise? – Comparing “High” to “Low” We have two “High Exercise” means Average would be about here We have two “Low Exercise” means Average would be about here Main Effect of Calorie Intake: Is there a difference between “High Exercise” and “Low Exercise”? Yes there is a difference in Weight depending on amount of exercise. There is a difference between High and Low levels of exercise intake HIGH Low Weight Calorie Intake LowHigh High Exercise Low Exercise High

36. Interaction? Main effect of calorie intake? Weight Calorie Intake LowHigh High Exercise Low Exercise Effect of exercise and calorie intake on weight Main effect of exercise? Yes, lower calorie intake: lower weight Yes, higher exercise: lower weight No, the lines are parallel 2x2 ANOVA

37. Interaction? No, the lines are parallel – lower calorie intake will reduce weight Whether or not you exercise. It does not depend on exercise to work Interaction occurs whenever the effects of one factor (Calorie intake) are not consistent for all values (or levels) of the second factor (whether or not you exercise) Weight Calorie Intake LowHigh High Exercise Low Exercise 2x2 ANOVA

38. Examples of two-way ANOVA Effect of “territory marking” and sex of rat on activity level in rats Q: What is dependent variable? A: Activity level of rats (like a measure of anxiety) Q: What is independent variable? A: Whether the territory was marked (sprayed) or not Q: What are the levels of this independent variable? A: Yes, sprayed versus not sprayed Q: What is other independent variable? A: Sex of rat Q: What are the levels of this independent variable? A: Male versus female

39. 2x2 ANOVA Interaction? Main effect of territory marking ? Activity Level Marking chemical NoneA lot Females Males Effect of “territory marking” and gender on activity level in rats Main effect of sex of rat? Yes, marking territory pulls mean activity level up Yes, males overall have higher levels of activity Yes, the lines are not parallel

40. Interaction? Yes, the lines are not parallel – males are much more affected by presence of chemical than females are. Effect of chemical does depend on gender Interaction occurs whenever the effects of one factor (marking chemical) are not consistent for all values (or levels) of the second factor (male or female) Activity Level Marking chemical NoneA lot Females Males 2x2 ANOVA

41. Main effect of A? Main effect of B? Interaction? Significant Fs? Dependent Variable Factor A A1A2 Factor B B1 B2 Dependent Variable Factor A A1A2 Factor B B1 B2 Yes, interaction No main effect of A No main effect of B No interaction Yes main effect of A Yes main effect of B

42. Main effect of A? Main effect of B? Interaction? Significant Fs? Dependent Variable Factor A A1A2 Factor B B1 B2 Dependent Variable Factor A A1A2 Factor B B1 B2 Yes, interaction No main effect of A Yes main effect of B No interaction Yes main effect of A No main effect of B

43. Let’s try one For the independent variable plotted on the x-axis a. there is a main effect b. There is not a main effect Dependent Variable Factor A A1A2 Factor B B1 B2

44. Dependent Variable Factor A A1A2 Factor B B1 B2 For the independent variable plotted with the two lines a. there is a main effect b. there is not a main effect

45. Let’s try one For the two independent variables a. there is an interaction b. there is not an interaction Dependent Variable Factor A A1A2 Factor B B1 B2

46. Let’s try one In a two-way ANOVA we have one dependent variable and two independent variables. Which of the following graphs shows no interaction Amount of Activity Adderall NoYes ADHD Control Weight Calories LowHigh High Exercise Low Exercise Cookies Sold Incentives NoneHawaii CollegeElementary Activity Another Male Spray SprayNo Spray Male Female A B C D a. A b. B c. C d. D

47. Let’s try one In a two-way ANOVA we have one dependent variable and two independent variables. This graph shows Weight Calories LowHigh High Exercise Low Exercise a. A main effect of exercise, but no main effect of calories b. A main effect of exercise, and a main effect of calories c. No main effect of exercise, and no main effect of calories d. No main effect of exercise, a main effect of calories

48. Let’s try one In a two-way ANOVA we have one dependent variable and two independent variables. This graph shows a. A main effect of incentive, but no main effect of age b. A main effect of incentive, and a main effect of age c. No main effect of incentive, and no main effect of age d. No main effect of incentive, a main effect of age Cookies Sold Incentives NoneHawaii CollegeElementary

49. Let’s try one In a 2 x 2 ANOVA there are how many tests of significance? (or how many “F”s are calculated?) a. 1 b. 2 c. 3 d. 4

50. Writing Assignment - In groups of 2 or 3 Generate an example of three different hypothetical 2 x 2 experiments: Dependent Variable Factor A A1A2 Factor B B1 B2 Interaction ? Main effect of A ? Main effect of B ? ? Independent Variable 1? Independent Variable 2? Dependent Variable?