Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2018 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. Welcome 3/26/18

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Before next exam (April 6th) Schedule of readings Before next exam (April 6th) Please read chapters 1 - 11 in OpenStax textbook Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

Labs continue this week Project 3 Lab sessions Labs continue this week Project 3

Project 3: Analysis of Variance (ANOVA)

Remember this?

One-way ANOVA Review One-way ANOVAs test only one independent variable Number of cookies sold One-way ANOVA None Bike Hawaii trip Incentives One-way ANOVAs test only one independent variable - although there may be many levels “Factor” = one independent variable “Level” = levels of the independent variable treatment condition groups “Main Effect” of independent variable = difference between levels Note: doesn’t tell you which specific levels (means) differ from each other A multi-factor experiment would be a multi-independent variables experiment Review

Comparing ANOVAs with t-tests Similarities still include: Using distributions to make decisions about common and rare events Using distributions to make inferences about whether to reject the null hypothesis or not The same 5 steps for testing an hypothesis Tells us generally about number of participants / observations Tells us generally about number of groups / levels of IV The three primary differences between t-tests and ANOVAS are: 1. ANOVAs can test more than two means 2. We are comparing sample means indirectly by comparing sample variances 3. We now will have two types of degrees of freedom t(16) = 3.0; p < 0.05 F(2, 15) = 3.0; p < 0.05 Tells us generally about number of participants / observations Review

Review A girl scout troop leader wondered whether providing an incentive to whomever sold the most girl scout cookies would have an effect on the number cookies sold. She provided a big incentive to one troop (trip to Hawaii), a lesser incentive to a second troop (bicycle), and no incentive to a third group, and then looked to see who sold more cookies. How many levels of the Independent Variable? What is Independent Variable? Troop 1 (nada) 10 8 12 7 13 Troop 2 (bicycle) 12 14 10 11 13 Troop 3 (Hawaii) 14 9 19 13 15 What is Dependent Variable? How many groups? n = 5 x = 10 n = 5 x = 12 n = 5 x = 14 Review

Hypothesis testing: Review Step 1: Identify the research problem Is there a significant difference in the number of cookie boxes sold between the girlscout troops that were given the different levels of incentive? Describe the null and alternative hypotheses Null hypotheses: No difference between the groups (e.g. group means) Alternative hypotheses: There is a difference between the means Review

Hypothesis testing: Review Decision rule = .05 Degrees of freedom (between) = number of groups - 1 = 3 - 1 = 2 Degrees of freedom (within) = # of scores - # of groups = (15 - 3) = 12* *or = (5-1) + (5-1) + (5-1) = 12. Critical F (2,12) = 3.98 Review

α= .05 Appendix B.4 (pg.518) F (2,12) Critical F(2,12) = 3.89 14

number of scores – number of groups “SS” = “Sum of Squares” - will be given for exams - you can think of this as the numerator in a standard deviation formula ANOVA table Source df MS F SS df between = number of groups minus 1 Between 40 ? ? ? ? Within 88 ? ? ? df within = number of scores – number of groups Total 128 ? ? Critical F(2,12) = 3.89

Writing Assignment - ANOVA 1. Write formula for standard deviation of sample 2. Write formula for variance of sample 3. Re-write formula for variance of sample using the nicknames for the numerator and denominator SS df = MS 4. Complete this ANOVA table ANOVA table Source SS df MS F Between 40 ? ? ? Within 88 ? ? Total 128 ? 4. Decide whether to reject the null 5. Write your conclusion

ANOVA table Source df MS F SS Between 40 ? 2 ? ? ? Within ? 88 12 ? ? “SS” = “Sum of Squares” - will be given for exams ANOVA table Source df MS F SS Between 40 ? 2 # groups - 1 ? ? ? 3-1=2 15-3=12 Within ? 88 12 ? ? # scores - number of groups Total 128 ? ? 14 # scores - 1 15- 1=14

“SS” = “Sum of Squares” - will be given for exams ANOVA table SSbetween dfbetween “SS” = “Sum of Squares” - will be given for exams 40 2 40 2 =20 MSbetween MSwithin ANOVA table Source df MS F SS 20 7.33 =2.73 Between 40 2 ? 20 ? 2.73 Within 88 12 7.33 ? Total 128 14 SSwithin dfwithin 88 12 =7.33 88 12

Make decision whether or not to reject null hypothesis Observed F = 2.73 Critical F(2,12) = 3.89 2.73 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis F(2,12) = 2.73; n.s. Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold 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.

incentive then the means are significantly different from each other Main effect of incentive: Will offering an incentive result in more girl scout cookies being sold? If we have a “effect” of incentive then the means are significantly different from each other we reject the null we have a significant F p < 0.05 To get an effect we want: Large “F” - big effect and small variability Small “p” - less than 0.05 (whatever our alpha is) We don’t know which means are different from which …. just that they are not all the same 20

Thank you! See you next time!!