2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2016 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays

4. By the end of lecture today 3/30/16 Analysis of Variance (ANOVA) Project 3

5. Before next exam (April 8 th ) 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

6. No Homework Due: Monday, April 4 th

7. Everyone will want to be enrolled in one of the lab sessions Labs continue this week, Completing ANOVAs Project 3

9. Study Type 2: t-test Study Type 3: One-way Analysis of Variance (ANOVA) Comparing more than two means We are looking to compare two means Prep Project 3 Prep Project 3

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. . Difference between means Variability of curve(s) “Between Groups” Variability “Within Groups” Variability

12. 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)

13. Sum of squares (SS): The sum of squared deviations of some set of scores about their mean Mean squares (MS): The sum of squares divided by its degrees of freedom Mean square within groups: sum of squares within groups divided by its degrees of freedom Mean square between groups: sum of squares between groups divided by its degrees of freedom Mean square total: sum of squares total divided by its degrees of freedom MS Within MS Between F =

14. ANOVA Variability within groups Variability between groups F = Variability Between Groups Variability Within Groups “Between” variability bigger than “within” variability so should get a big (significant) F Variability Between Groups Variability Within Groups “Between” variability getting smaller “within” variability staying same so, should get a smaller F Variability Between Groups “Between” variability getting very small “within” variability staying same so, should get a very small F Variability Within Groups

15. ANOVA Variability within groups Variability between groups F = “Between” variability bigger than “within” variability so should get a big (significant) F “Between” variability getting smaller “within” variability staying same so, should get a smaller F “Between” variability getting very small “within” variability staying same so, should get a very small F (equal to 1) Variability Within Groups Variability Between Groups Variability Within Groups Variability Between Groups

16. Questions?

17. Writing Assignment - Quiz 1. When do you use a t-test and when do you use an ANOVA 2. What is the formula for degrees of freedom in a two-sample t-test 3. What is the formula for degrees of freedom “between groups” in ANOVA 4. What is the formula for degrees of freedom “within groups” in ANOVA 7. Draw and match each with proper label Between Group Variability Within Group Variability Total Variability 5. How are “levels”, “groups”, “conditions” “treatments” related? 6. How are “significant difference”, “p< 0.05”, “main effect” and “we reject the null” related?

18. Writing Assignment - Quiz 9. Complete this ANOVA table 11. Is there a main effect of type of running shoe? Is “p< 0.05”? 10. Find the critical F value from the table 8. Daphne compared running speed for three types of running shoes. She asked 10 people to run as fast as they could wearing one type of shoe. So, there were 30 people altogether What is the independent variable? What is the dependent variable? How many factors do we have (what are they)? How many treatments do we have (what are they)?

19. Writing Assignment - Quiz 1. When do you use a t-test and when do you use an ANOVA 2. What is the formula for degrees of freedom in a two-sample t-test 3. What is the formula for degrees of freedom “between groups” in ANOVA 4. What is the formula for degrees of freedom “within groups” in ANOVA 7. Draw and match each with proper label Between Group Variability Within Group Variability Total Variability 5. How are “levels”, “groups”, “conditions” “treatments” related? 6. How are “significant difference”, “p< 0.05”, “main effect” and “we reject the null” related? t-tests compare two means ANOVA compares more than two means t-tests compare two means ANOVA compares more than two means n -1 per group or n-2 or Total n - # of groups n -1 per group or n-2 or Total n - # of groups n -1 per group or Total n - # of groups n -1 per group or Total n - # of groups # of groups - 1 They all mean the same thing

20. Writing Assignment - Quiz 9. Complete this ANOVA table 11. Is there a main effect of type of running shoe? Is “p< 0.05”? 10. Find the critical F value from the table 8. Daphne compared running speed for three types of running shoes. She asked 10 people to run as fast as they could wearing one type of shoe. So, there were 30 people altogether What is the independent variable? What is the dependent variable? How many factors do we have (what are they)? How many treatments do we have (what are they)? Type of running shoe Running Speed Running Speed 1 Factor Yes F(2,27)=4.00; p< 0.05 Yes F(2,27)=4.00; p< 0.05 3.37 Type 1 Type 2 Type 3 Type 1 Type 2 Type 3 3 groups # groups - 1 n - # groups n - 1 SS B df B SS B df B SS W df W SS W df W MS B MS W MS B MS W