Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. March 27 http://www.youtube.com/watch?v=oSQJP40PcGI

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Before next exam (April 5th) Schedule of readings Before next exam (April 5th) 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 Lab sessions Everyone will want to be enrolled in one of the lab sessions Labs continue this week

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

F = MSBetween MSWithin 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)? Still, difference between means Critical statistic (e.g. z or t or F or r) value? Step 3: Calculations MSWithin MSBetween F = Still, variability of curve(s) 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

Sum of Squares Degrees of freedom Question: Using nicknames…. what is formula for SAMPLE variance? SS df “SS” = “Sum of Squares” “SS” = “Sum of Squares” “df” = degrees of freedom “SS” = “Sum of Squares” We lose one degree of freedom for every parameter we estimate Remember, you should know these formulas by heart

This is our sample variance… what is formula for SAMPLE variance? SS df ANOVA table Source df MS F SS Between 40 ? ? ? Within 88 ? ? Total 128 ?

Writing Assignment - Quiz

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 5. How are “levels”, “groups”, “conditions” “treatments” related? 6. How are “significant difference”, “p< 0.05”, “main effect” and “we reject the null” related? 7. Draw and match each with proper label Within Group Variability Total Variability Between Group Variability

Writing Assignment - Quiz 10. 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)? 11. Complete this ANOVA table 12. Find the critical F value from the table 13. Is there a main effect of type of running shoe? Is “p< 0.05”?

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

Writing Assignment - Quiz 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 Type 1 Type 2 Type 3 3 groups 1 Factor 9. Complete this ANOVA table SSB dfB # groups - 1 n - # groups MSB MSW SSW dfW n - 1 Yes F(2,27)=4.00; p< 0.05 10. Find the critical F value from the table 3.37 11. Is there a main effect of type of running shoe? Is “p< 0.05”?

Homework

Type of major in school 4 (accounting, finance, hr, marketing) Grade Point Average 0.05 2.83 3.02 3.24 3.37

# scores - number of groups 3 24 0.3937 If observed F is bigger than critical F: Reject null & Significant! If observed F is bigger than critical F: Reject null & Significant! 0.1119 If p value is less than 0.05: Reject null & Significant! 0.3937 / 0.1119 = 3.517 3.517 3.009 0.03 4-1=3 # groups - 1 # scores - number of groups 28 - 4=24 # scores - 1 28 - 1=27

Yes F (3, 24) = 3.517; p < 0.05 The GPA for four majors was compared. The average GPA was 2.83 for accounting, 3.02 for finance, 3.24 for HR, and 3.37 for marketing. An ANOVA was conducted and there is a significant difference in GPA for these four groups (F(3,24) = 3.52; p < 0.05).

Average for each group (We REALLY care about this one) Number of observations in each group

Number of groups minus one (k – 1)  4-1=3 “SS” = “Sum of Squares” - will be given for exams Number of people minus number of groups (n – k)  28-4=24

SS between df between MS between MS within SS within df within

Type of executive 3 (banking, retail, insurance) Hours spent at computer 0.05 10.8 8 8.4

2 12 11.46 If observed F is bigger than critical F: Reject null & Significant! If observed F is bigger than critical F: Reject null & Significant! 2 11.46 / 2 = 5.733 If p value is less than 0.05: Reject null & Significant! 5.733 3.88 0.0179

Yes F (2, 12) = 5.73; p < 0.05 The number of hours spent at the computer was compared for three types of executives. The average hours spent was 10.8 for banking executives, 8 for retail executives, and 8.4 for insurance executives. An ANOVA was conducted and we found a significant difference in the average number of hours spent at the computer for these three groups , (F(2,12) = 5.73; p < 0.05).

Number of observations in each group Average for each group Number of observations in each group Just add up all scores

Number of groups minus one (k – 1)  3-1=2 “SS” = “Sum of Squares” - will be given for exams Number of people minus number of groups (n – k)  15-3=12

MS between MS within SS between df between SS within df within

Writing Assignment - Quiz Hand in Quiz and homework

Thank you! See you next time!!