1. 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

2. Even if you have not yet registered your clicker you can still participate
The
Green
Sheets

3. Before next exam (April 5th)
Schedule of readings
Before next exam (April 5th)
Please read chapters 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

4. Labs continue this week
Lab sessions
Everyone will want to be enrolled
in one of the lab sessions
Labs continue this week

8. 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 < F(2, 15) = 3.0; p < 0.05
Tells us generally about number of participants / observations

9. 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

10. 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

11. 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 ?

12. Writing Assignment - Quiz

13. 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

14. 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”?

15. 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

16. 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”?

17. Homework

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

21. # scores - number of groups3 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!
/ = 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

22. 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).

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

24. 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

25. SS between
df between
MS between
MS within
SS within
df within

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

29. 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

30. 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).

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

32. 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

33. MS between
MS within
SS between
df between
SS within
df within

35. Writing Assignment - Quiz
Hand in Quiz and homework

36. Thank you!
See you next time!!