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 25

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

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

10. Review Study Type 3: One-way ANOVA
Single Independent Variable comparing more than two groups
Single Dependent Variable (numerical/continuous)
Used to test the effect of the IV on the DV
Ian was interested in the effect of incentives for girl scouts on the number
of cookies sold. He randomly assigned girl scouts into one of three groups.
The three groups were given one of three incentives and looked to see who
sold more cookies. The 3 incentives were 1) Trip to Hawaii, 2) New Bike
or 3) Nothing. This is an example of a true experiment
Dependent
variable is always quantitative
Sales per
Girl scout
Sales per
Girl scout
None
New
Bike
Trip
Hawaii
None
New
Bike
Trip
Hawaii
In an ANOVA, independent variable is qualitative
(& more than two groups)
Review

11. One-way ANOVA versus Chi Square
Be careful you are not designing a Chi Square
If this is just frequency you may have a problem
This is a
Chi Square
Total Number
of Boxes Sold
Sales per
Girl scout
This is an ANOVA
None
New
Bike
Trip
Hawaii
None
New
Bike
Trip
Hawaii
These are just frequencies
These are just frequencies
These are just frequencies
These are means
These are means
These are means

12. One way analysis of variance Variance is divided
Remember, one-way = one IV
Total variability
Between
group
variability
(only one factor)
Within
group
variability
(error variance)
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

13. The sum of squared deviations of some set of scores about their mean
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 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
MSWithin
MSBetween
F =
Mean square within groups:
sum of squares within groups
divided by its degrees of freedom 13

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

16. In a one-way ANOVA we have three types of variability.
Let’s try one
In a one-way ANOVA we have three types of variability.
Which picture best depicts the random error variability (also known as the within variability)?
a. Figure 1
b. Figure 2
c. Figure 3
d. All of the above 1.
correct 2. 3.

17. In a one-way ANOVA we have three types of variability.
Let’s try one
In a one-way ANOVA we have three types of variability.
Which picture best depicts the between group variability?
a. Figure 1
b. Figure 2
c. Figure 3
d. All of the above
correct 1. 2. 3.

18. One-way ANOVA 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

19. 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

20. 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

21. Sum of Squares divided by degrees of freedom
Variance = “MS”
SS/df
Remember this?

22. Writing Assignment - Quiz

23. 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

24. 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”?

25. Writing Assignment - Quiz
Complete Worksheet for next class

26. Thank you!
See you next time!!