1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2017 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

2. Lecturer’s desk Projection Booth Screen Screen Harvill 150 renumbered
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Harvill 150
renumbered
table 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Projection Booth
Left handed desk

4. A note on doodling

5. Project 3 And Start Project 4
Lab sessions
Everyone will want to be enrolled
in one of the lab sessions
Hand in
Project 3 And Start Project 4

6. Schedule of readings Before next exam (November 17th)
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

7. Two-way analysis of variance Variance is divided further
College
Number of
cookies sold
Elementary
Remember, two-way = two IV
None
Bike
Hawaii trip
Total variability
Between
group
variability
Within
group
variability
Remember, factor = independent variable
Remember, within group variability = error variability = random error
Factor A
Variability
Factor B
Variability
Interaction
Variability

8. Main effects and interactions
Does incentive have an effect?
We have two main effects
and an interaction
Do age and the
type of incentive interact?
Number of
cookies sold
Incentives
None
Bike
Hawaii trip
Number of
cookies sold
Incentives
None
Bike
Hawaii trip
Elementary
College
No incentive
Number of
cookies sold
Age
Elementary
College
Bike
Hawaii trip
Number of
cookies sold
Age
Elementary
College
Does age have an effect?
Rule for interactions:
No interaction: If lines are parallel
Yes interaction: If lines are (in any way) NOT parallel 8

9. What if there were no interactions?
Do age and the
type of incentive interact?
Does incentive have an effect?
Does the age and the type of incentive interact?
Incentives
Number of
cookies sold
None
Bike
Hawaii trip
College
Elementary
Number of
cookies sold
None
Bike
Hawaii trip
Incentives
Number of
cookies sold
Age
Elementary
College
Hawaii trip
Bike
Number of
cookies sold
No incentive
Elementary
College
Does age have an effect?
Age
We have no interaction
Rule for interactions:
No interaction: If lines are parallel
Yes interaction: If lines are (in any way) NOT parallel 9

10. What would this 2 x 3 design look like?
Number of
cookies sold
Incentives
None
Bike
Hawaii trip
Two-way ANOVA with one factor having two levels,
and the other factor having three levels
2 x 3 design
Number of
cookies sold
Age
Elementary
College
mean=2.67
mean=5.33
Elementary
College
Age
0.5
1.5
Incentive
Type
None
Bike
Hawaii
mean = 1
mean = 5
mean = 6
4.5
5.5 3 9 10

11. What would this 2 x 3 design look like?
Number of
cookies sold
Number of
cookies sold
None
Bike
Hawaii trip
Elementary
College
None
Bike
Hawaii trip
Incentives
Number of
cookies sold
Age
Elementary
College
mean=2.67
mean=5.33
Elementary
College
Age
0.5
1.5
None
mean = 1
mean = 5
mean = 6
Incentive
Type
Bike
4.5
5.5
Hawaii 3 9 11

12. What would this 2 x 3 design look like?
Number of
cookies sold
Number of
cookies sold
None
Bike
Hawaii trip
Elementary
College
None
Bike
Hawaii trip
Incentives
Number of
cookies sold
Age
Elementary
College
mean=2.67
mean=5.33
Elementary
College
Age
Main effect
of incentive
0.5
1.5
None
mean = 1
mean = 5
mean = 6
Incentive
Type
Bike
4.5
5.5
Hawaii 3 9 12

13. What would this 2 x 3 design look like?
Number of
cookies sold
Number of
cookies sold
None
Bike
Hawaii trip
Elementary
College
None
Bike
Hawaii trip
Incentives
Number of
cookies sold
Age
Elementary
College
mean=2.67
mean=5.33
Elementary
College
Age
0.5
1.5
Main effect
of age
None
mean = 1
mean = 5
mean = 6
Incentive
Type
Bike
4.5
5.5
Hawaii 3 9 13

14. What would this 2 x 3 design look like?
Number of
cookies sold
Number of
cookies sold
None
Bike
Hawaii trip
Elementary
College
None
Bike
Hawaii trip
Incentives
Number of
cookies sold
Interaction
Age
Elementary
College
mean=2.67
mean=5.33
Elementary
College
Age
0.5
1.5
None
mean = 1
mean = 5
mean = 6
Incentive
Type
Bike
4.5
5.5
Hawaii 3 9 14

15. Examples of two-way ANOVA
Effect of Adderall in subjects who have ADHD and who don’t on activity level
Q: What is dependent variable?
A: Activity level of subjects (like a measure of hyperactivity)
Q: What is independent variable?
A: Whether the subjects received Adderall or not
Q: What are the levels of this independent variable?
A: Yes received Adderall vs no, did not receive Adderall
Q: What is other independent variable?
A: Type of subject
Q: What are the levels of this independent variable?
A: Yes have ADHD versus no, do not have ADHD 15

16. What if we had done just a one-way ANOVA?
2x2 ANOVA
Control
Amount of Activity
ADHD No
Yes
Adderall
Effect of Adderall and subject type on activity level
Dependent Variable?
Why even do a 2-way ANOVA??!
What if we had done just a one-way ANOVA?
Amount of activity
Independent Variable?
No Adderall versus yes Adderall
Independent Variable?
Type of subject (ADHD vs no ADHD) . 16

17. 2x2 ANOVA No Yes Amount of Activity Adderall Main effect:
Whether there was a significant finding for one
of the independent variables, ignoring the others
When understanding a main effect it may be helpful to
pretend we don’t know anything about the other
variable, what would the results be if this had been a one-way ANOVA
The effect of a single factor when any other factor is ignored 17

18. Interactions Q: Does Adderall increase or decrease activity level?
A: Depends on who is using it
Interaction
Whether levels of one independent variable respond
differently to different levels of the other
independent variable
The joint effect of two (or more) factors on the dependent
variable, independent of the separate effects of either
factor.
Interaction occurs whenever the effects of one factor
are not consistent for all values (or levels) of the second
factor 18

19. Interactions No Yes Amount of Activity Adderall Interaction
Control
Amount of Activity
ADHD No
Yes
Adderall
Interaction
Whether levels of one independent variable respond
differently to different levels of the other
independent variable
The joint effect of two (or more) factors on the dependent
variable, independent of the separate effects of either
factor.
Interaction occurs whenever the effects of one factor
are not consistent for all values (or levels) of the second
factor 19

20. Interactions No Yes Amount of Activity Adderall Interaction
Control
Amount of Activity
ADHD No
Yes
Adderall
Interaction
Whether levels of one independent variable respond
differently to different levels of the other
independent variable
The joint effect of two (or more) factors on the dependent
variable, independent of the separate effects of either
factor.
Interaction occurs whenever the effects of one factor
are not consistent for all values (or levels) of the second
factor 20

21. Main effect of Adderall? – Comparing “Yes” Adderall to “No” Adderall
Average would
be about here
Adderall
Yes
ADHD
Control
Amount of Activity No
Main Effect of Adderall:
Is there a difference between “Yes” Adderall and “No” Adderall?
We have two
“Yes Adderall” means
YES
Average would
be about here
Adderall
ADHD
Control
Amount of Activity No
Yes
Main effect of Adderall?
We have two
“No Adderall” means NO
YES
No, no difference in
activity level in “yes” vs “no”
Adderall groups 21

22. Main effect of Subject? – Comparing “Control” to “ADHD” Subjects
Average would
be about here
Main Effect of Subject Type:
Is there a difference between “Control” and “ADHD”?
Adderall
Yes
ADHD
Control
Amount of Activity No
We have two
“Contol” means
Control
Average would
be about here
Adderall
Yes
ADHD
Control
Amount of Activity No
We have two
“ADHD” means
ADHD
Control
Main effect of Subject Type?
No, no difference in
activity level in “control” vs “ADHD” groups 22

23. 2x2 ANOVA No No Yes Yes Amount of Activity Amount of Activity Adderall
Control
Control
Amount of Activity
Amount of Activity
ADHD
ADHD No No
Yes
Yes
Adderall
Adderall
Effect of Adderall and subject type on activity level
Main effect of Adderall?
No, no difference in activity level in “yes” vs “no” Adderall groups
Main effect of type of subject?
No, no difference in activity level of two groups
Interaction?
Yes, the lines are not parallel – and it depends on who is using it 23

24. 2x2 ANOVA No No Yes Yes Amount of Activity Amount of Activity Adderall
Control
Control
Amount of Activity
Amount of Activity
ADHD
ADHD No No
Yes
Yes
Adderall
Adderall
Interaction?
Yes, the lines are not parallel – and it depends on who is using it
Interaction occurs whenever the effects of one factor (Adderall) are not consistent for all values (or levels) of the second
factor (who is using it – or type of subject) 24

25. Examples of two-way ANOVA
Effect of exercise and calorie intake on weight
Q: What is dependent variable?
A: Amount each person weighs
Q: What is independent variable?
A: Amount of exercise
Q: What are the levels of this independent variable?
A: A lot versus a little exercise
Q: What is other independent variable?
A: Amount of calorie intake
Q: What are the levels of this independent variable?
A: More than 3000 versus less than 1000 per day 25

26. 2x2 ANOVA Weight Low High Calorie Intake
Low Exercise
Weight
High Exercise
Low
High
Calorie Intake
Effect of exercise and calorie intake on weight
Main effect of calorie intake?
Yes, lower calorie intake: lower weight
Main effect of exercise?
Yes, higher exercise: lower weight
Interaction?
No, the lines are parallel 26

27. Main effect of Calorie Intake? – Comparing “High” to “Low”
Average would
be about here
Main Effect of Calorie Intake:
Is there a difference between “High Intake” and “Low Intake”?
Low Exercise
We have two
“High Intake” means
Weight
High
High Exercise
Low
High
Calorie Intake
Yes there is a difference in Weight
Depending on calorie intake.
There is a difference between
High and Low levels of calorie intake
Average would
be about here
Weight
Calorie Intake
Low
High
High Exercise
Low Exercise
We have two
“Low Intake” means
Low
High 27

28. Low High Low High Main effect of Exercise? – Comparing “High” to “Low”
Average would
be about here
Weight
Calorie Intake
Low
High
Main Effect of Calorie Intake:
Is there a difference between “High Exercise” and “Low Exercise”?
High Exercise
Low Exercise
We have two
“High Exercise” means
High
Yes there is a difference in Weight
depending on amount of exercise.
There is a difference between
High and Low levels of exercise intake
Average would
be about here
Weight
Calorie Intake
Low
High
High Exercise
Low Exercise
We have two
“Low Exercise” means
Low
HIGH 28

29. 2x2 ANOVA Weight Low High Calorie Intake
Low Exercise
Weight
High Exercise
Low
High
Calorie Intake
Effect of exercise and calorie intake on weight
Main effect of calorie intake?
Yes, lower calorie intake: lower weight
Main effect of exercise?
Yes, higher exercise: lower weight
Interaction?
No, the lines are parallel 29

30. 2x2 ANOVA Weight Low High Calorie Intake Interaction?
Low Exercise
Weight
High Exercise
Low
High
Calorie Intake
Interaction?
No, the lines are parallel – lower calorie intake will reduce weight
Whether or not you exercise. It does not depend on exercise to work
Interaction occurs whenever the effects of one factor (Calorie intake) are not consistent for all values (or levels) of the second
factor (whether or not you exercise) 30

31. Examples of two-way ANOVA
Effect of “territory marking” and sex of rat on activity level in rats
Q: What is dependent variable?
A: Activity level of rats (like a measure of anxiety)
Q: What is independent variable?
A: Whether the territory was marked (sprayed) or not
Q: What are the levels of this independent variable?
A: Yes, sprayed versus not sprayed
Q: What is other independent variable?
A: Sex of rat
Q: What are the levels of this independent variable?
A: Male versus female 31

32. 2x2 ANOVA Activity Level Marking chemical
Males
Activity
Level
Females
None
A lot
Marking chemical
Effect of “territory marking” and gender on activity level in rats
Main effect of territory marking ?
Yes, marking territory pulls mean activity level up
Main effect of sex of rat?
Yes, males overall have higher levels of activity
Interaction?
Yes, the lines are not parallel 32

33. 2x2 ANOVA Activity Level Interaction? Marking chemical
Males
Activity
Level
Females
None
A lot
Interaction?
Marking chemical
Yes, the lines are not parallel – males are much more affected
by presence of chemical than females are. Effect of chemical does
depend on gender
Interaction occurs whenever the effects of one factor (marking chemical) are not consistent for all values (or levels) of the second factor (male or female) 33

34. Main effect of A? Main effect of B? Interaction? Significant Fs?
Dependent Variable
Factor A A1 A2
Factor B B1 B2
No main effect of A
No main effect of B
Yes, interaction
Dependent Variable
Factor A A1 A2
Factor B B1 B2
Yes main effect of A
Yes main effect of B
No interaction 34

35. Main effect of A? Main effect of B? Interaction? Significant Fs?
Dependent Variable
Factor A A1 A2
Factor B B1 B2
No main effect of A
Yes main effect of B
Yes, interaction
Dependent Variable
Factor A A1 A2
Factor B B1 B2
Yes main effect of A
No main effect of B
No interaction 35

36. Thank you!
See you next time!!