1. Factorial Design Two Way ANOVAs
2 Independent Variables
Examples
IV#1 IV#2 DV
Drug Level Age of Patient Anxiety Level
Type of Therapy Length of Therapy Anxiety Level
Type of Exercise Type of Diet Weight Change
Toy Color Gender Satisf. with Toy
Key Advantages
Compare relative influences on DV
Examine interactions between IV
Dr. Sinn, PSYC 301
2 Way ANOVA

2. Example Two Way ANOVAs Toy Study IV: Toy Color (Blue, Pink)
IV: Gender (Boy, Girl)
DV: Satisfaction with Toy
Terms
Factors: __ * ___ * ___
Levels (a,b)
Design: ___ x ___
Main Effect, collapsing
Interaction
Dr. Sinn, PSYC 301
2 Way ANOVA

3. Main Effects Two Way ANOVAs
Toy Color
Blue (1)
Pink (2)
Sex
Boy (1) 7 6 5 2 3 4
Girl (2) 12 10 11
Main Effect for Toy Color?
Compare Column Means
M=5.5
M=7.0
M=8.0
M=4.5
Main Effect for Gender?
Compare Row Means
Dr. Sinn, PSYC 301
2 Way ANOVA

4. Interactions- Cell Means Two Way ANOVAs
Toy Color
Blue (1)
Pink (2)
Sex
Boy (1) 7 6 5 2 3 4
Girl (2) 12 10 11
Graph cell means to examine possibility of interaction
M=6
M=3
M=5
M=11
Dr. Sinn, PSYC 301
2 Way ANOVA

5. Interactions-Graph Two Way ANOVAs
General rule of life:
If two lines cross, it probably means something.
Non-parallel lines suggests interaction.
Dr. Sinn, PSYC 301
2 Way ANOVA

6. SPSS: Data Input #1 Two Way ANOVAs
Dr. Sinn, PSYC 301
2 Way ANOVA

7. SPSS: Data Input #2 Two Way ANOVAs
Dr. Sinn, PSYC 301
2 Way ANOVA

8. SPSS: Analysis, Step #1 Two Way ANOVAs
Go to Analyze, General Linear Model, Univariate
Move DV to Dependent Variable
Move 2 IVs to Fixed Faxtors
Dr. Sinn, PSYC 301
2 Way ANOVA

9. SPSS: Analysis, Step #2 Two Way ANOVAs
Select Plots; Graph sample means with two IVs
If one IV has more levels, put on Horizontal Axis
Dr. Sinn, PSYC 301
2 Way ANOVA

10. SPSS: Analysis, Step #3 Two Way ANOVAs
Select Options
Ask for Descriptive Statistics
Dr. Sinn, PSYC 301
2 Way ANOVA

11. SPSS: Analysis, Step #4 Two Way ANOVAs
Select Post Hoc
Do Post Hoc (SNK) for IVs with 3+ levels
Not required in this example; both IVs have only 2 levels: color (blue & pink), sex (boy & girl)
Dr. Sinn, PSYC 301
2 Way ANOVA

12. SPSS Output #1 Two Way ANOVAs
SPSS Output #1 Two Way ANOVAs
Dr. Sinn, PSYC 301
2 Way ANOVA

13. SPSS Output #2: Two Way ANOVAsBG WG
Dr. Sinn, PSYC 301
2 Way ANOVA

14. SPSS Output #3: Two Way ANOVAs
Note: post-hoc tests are needed only when you have 3+ levels of an IV (here we don’t).
Dr. Sinn, PSYC 301
2 Way ANOVA

15. Write-up Two Way ANOVAs
The hypotheses were supported. [1] There was a main effect for toy color. Pink toys (M=7.00) elicited significantly more satisfaction than blue toys (M=5.5), F(1,8) = 6.750, p≤ [2]There was also a main effect for sex. Girls were significantly more satisfied (M=8.00) than boys (M=4.50), F(1,8)=36.750, p≤ .05.
Dr. Sinn, PSYC 301
2 Way ANOVA

16. Write-up (cont.)Two Way ANOVAs
[3] Additionally, there was a significant interaction between color and sex, F(1,8) = , p≤.05. Boys and girls appear equally satisfied with blue toys. Switching to pink toys, however, raised satisfaction for girls but decreased satisfaction for boys. Sex accounted for only a small amount of variance in satisfaction (η2 = .0601), but color (η2 = .3274) and the interaction (η2 = .5412) accounted for a large amount of variance.
Dr. Sinn, PSYC 301
2 Way ANOVA

17. Two-Way ANOVA Cont. Announcements Review Study Guide for Final
Homework: Influence Study
Homework: Teamwork & Feedback Study, write-ups
Explain Purpose of 2nd ANOVA Lab
Studying for Final
Computational Review for Final
Review Name That Stat Exercises
Practice SPSS on computer
Review Old Computations
Dr. Sinn, PSYC 301
2 Way ANOVA

18. Source of Variation Table for 2-way ANOVA
Three possible influences on DV -- factors
A: IV #1
B: IV #2
C: Interaction
Sum of Squares (SS) always given
Calculating Degrees of Freedom by hand
dfA = a-1
dfB = b-1
dfA*B = (a-1)*(b-1)
dfwg = a * b * (n-1)
dfTotal = N – 1
Dr. Sinn, PSYC 301
2 Way ANOVA

19. Table Reading Keys Three F’s use same formula
MSBG / MSWG = MSSpecific Factor / MSError
For example: MSA / MSError
Factor significant if p ≤ .05
MS = SS/df for each factor and error
Dr. Sinn, PSYC 301
2 Way ANOVA

20. Source of Variation Table from Toy StudyBG WG
Dr. Sinn, PSYC 301
2 Way ANOVA

21. Age & Intelligence (2-way ANOVA)
Task
Fluid
Crystalized
Age 65
105
100 95
110 75 85 90 80
Age & Intelligence (2-way ANOVA)
Dr. Sinn, PSYC 301
2 Way ANOVA

22. Important Means Main effect for Task? Main effect for Age? Graph it
Dr. Sinn, PSYC 301
2 Way ANOVA

23. Calculate degrees of freedom by hand:
dfA
dfB
dfA*B
dfError
dfTotal
Dr. Sinn, PSYC 301
2 Way ANOVA

24. Complete Table with these SS
SSTask =
SSAge =
SSTask*Age =
SSError =
Dr. Sinn, PSYC 301
2 Way ANOVA

25. SPSS Data Entry
Dr. Sinn, PSYC 301
2 Way ANOVA

26. Check Output What means pertain to… Is there a ….
Effect of Task
Effect of Age
Effect of interaction
Is there a ….
Main effect for Task
Main effect for Age
Interaction
Is Post Hoc Required?
Explain graph
Do complete Write-up
Dr. Sinn, PSYC 301
2 Way ANOVA

27. 2-way ANOVA: Age & Intelligence
First, I’d like to thank my statistics teacher for devising such a creative, exciting, and enriching exercise. My life will never be the same.
Dr. Sinn, PSYC 301
2 Way ANOVA

28. 2-way ANOVA: Age & Intelligence
I’m still smarter than you are, missy.
The hypotheses were supported.
Participants scored significantly lower on tasks using fluid (M=89.58) rather than crystallized intelligence (M=100.83), F(1,18) = 33.46, p<=.05.
In addition, participants aged 85 years scored lower (M=90.00) than those aged 75 years (M=95.00), who in turn scored lower than those aged 65 years (M=100.63), F(2,18)=10.015, p<=.05.
Additionally, age interacted with type of task, F(2,18)=7.812, p<=.05. Although scores on crystallized tasks remain relatively constant, scores on fluid tasks decline with age.
Dr. Sinn, PSYC 301
2 Way ANOVA

29. Interpreting 2-way Outcomes
Dr. Sinn, PSYC 301
2 Way ANOVA

30. Interpreting 2-way Outcomes (cont.)
Dr. Sinn, PSYC 301
2 Way ANOVA

31. Bogus Winthrop Data – 2-way ANOVA
Some of the hypotheses were supported.
There was a main effect for residence. On-campus students earned higher GPAs (M=3.2545) than off-campus students (M=1.9667), F(1,14)=21.625,p<=.05.
However, there was no main effect for program. GPAs for students in the control (M=2.5857), mentoring (M=2.5286), and study hall condition (M=2.9500) did not differ significantly, F(2,14)=.069, n.s.
There was no interaction, F(2,14)=.205, n.s.
Residence accounted for a moderate amount of variance in GPA, eta2 =
Overall, it appears residence, but not type of program, affects GPA.
Dr. Sinn, PSYC 301
2 Way ANOVA

32. Is there a sig. difference in funniness
Is there a sig. difference in funniness? Yet another excuse for a 1-way Anova #2 #1
Rate each video on the following scale:
Not funny Funny #3
Dr. Sinn, PSYC 301
2 Way ANOVA