1. Factorial Design Part II

2. Interaction Variability
TOTAL VARIABILITY
SStotal
Between Treatment
Variability
SSbetween treatment
Within Treatment
Variability
SSWithin/ERROR
Factor A Variability
SSA
Factor B Variability
SSB
Interaction Variability
SSAB

3. SS df MS F SS df MS F Source Between [(T2/n)] - G2/N Within/ErrorSS df MS F
Between
[(T2/n)] - G2/N
ab-1
SSBT/dfbt
MSBT/MSE
Within/Error
[(x2) – (T2/n)]
or…SST-SSBT
N-ab
SSE/dfE
Total
(x2) - G2/N
N-1
Source SS df MS F
Factor A
(Ta2/n) - G2/N
a-1
SSA/dfa
MSA/MSE
Factor B
(Tb2/n) - G2/N
b-1
SSB/dfb
MSB/MSE
Interact
SSBT-SSA-SSB
dfbt– dfA-dfB
SSAB/dfab
MSAxB/MSE

4. Using RC ….so much easier

5. Last Class Full Example
Does playing soccer lead to neurological damage from heading the ball? Perhaps…but maybe the results don’t show up until later. Downs et al (2002) collect data on older and younger soccer players and swimmers. They administer a cognitive test to these subjects and measure the results. Do the data suggest that cognitive ability differs depending on the sport played and age of participant? Alpha = .05
Soccer
Swimming
Younger
2, 4, 5, 3, 6
7, 7, 5, 5, 6
Older
3, 1, 2, 3, 1
10, 8, 7, 7, 8

6. Hand Calc Results Source SS df MS F p Model Error Total 100 24 124 3SS df MS F p
Model
Error
Total
100 24
124 3 16 19
33.33
1.5
6.53
22.22
< .05
Source SS df MS F p
Sport
Age
SxA 80 20 1
53.3
13.33
< .05
> .05

8. Factorial ANOVA steps Define null and alternative for: Set alpha
Omnibus, main effects, and interaction
Set alpha
Calculate sums of squares:
Total, Between treatments, Error/within
Partition SS between treatments into:
SS for each main effect and SS interaction
Calculate mean squares and F ratios:
omnibus, main effects, interaction
Identify F critical values for:
Make decisions about rejecting the null
Interpret results

9. Social support in Stressful Situations
The subjects in an experiment were told that they were going to experience a mildly painful medical procedure. They were asked to rate how much they would like to wait with another subject, who was a confederate, and either identified as male or female. The two independent variables were the gender of the subject, and the gender of the confederate. 20 subjects participated; 5 in each group. The data are presented in the table below. Conduct a 2-way ANOVA to examine the effect of these two variables on the subjects' desire to wait with another person ( = .05).
Confederate
Subject
Male
Female
M = 4
x = 20
x2 = 88
x2 = 86
M = 5
x = 25
x2 = 129
M = 8
x = 40
x2 = 324

10. Social Support ANOVA table
Source SS df MS F
Model
Error
Total
Source SS df MS F
Subject
Confed
SxC
Confederate
Male
Female
Subject 4 5 8
6.5
4.5 6

11. Participant Gender and Confederate Gender Predicting Preference to Wait with Another Person

12. Reporting the results of a 2-Way ANOVA
The 2x2 ANOVA indicated that there was an overall effect, F (3, 16) = 13.03, p < .05, suggesting the independent variables influenced how much people wanted to wait with someone else. There was a significant main effect of subject gender, F (1, 16) = 22.73, p < .05; women indicated a greater desire to wait with someone else than men. The main effect of confederate gender was also significant, F (1, 16) = 8.18, p < People preferred to wait with a woman rather than a man. Finally, the interaction effect was significant, F (1, 16) = 8.18, p < .05. Males’ ratings were the same regardless of whether the confederate was male (M = 4) or female (M=4) but females’ ratings were higher if the confederate was a female (M 8), rather than a male (M = 5).

13. Reporting the results of a 2-Way ANOVA
The 2x2 ANOVA indicated that there was an overall effect, F (3, 16) = 13.03, p < .05, suggesting the independent variables influenced how much people wanted to wait with someone else. There was a significant main effect of subject gender, F (1, 16) = 22.73, p < .05; women indicated a greater desire to wait with someone else than men. The main effect of confederate gender was also significant, F (1, 16) = 8.18, p < People preferred to wait with a woman rather than a man. Finally, the interaction effect was significant, F (1, 16) = 8.18, p < .05. Males’ ratings were the same regardless of whether the confederate was male (M = 4) or female (M=4) but females’ ratings were higher if the confederate was a female (M 8), rather than a male (M = 5).

14. Reporting the results of a 2-Way ANOVA
The 2x2 ANOVA indicated that there was an overall effect, F (3, 16) = 13.03, p < .05, suggesting the independent variables influenced how much people wanted to wait with someone else. There was a significant main effect of subject gender, F (1, 16) = 22.73, p < .05; women indicated a greater desire to wait with someone else than men. The main effect of confederate gender was also significant, F (1, 16) = 8.18, p < People preferred to wait with a woman rather than a man. Finally, the interaction effect was significant, F (1, 16) = 8.18, p < .05. Males’ ratings were the same regardless of whether the confederate was male (M = 4) or female (M=4) but females’ ratings were higher if the confederate was a female (M 8), rather than a male (M = 5).

15. Calculating simple main effects
When there is a significant interaction, we will perform a separate analysis of variance for each column (or row) to examine individual group differences.
Caffeine, Studying, and Exam Performance
No Coffee
1-2 Cups
> 2 Cups
Studied 82 95 80
Did not Study 74 73 60

16. Calculating simple main effects
One-way ANOVA for No Coffee condition: compare studied vs. not
Caffeine, Studying, and Exam Performance
No Coffee
2 Cups
> 2 Cups
Studied 82 95 80
Did not Study 74 73 60
One-way ANOVA

17. Calculating simple main effects
One-way ANOVA for 2 cups condition: compare studied vs. not
Caffeine, Studying, and Exam Performance
1-2 Cups
> 2 Cups
Studied 95 80
Did not Study 73 60
One-way ANOVA

18. Calculating simple main effects
One-way ANOVA for > 2 cups condition: compare studied vs. not
Caffeine, Studying, and Exam Performance
> 2 Cups
Studied 80
Did not Study 60
One-way ANOVA

19. Calculating simple main effects
And/or…
4. One-way ANOVA for the studied condition:
no vs. 2 vs. >2 cups
5. One-way ANOVA for the did not study condition:
Caffeine, Studying, and Exam Performance
No Coffee
1-2 Cups
> 2 Cups
Studied 82 95 80
Did not Study 74 73 60
One-Way
ANOVA
One-Way
ANOVA

20. More practice with Interpretation

21. Caspi et al..
DV: self-reported depression symptoms
IV #1: number of stressful life events participants experienced in past year (5 levels)
IV #2: Genetic risk (3 levels: s/s allele; s/l allele, or l/l allele)

22. Kong et al. (2008)
DV: number of words remembered (# Yes responses)
IV #1: Diagnosis (2 levels: Dissociative Identity Disorder-DID and Controls
IV#2: Condition (3 levels: List A, List B, Distractor List)

23. DV: Physical aggression (higher suggests more aggression)
McQuade (2017)
DV: Physical aggression (higher suggests more aggression)
IV#1: Children’s level of physical victimization (i.e., how much bullied; 2 levels low and high)
IV#2: Children’s executive functioning skills (EF: cognitive abilities; 3 levels: low, average, high)

24. IV#1: Harsh parenting (2 levels: - 1 SD = low and + 1 SD = high)
Erath et al. (2009)
DV: externalizing problems (e.g., aggression, noncompliance, rule-breaking)
IV#1: Harsh parenting (2 levels: - 1 SD = low and + 1 SD = high)
IV#2: Girls’ stress reaction (e.g., how they respond physiologically to a stressful task; 2 levels: Higher SCLR = high stress reaction; Lower SCLR = low stress reaction)