The following data are from a two-factor study examining the effects of three tr
ID: 3257450 • Letter: T
Question
The following data are from a two-factor study examining the effects of three treatment conditions on male and female participants. The study includes two factors: Factor A: "Gender (male or female) and Factor B: "Treatment Condition"(I, II, or III). The study recruited a total of N = 18 participants, with n = 3 participants in each condition or "cell." The table below shows each participant's score, along with the mean, sum of scores (T), and SS within each "cell." The sum of scores (T) is also provided for each row (each level of factor A) and column (each level of factor B). Use a two-factor ANOVA to evaluate the statistical significance of 1) the main effect of gender, 2) the main effect of treatment condition, and 3) the interaction between gender and treatment condition. Use alpha = 05 for all tests. You do not need to calculate effect size or conduct post-hoc tests.Explanation / Answer
Answer:
Two factor ANOVA
Treatment
Means:
T1
T2
T3
Male
3.0
6.0
9.0
6.0
Gender
Female
3.0
12.0
15.0
10.0
3.0
9.0
12.0
8.0
3
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Gender
72.00
1
72.000
9.00
.0111
Treatment
252.00
2
126.000
15.75
.0004
Interaction
36.00
2
18.000
2.25
.1480
Error
96.00
12
8.000
Total
456.00
17
1). To test main effect of Gender, calculated F= 9.00 which is greater than critical value F(1,12)=4.75
The gender effect is significant.
2). To test main effect of treatment, calculated F= 15.75 which is greater than critical value F(2,12)=3.89
The Treatment effect is significant.
1). To test interaction effect, calculated F= 2.25 which is < critical value F(2,12)=3.89
The interaction effect is not significant.
Two factor ANOVA
Treatment
Means:
T1
T2
T3
Male
3.0
6.0
9.0
6.0
Gender
Female
3.0
12.0
15.0
10.0
3.0
9.0
12.0
8.0
3
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Gender
72.00
1
72.000
9.00
.0111
Treatment
252.00
2
126.000
15.75
.0004
Interaction
36.00
2
18.000
2.25
.1480
Error
96.00
12
8.000
Total
456.00
17
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