A researcher is interested to learn if there is a relationship between the level
ID: 3203895 • Letter: A
Question
A researcher is interested to learn if there is a relationship between the level of interaction a women in her 20s has with her mother and her life satisfaction ranking. Below is a list of women who fit into each of four level of interaction. Conduct a One-Way ANOVA on the data to determine if a relationship exists.
No Interaction
Low Interaction
Moderate Interaction
High Interaction
2
3
3
9
4
3
10
10
4
5
2
8
4
1
1
5
7
2
2
8
8
2
3
4
1
7
10
9
1
8
8
4
8
6
4
1
4
5
3
8
No Interaction
Low Interaction
Moderate Interaction
High Interaction
2
3
3
9
4
3
10
10
4
5
2
8
4
1
1
5
7
2
2
8
8
2
3
4
1
7
10
9
1
8
8
4
8
6
4
1
4
5
3
8
Explanation / Answer
To calculate One-way anova we see the anova table
ANOVA Table for One-Way Analysis of Variance
Source
Sum of Squares
Df
Mean Square
F-Ratio
P-Value
Between groups
SSR
k - 1
MSR = SSR/(k-1)
F = MSR/MSE
Within groups
SSE
n - k
MSE = SSE/(n-k)
Total (Corr.)
SST
n - 1
We now calculate Treatment means for given 4 treatmeants. Ler us take these to be A(No Interaction), B(Low Interaction), C(Moderate Interaction) and D(High Interaction)
Thus we calculate treatment means which come out to be
Mean(A)=4.3
Mean(B)=4.2
Mean(C)=4.6
Mean(D)=6.6
And overall mean
u=4.92
The estimated effects Ai are the difference between the ”estimated treatment mean” and the ”estimated overall mean”, i.e. Ai = Meani u
Thus
A1=-0.62 A2=-0.72 A3=-0.32 A4=1.68
Now we calculate degrees of freedom
We have 4 different Treatments dftreat = 4 1 = 3
We have 10 different measurements dftot = 10 1 = 9
dftreat + dfres = dftot dfres = 9 3 = 6
To calculate SS
SStreat = ”sum of squares between treatment groups” = XAi^2*measures = 38.275
SSres = ”sum of squares within treatment groups”= 292.5
SStot = ”Total sum of squares” = 330.775
For the column MS (mean square) just remember the rule MS = SS/df, then:
MStreat = SStreat/dftreat = 12.7583
MSres = SSres/dfres = 8.125
Putting all this in anova table we calculate F value
F = MStreat/MSres =1.57026
The F-ratio value is 1.57026. The p-value is .213434. The result is not significant at p < .05.
Source
Sum of Squares
Df
Mean Square
F-Ratio
P-Value
Between groups
SSR
k - 1
MSR = SSR/(k-1)
F = MSR/MSE
Within groups
SSE
n - k
MSE = SSE/(n-k)
Total (Corr.)
SST
n - 1
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