Question: Provide a narrative discussion of both tables. Include Eta, the Levene
ID: 3264663 • Letter: Q
Question
Question: Provide a narrative discussion of both tables. Include Eta, the Levene test, and the observed change in the F-value of current family income when moving from a one-way to a two-way analysis. DATA BELOW
Table 1 shows the results of a one-way ANOVA based on current family income, including Eta.
ANOVA
life satisfaction
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
18.618
6
3.103
4.193
.001
Within Groups
164.304
222
.740
Total
182.922
228
Tests of Between-Subjects Effects
Dependent Variable: life satisfaction
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Partial Eta Squared
Corrected Model
18.618a
6
3.103
4.193
.001
.102
Intercept
1934.535
1
1934.535
2613.859
.000
.922
income
18.618
6
3.103
4.193
.001
.102
Error
164.304
222
.740
Total
5492.225
229
Corrected Total
182.922
228
a. R Squared = .102 (Adjusted R Squared = .078)
Table 2 shows the results of a two-way ANOVA based on both current family income and gender, including Eta
Tests of Between-Subjects Effects
Dependent Variable: life satisfaction
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Partial Eta Squared
Corrected Model
25.957a
13
1.997
2.735
.001
.142
Intercept
1765.270
1
1765.270
2417.945
.000
.918
income
18.663
6
3.110
4.260
.000
.106
sex
1.998
1
1.998
2.737
.100
.013
income * sex
4.395
6
.733
1.003
.424
.027
Error
156.965
215
.730
Total
5492.225
229
Corrected Total
182.922
228
a. R Squared = .142 (Adjusted R Squared = .090)
ANOVA
life satisfaction
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
18.618
6
3.103
4.193
.001
Within Groups
164.304
222
.740
Total
182.922
228
Explanation / Answer
Here from the first table we can say that the oveall model is significant at 5% level of significance.
Since p-value = 0.001
Test statistic = 4.193
P-value <alpha
Reject H0 at 5% level of significance.
We get significant result about ANOVA.
Now in the second table :
Dependent variable is life satisfaction.
And we see that corrected model and income are significant variable since p-value for these variables are 0.001 and 0.001 respectively.
P-value < alpha
So reject H0 at 5% level of significance.
Partial eta squared = 0.102
R-sq = 0.102
It expresses the proportion of variation in dependent variable which is explained by independent variables.
In table 2 corrected model and income are significant variables whereas sex and income*sex are insignificant variables.
Partial eta squared :
Corrected model = 0.142
income = 0.106
sex = 0.013
income*tax = 0.027
R-sq = 0.142
It expresses the proportion of variation in dependent variable which is explained by independent variables.
Eta squared measures the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable.
Partial eta squared is a similar measure in which the effects of other independent variables and interactions are partialled out.
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