educations at 0.05 level of significance?
Step 1)
𝐻
0
: 𝜇
1
= 𝜇
2
= 𝜇
3
= 𝜇
4
= 𝜇
5
𝐻
1
: 𝑁?? 𝑎?? ?ℎ𝑒 ?𝑒𝑎?? 𝑎?𝑒 𝑒??𝑎?
1 = Did not complete high school
2 = High school degree
3 = Some college
4 = College degree
5 = Post-undergraduate degree
Step 2)
Find the mean for each group
Analyze >
Compare Means > Means…
Step 3)
In the ANOVA table, the p-value = 0.000 < 0.05
We reject the null hypothesis. We conclude that there is a significant difference in the mean
Household income among the 5 level of educations.
Report
Household income in thousands
Level of education
Mean
N
Std. Deviation
Did not complete high school
59.8662
1390
61.30036
High school degree
66.2071
1936
72.72591
Some college
70.1346
1360
81.03878
College degree
78.6502
1355
92.87753
Post-undergraduate degree
87.1699
359
94.79998
Total
69.4748
6400
78.71856
ANOVA
Household income in thousands
Sum of
Squares
df
Mean Square
F
Sig.
Between Groups
376079.699
4
94019.925
15.309
.000
Within Groups
39276042.251
6395
6141.680
Total
39652121.950
6399

17
Step 4)
Multiple Comparisons
Dependent Variable:
Household income in thousands
Tukey HSD
(I) Level of education
(J) Level of education
Mean
Difference
(I-J)
Std.
Error
Sig.
95% Confidence Interval
Lower
Bound
Upper
Bound
Did not complete high
school
High school degree
-6.34094
2.75515
.144
-13.8585
1.1766
Some college
-10.26837
*
2.98905
.005
-18.4242
-2.1126
College degree
-18.78400
*
2.99184
.000
-26.9474
-10.6206
Post-undergraduate
degree
-27.30373
*
4.63964
.000
-39.9632
-14.6442
High school degree
Did not complete high
school
6.34094
2.75515
.144
-1.1766
13.8585
Some college
-3.92743
2.77278
.617
-11.4931
3.6382
College degree
-12.44306
*
2.77578
.000
-20.0169
-4.8692
Post-undergraduate
degree
-20.96279
*
4.50334
.000
-33.2504
-8.6752
Some college
Did not complete high
school
10.26837
*
2.98905
.005
2.1126
18.4242
High school degree
3.92743
2.77278
.617
-3.6382
11.4931
College degree
-8.51563
*
3.00808
.038
-16.7233
-.3079
Post-undergraduate
degree
-17.03536
*
4.65013
.002
-29.7235
-4.3472
College degree
Did not complete high
school
18.78400
*
2.99184
.000
10.6206
26.9474
High school degree
12.44306
*
2.77578
.000
4.8692
20.0169
Some college
8.51563
*
3.00808
.038
.3079
16.7233
Post-undergraduate
degree
-8.51973
4.65192
.355
-21.2127
4.1733
Post-undergraduate
degree
Did not complete high
school
27.30373
*
4.63964
.000
14.6442
39.9632
High school degree
20.96279
*
4.50334
.000
8.6752
33.2504
Some college
17.03536
*
4.65013
.002
4.3472
29.7235
College degree
8.51973
4.65192
.355
-4.1733
21.2127
*. The mean difference is significant at the 0.05 level.
In Did not complete high school & High school degree, the hypothesis is
𝐻
0
: 𝜇
1
= 𝜇
2
𝐻
1
: 𝜇
1
≠ 𝜇
2
The mean difference = -6.34. P-value = 0.144 > 0.05
In High school degree & Some college, the hypothesis is
𝐻
0
: 𝜇
2
= 𝜇
3
𝐻
1
: 𝜇
2
≠ 𝜇
3

18
The mean difference = -3.93. P-value = 0.617 > 0.05
In College degree & Post-undergraduate degree, the hypothesis is
𝐻
0
: 𝜇
4
= 𝜇
5
𝐻
1
: 𝜇
4
≠ 𝜇
5
The mean difference = -8.52. P-value = 0.355 > 0.05
We do not reject the above null hypothesises. We do not have evidences to conclude that there
are significant differences between the means of Did not complete high school & High school
degree, High school degree & Some college, College degree & Post-undergraduate degree.
All other p-values< 0.05. We reject these null hypotheses. We have enough evidence to conclude
that there are significant differences between Did not complete high school and Some College,
between Did not complete high school and College degree, between Did not complete high school
and Post-undergraduate degree, High school degree and College degree, High school degree and
Post-undergraduate degree, Some college and College degree, Some college and Post-
undergraduate degree.

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