Analysis of Variance

Running Head: ANALYSIS OF VARIANCE 1
Analysis of Variance
Student Name Here
Institution
ANALYSIS OF VARIANCE 2
Table of Contents
Introduction ............................................................................................................................................... 4
Research Question .................................................................................................................................. 4
Hypotheses ................................................................................................................................................ 4
Methodology .............................................................................................................................................. 4
Variables .................................................................................................................................................... 5
Results ................................................................... …………………………………………………………………………………......5
Conclusion ................................................................................................................................................. 6
Social Implication of the study .............................................................................................................. 6
References ................................................................................................................................................ 7
Appendix: SPSS Output (Factoring Analysis of Variance) ............................................................ 8
ANALYSIS OF VARIANCE 3
FACTORING ANALYSIS OF VARIANCE
4
Introduction
With the use of Afrobarometer 2015 dataset, this paper tests to determine whether there
are statistical significant differences between economic status averages of education condition
groups. Therefore, the analysis of variance is the most appropriate to conduct the test. According
to Lane (2013), analysis of variance (ANOVA) is a statistical method utilized to test differences
between two or more means. The independent variable must be categorical and dependent
variable continuous (interval or ratio level) for the test to give a valid results.
Research Question
Is there a statistically significant difference on economic status by education condition?
Hypotheses
H
0
: There is not statistically significant difference on economic status by education condition.
H
a
: There is a statistically significant difference on economic status by education condition.
Methodology
Two variables were selected to perform the analysis. They consist of Education Condition
allotted in column BA (Educ Cond) and column BC (Economy) of the Afrobaromter dataset.
Education was categorical whereas Economy variable was continuous. The two variables were
imported into SPPS for testing. Groups were classified into Certificate, Diploma, and Degree
holders. In addition, each group comprised of unrelated observations Laerd Statistics (2017)
proposes that for Anova to be valid, there must be independence of observations between each
group.
FACTORING ANALYSIS OF VARIANCE
5
Variables
Education condition is an independent variable, measured categorically for Certificate=1,
Diploma=2, and Degree=3. On the other hand, Economic status is the dependent variable and is
measured on an interval scale such as 11.0.
Results
Analysis of variance was performed, each group having 2147 observations. The results of
the test were displayed in table 1.1 and table set 2.1 in the appendix section. Table 1.1 shows the
output of the ANOVA analysis and whether there is a statistically significant difference among
group means. Based on the results, the significance value is 0.019 p = .019), it is below 0.05,
F=25.031. Hence, there is a statistically significant difference in the mean of economic status
between person’s having different education condition.
In addition, a simplified interpretation of descriptive result, table set 2.1a confirms that
there is a mean difference in economic status among group of education condition. Degree
holders scored the highest mean, with certificate holder having the lowest mean. Results of
Multiple comparison in Table set 2.1c (appendix section), show that there is statistically
significant difference in economic status between the group that holds a certificate and
Diploma/Degree (p = 0.00), as well as between the Diploma and Degree (p = 0.019)
Table 1.1: Analysis of Variance :(Source: SPSS)
ANOVA
Economy
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
644.406
2
322.203
25.031
.019
Within Groups
82871.558
6438
12.872
Total
83515.965
6440
FACTORING ANALYSIS OF VARIANCE
6
Conclusion
We can make a conclusion that there is a statistically significant difference between
economic status averages for groups with different education condition. Therefore, the null
hypothesis is rejected and an alternative hypothesis accepted.
Social Implication of the study
The study suggests that education condition of a person determines their economic status.
Numerous studies have also established that education can change a person’s socioeconomic
status, for instance, degree holders are considered to have better economic status as compared to
diploma and certificate holders. A study by (Turcinkova, 2012) found out that attained level of
education effects a person’s income situation. He further claims that Czech Republic’s citizens
with higher education attainment are economically stable compared to those with no or lower
education.
FACTORING ANALYSIS OF VARIANCE
7
References
Lane, D. M. (2013). Introduction . In Analysis of Variance (pp. 1-4).
Statistics, L. (2013, January). One-way ANOVA in SPSS Statistics.
Turcinkova, J. (2012, October 5). ScienceDirect. Retrieved from Does the Attained Level of
Education Affect the Income Situation of Households?:
http://www.sciencedirect.com/science/article/pii/S1877042812040578
FACTORING ANALYSIS OF VARIANCE
8
Appendix: SPSS Output (Factoring Analysis of Variance)
Table set 2.1 Factoring Analysis of Variance (Source: SPSS)
a
Descriptives
Economy
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Lower Bound
Upper Bound
Cert
2147
9.21
3.796
.082
9.05
9.37
1
Dip
2147
9.50
3. 806
.082
9.34
9.66
4
Degree
2147
9.97
3. 118
.067
9.84
10.11
5
Total
6441
9.56
3.601
.045
9.47
9.65
1
b
ANOVA
Economy
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
644.406
2
322.203
25.031
.019
Within Groups
82871.558
6438
12.872
Total
83515.965
6440
C
Post Hoc Tests
Multiple Comparisons
Dependent Variable: Economy
Tukey HSD
(I) Education
(J) Education
Mean Difference
(I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Cert
Diploma
-.768
*
.110
.000
-1.02
-.51
Degree
-.296
*
.110
.019
-.55
-.04
Diploma
Cert
.768
*
.110
.000
.51
1.02
Degree
.472
*
.110
.000
.22
.73
Degree
Cert
.296
*
.110
.019
.04
.55
Diploma
-.472
*
.110
.000
-.73
-.22
*. The mean difference is significant at the 0.05 level.

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