Statistical Report: Analyzing Graduate Employment and Income Data

This report presents a statistical analysis of a research project examining the employment status and income levels of graduates from various disciplines, including health science, commerce, law, and engineering. The analysis employs Analysis of Variance (ANOVA) to compare employment status and annual income across the groups, and t-tests to compare the income of commerce and health science graduates. The report also investigates the proportions of employed graduates in law and engineering. The analysis reveals that while employment status is normally distributed across the groups, annual income is skewed. The study concludes that there is no significant difference in overall employment status among the four groups, but there are income differences between the groups, with commerce graduates earning less than health science graduates. The proportions of employed graduates in law and engineering are found to be similar.

Research project analysis 1
Student’s name
Professor
Course title
Date
Business report

Research project analysis 2
Question one
Are there differences in employment status among the four groups of graduates?
To test whether there are differences in more than two variables, then an analysis of variance is
employed. However prior to ANOVA test, there are assumptions that must be made. They
include,
• The data is normally distributed
• There is independence of variables
• There is homogeneity of variance
 The data is randomly collected
To test whether the data is normally distributed, a histogram is constructed to have a graphical
view of the same.

Research project analysis 3
Figure 1
From the figure above, it can be observed that the employment status of the graduates is
normally distributed. The curve is bell-shaped indicating perfect normal distribution. Since it has
been confirmed that the data is normally distributed, an analysis of variance is now employed to
test whether there differences in employment status among the four groups of graduates.
The ANOVA tests for equality of means among variables. The test hypothesis is therefore as
below;
Hypothesis
Null hypothesis: There is no significant difference in employment status among the four groups
of graduates.
Alternative hypothesis: At least one group is different
At 0.05 level of significance, the results are as below;
Anova: Single Factor
SUMMARY
Groups Count Sum
Averag
e
Varianc
e
health science 200 389 1.945
0.46429
6
commerce 179 365
2.03910
6
0.20632
7
law 121 248
2.04958
7
0.33085
4
engineering 148 299 2.02027
0.49618
5
ANOVA
Source of
Variation SS df MS F P-value F crit
Between 1.19849 3 0.39949 1.06417 0.36366 2.61873

Research project analysis 4
Groups 4 8 9 6
Within
Groups
241.762
9 644
0.37540
8
Total
242.961
4 647
Table 1
For the research to make decision, the p-value computed and the level of significance are
compared. From the results tabulated above, it can be observed that the p-value computed 0.36 is
more than the level of significance which is 0.05. The decision rule therefore is to accept the null
hypothesis and reject the alternative. The conclusion is therefore that there is no significant in
employment status among the four groups of graduates.
QUESTION TWO
Are there differences among the four groups?
To test whether there are differences in more than two variables, then an analysis of variance is
employed. However prior to ANOVA test, there are assumptions that must be made. They
include,
• The data is normally distributed
• There is independence of variables
• There is homogeneity of variance
 The data is randomly collected
To test whether the data is normally distributed, a histogram is constructed to have a graphical
view of the same.

Research project analysis 5
35000-
45000 45001-
55000 55001-
65000 65001-
75000 75001-
85000 85001-
95000
0
50
100
150
200
250
Figure 2
It can be observed that the annual income is not normally distributed. The distribution is skewed
to the left. Those who are earning less are more while those who are earning more are very few.
This kind of distribution can only be analyzed through non-parametric tests which are usually not
sensitive to normality. However, the research project employed ANOVA test which is a
parametric test. This off course has limitations.
The ANOVA tests for equality of means among variables. The test hypothesis is therefore as
below;
Hypothesis
Null hypothesis: There is no significant difference in annual income among the four groups of
graduates.
Alternative hypothesis: At least one group is different
At 0.05 level of significance, the results are as below;

Research project analysis 6
SUMMARY
Groups Count Sum Average
Varianc
e
health
science 107
442106
2
41318.3
4
1.01E+0
8
commerce 142
614839
2
43298.5
4
8550784
9
law 81
478653
2
59092.9
9
1.76E+0
8
engineering 75
475591
3
63412.1
7
2.13E+0
8
ANOVA
Source of
Variation SS df MS F
P-
value F crit
Between
Groups
3.46E+1
0 3
1.15E+1
0 87.942
9.61E-
44
2.62715
8
Within
Groups
5.26E+1
0 401
1.31E+0
8
Total
8.71E+1
0 404
Table 2
In making decision, the p-value computed and the level of significance are compared. From the
results tabulated above, it can be observed that the p-value computed 0.00 is less than the level of
significance which is 0.05. The decision rule therefore is to reject the null hypothesis and accept
the alternative. The conclusion is therefore that at least one or more groups have different income
levels.
The limitation of using a parametric test on a data that is not normally distributed is that since
they are sensitive to normality, the results obtained might not be very accurate.
QUESTION THREE
Test for the difference in annual income between commerce and health science graduates

Research project analysis 7
To test for the difference in means of two variables, then a t-test is appropriate. T-test unlike
anova, tests for difference between two variables and not more than two. Since t-test is also
sensitive to normality, the data being analyzed must be normally distributed. Apart from
normality other assumptions include that the data should have been randomly selected,
independent and has homogeneity of variance. As has been established above using a histogram,
the data is not normally distributed as shown below;
35000-
45000 45001-
55000 55001-
65000 65001-
75000 75001-
85000 85001-
95000
0
50
100
150
200
250
Figure 3
The t-test normally tests the hypothesis that there is no significant difference in the means of any
two variables; therefore the test hypothesis is as below;
Hypothesis
Null hypothesis: There is no significant difference in annual income between commerce and
health science graduates.

Research project analysis 8
Alternative hypothesis: Income of Commerce graduates lower than income of Health Science
graduates
At 0.05 level of significance, the results are as below;
One-Sample Statistics
N Mean Std.
Deviation
Std. Error
Mean
Commerce
income
142 43298.5366 9247.04543 775.99481
One-Sample Test
Test Value = 41318
t df Sig. (2-
tailed)
Mean
Difference
95% Confidence Interval of
the Difference
Lower Upper
Commerce
income
2.552 141 .012 1980.53662 446.4480 3514.6252
Table 3
In making decision, the p-value computed and the level of significance are compared. From the
results tabulated above, it can be observed that the p-value computed 0.01 is less than the level of
significance which is 0.05. The decision rule therefore is to reject the null hypothesis and accept
the alternative. The conclusion is therefore that Income of Commerce graduates lower than
income of Health Science graduates
The limitation of using a parametric test on a data that is not normally distributed is that since
they are sensitive to normality, the results obtained might not be very accurate.
QUESTION FOUR

Research project analysis 9
Is the proportion of employed graduates in Law discipline different from the proportion of
employed graduates in engineering discipline?
For us to establish whether there is a difference in proportion between the two variables, then a
contingency table is employed. In excel, a pivot table is used as below. The results for the
proportion are tabulated in table 4 below.
Row Labels
Count of health
sciences
commerce 142
Engineering 75
health
sciences 106
law 81
Grand
Total 404
Table 4
The proportions are as calculated below;
proportion of employed law 0.20049505
proportion of employed
engineering 0.185643564
Table 4
It can be observed that the proportion of employed graduates in law discipline is not significantly
different to the proportion of graduates employed in engineering discipline. The difference is just
0.01.
CONCLUSION
From the analysis of the research project data, the research came up with several conclusions.
Firstly, the employment status is normally distributed across the four groups of graduates. This is
to mean that no graduate school has less or more proportion of employed or unemployed
individuals. In short the employment status is the same in all the graduate schools. Secondly, it

Research project analysis 10
can be concluded that the earnings among the students is not normally distributed. This has been
illustrated by the histogram. Those who earn less are many while those who earn more are less.
This has led to a skewed distribution in income. It has also been discovered that the proportion of
the employed students in law school is almost the same as the proportion of the employed in
school of engineering. There is no significant difference between the two proportions. Lastly, the
income of commerce graduates is lower than the income of health science graduates.