Research Project Analysis: Comparing Graduate Employment and Income

This report presents an analysis of a research project examining the employment status and income levels of graduates from four different disciplines. The study employs statistical methods, including ANOVA and t-tests, to compare groups and test hypotheses. The analysis investigates whether there are significant differences in employment status and annual income among the graduate groups, considering assumptions of normality and homogeneity of variance. The report also compares the annual income between commerce and health science graduates, as well as the proportion of employed graduates in law and engineering disciplines. The findings indicate no significant differences in overall employment status, but do show disparities in income levels. The report concludes with a summary of the key insights derived from the statistical analyses and offers conclusions on the employment and income trends across the graduate groups.

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

Research project analysis 2
Question one
The first test of the research project was to establish whether there significant differences in
employment status in the four groups of students. Testing for the presence of difference can
attract the use of t-test or ANOVA. However since the variables are more than two (four
graduate schools), the use of analysis of variance will be appropriate. Prior to using analysis of
variance, some assumptions need to be made and verified. The assumptions are as listed below;
• The data is normally distributed
• There is independence of variables
• There is homogeneity of variance
 The data is randomly collected
Test of normality can either be done using box-plot analysis of drawing histograms. In this case a
histogram has been drawn as below;

Research project analysis 3
Figure 11 1.5 2 2.5 3
employment status
Figure 2

Research project analysis 4
The assumption of normality has been confirmed from the histogram and box-plot above. As can
be observed, the distribution of employment status has taken a bell-shaped curve depicting a
perfect normal distribution. It is at this point after confirming that the data is normally distributed
that an analysis of variance is employed to establish whether there is difference in employment
status of among the four graduate schools.
Below is the test hypothesis;
Hypothesis
Null hypothesis: Employment status among the four groups of graduates is the same.
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 Average Variance
health science 200 389 1.945 0.464296
commerce 179 365 2.03910
6
0.206327
law 121 248 2.04958
7
0.330854
engineering 148 299 2.02027 0.496185
ANOVA
Source of
Variation
SS df MS F P-value F crit
Between
Groups
1.198494 3 0.39949
8
1.06417 0.36366
9
2.618736
Within Groups 241.7629 644 0.37540
8
Total 242.9614 647
Table 1

Research project analysis 5
In any ANOVA test, prior to making decision and hence conclusion, a comparison is done
between the p-value calculated and the level of significance. The decision to reject the null
hypothesis is arrived at if the p-value is less than the level of significance. In this case, the results
show that the level of significance (0.05) is less than the p-value computed (.36). The decision is
to accept the null hypothesis and reject the alternative hypothesis. It is concluded that that
employment status among the four groups of graduates is the same.
QUESTION TWO
Testing whether there differences among the four groups in terms of annual income?
Testing for the presence of difference can attract the use of t-test or ANOVA. However since the
variables are more than two (four graduate schools), the use of analysis of variance will be
appropriate. Prior to using analysis of variance, some assumptions need to be made and verified.
The assumptions are as listed below;
• The data is normally distributed
• There is independence of variables
• There is homogeneity of variance
 The data is randomly collected
Test of normality can either be done using box-plot analysis of drawing histograms. In this case a
histogram has been drawn as below;

Research project analysis 6
35000-
45000 45001-
55000 55001-
65000 65001-
75000 75001-
85000 85001-
95000
0
50
100
150
200
250
Figure 2
Box-plot to check normality
20,000 40,000 60,000 80,000 100000
annual income
Figure 3

Research project analysis 7
The assumption of normality has been confirmed from the histogram and box-plot above. As can
be observed, the distribution of income of students has shown a long tail to the right depicting a
perfect skewed distribution. It is at this point after confirming that the data is normally
distributed that an analysis of variance is employed to establish whether there is difference in
employment status of among the four graduate schools. Though anova test will be used in a data
that is not normally distributed, there are going to be limitations.
The test hypothesis is therefore as below;
Hypothesis
Null hypothesis: Annual income among the four groups of graduates is equal.
Alternative hypothesis: At least one group is different
At 0.05 level of significance the results are as below;
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+1 404

Research project analysis 8
0
Table 2
Prior to making decision and hence conclusion, a comparison is done between the p-value
calculated and the level of significance. The decision to reject the null hypothesis is arrived at if
the p-value is less than the level of significance. In this case, the results show that the level of
significance (0.05) is greater than the p-value computed (.00). The decision is to reject the null
hypothesis and accept the alternative hypothesis. It is concluded that at least one or more groups
is different in terms of income.
The limitation of using anova in this case is that it is very sensitive to normality and therefore the
results obtained might not be too accurate.
QUESTION THREE
Test for the difference in annual income between commerce and health science graduates
The third test of the research project was to establish whether there significant difference in
annual income between commerce and health science graduates. Testing for the presence of
difference can attract the use of t-test or ANOVA. However since the variables are only two
(commerce and health), the use of analysis of paired t-test will be appropriate. Prior to using t-
test analysis, some assumptions need to be made and verified. The assumptions are as listed
below;
• The data is normally distributed
• There is independence of variables
• There is homogeneity of variance

Research project analysis 9
 The data is randomly collected
Test of normality can either be done using box-plot analysis of drawing histograms. In this case a
histogram has been drawn as below;
35000-
45000 45001-
55000 55001-
65000 65001-
75000 75001-
85000 85001-
95000
0
50
100
150
200
250
Figure 3
The assumption of normality has been confirmed from the histogram above. As can be observed,
the distribution of income of students has shown a long tail to the right depicting a perfect
skewed distribution. It is at this point after confirming that the data is normally distributed that
an analysis of variance is employed to establish whether there is difference in employment status
of among the four graduate schools. Though t-test test will be used in a data that is not normally
distributed, there are going to be limitations.
The test hypothesis is therefore as below;
Hypothesis
Null hypothesis: There is no significant difference in annual income between commerce and
health science graduates.

Research project analysis 10
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
Prior to making decision and hence conclusion, a comparison is done between the p-value
calculated and the level of significance. The decision to reject the null hypothesis is arrived at if
the p-value is less than the level of significance. In this case, the results show that the level of
significance (0.05) is greater than the p-value computed (.01). The decision is to reject the null
hypothesis and accept the alternative hypothesis. The conclusion is therefore that Income of
Commerce graduates lower than income of Health Science graduates
QUESTION FOUR

Research project analysis 11
Testing whether the proportion of employed graduates in Law discipline different from the
proportion of employed graduates in engineering discipline?
A contingency table has been used to tabulate the number of graduates who are employed from
all the four schools in the university. This has been done using pivot table in excel. The results
are as below;
Row Labels Count of health
sciences
commerce 142
Engineering 75
health
sciences
106
law 81
Grand
Total
404
Table 4
The table above shows the distribution of graduates who are employed in every school. As can
be observed, the highest number of those who are employed come from the school of commerce.
The proportion of this group is 0.35. Those who are graduates of health sciences constitute to
0.26 in terms of proportion. That the fraction of students of law school employed is 0.2 while the
proportion of their counterparts in school of engineering is 0.19. Comparing the two, it can be
concluded that there is no significant difference between the two proportions.
The proportions are as calculated below;
proportion of employed law 0.20049505
proportion of employed
engineering
0.185643564
Table 4
From the table above, it can be observed that the fraction of students of law school employed is
0.2 while the proportion of their counterparts in school of engineering is 0.19. Comparing the

Research project analysis 12
two, it can be concluded that there is no significant difference between the two proportions.
CONCLUSION
The research project came out with several insights from the various analyses that enabled it
make the following conclusions. To start with among all the disciplines, employment status is
normally distributed. There are no glaring differences in employment status among the four
groups. To add on, earnings from the four groups of students are also not normally distributed.
This has been illustrated by the shape of the histogram. The distribution is skewed in that those
who earn less are the majority while those who earn more are the minority. Lastly, the proportion
of the students who are employed from law school is almost the same as the proportion of
students in school of engineering. The proportion of students who are from engineering
discipline is 0.19 while the proportion of students who are employed from the law school is 0.2.
This is very insignificant as the difference in proportion is just 0.01.