Retention vs. Graduation Rates: An Analysis of Online Universities

This report examines the association between retention rates and graduation rates in online universities in the United States, using a dataset of 29 colleges. The study aims to determine if there's a link between student retention and the likelihood of graduation. The report includes a descriptive analysis, calculating mean, standard deviation, and coefficient of variation for both retention and graduation rates. A scatter plot is used to assess linearity and homoscedasticity, and inferential statistics, including regression analysis and ANOVA, are employed to test the hypothesis. The results reveal a positive correlation between the two variables, with a regression equation provided to predict graduation rates based on retention rates. The discussion analyzes the findings, highlighting the implications for online universities and potential factors influencing graduation rates beyond retention. The report concludes with recommendations for improving graduation rates by addressing factors such as socioeconomic status and employment status.

Association Between Retention Rate And Graduation Rate 1
ASSOCIATION BETWEEN RETENTION RATE AND GRADUATION RATE FOR ONLINE
UNIVERSITIES IN UNITED STATES
By Student’s Name
Code + Course Name
Professor’s Name
University Name
City, State
Date

Association Between Retention Rate And Graduation Rate 2
Table of Contents
Table of Contents.............................................................................................................................2
Purpose of the Study........................................................................................................................3
Background......................................................................................................................................3
Method.............................................................................................................................................4
Results..............................................................................................................................................5
Descriptive Analysis........................................................................................................................5
Inferential Statistics.........................................................................................................................7
Discussion......................................................................................................................................10
Recommendations..........................................................................................................................10
References......................................................................................................................................12

Association Between Retention Rate And Graduation Rate 3
Purpose of the Study
The aim of this report was to give insight students may opt to drop out of virtual learning
programs with a specific aim of identifying possible factors that may have an effect on student’s
decision to drop out of online programs. This is against a backdrop of recent reports of the
continued popularity of online learning for institutions of higher learning across the United
States. However, there several question on efficiency in particular of slow learning students. This
report engaged on that issue by examining recent studies on the success of online colleges.
Hence the aim of this report is to determine the link between rate of retention and rate of
graduation of online universities in United States.
Background
In the American higher education, virtual learning is not irregular. Allen and Seaman
(2015) report that according to national data provided in the fall of 2013 semester over 5 million
of all higher education learners in the US engaged in at least one online course. There are
suggestions virtual learning will continue to grow in future. According to Jaggars (2011),
numerous research reviews indicate that withdrawal rates of mid-semester for online programs
may be higher than those that require a student to attend a physical classroom. The study by
Levy’s (2007) reveals that there is a higher risk slow learning college student’s dropout than that
of fast learning students. Less experienced students who are at the initial stages of the semester
of their course are more likely to drop out of the program. The author stated that learners in the
initial stages of their studies feel less prepared to handle the rigorous academic programs.
Conversely, learners who have stayed longer in the program would feel better motivated to finish
the programs since they have invested much time and effort on the course. The input of time and

Association Between Retention Rate And Graduation Rate 4
effort is a major factor of graduation rate. The understanding that learners are likely to drop out
at any stage of learning due to other factors shows that it is important to examine ways and
means of improving graduation rate. To increase retention rates, it’s essential to clearly
comprehend why students drop out of online programs. Accordingly, Mansfield, O’Leary and
Webb (2011) note that some studies postulate school dropout is more of a progression than an
occurrence and as such it would be caused by a number of aspects. In the event that stakeholders
comprehend better the reason learners drop out of their learning programs, endeavors to
intervene and assist overcome the challenge and probably predict slow learning students by
offering them support may be implemented.
Method
The higher education sector has seen an influx of more online universities in the recent
past. It has become necessary to examine why this is so. Learners’ success rate statistics are
considered the major parameters of institutional performance. Over the years they have been
considered as a benchmark of assessing the overall quality of students’ studies and the
intellectual component in addition to how well students relate with others in campus and how
effective the school administration delivers to students’ expectations and needs.
It is important to determine the link rate of retention and rate of graduation in some of the
major online universities in the US. The Online Education Database is an autonomous
organization whose purpose is to construct a broad list of endorsed online colleges based in
United States. This report comprised of a sample list of 29 online colleges obtained from Online
Education Database. The data was based on rate of retention and rate of graduation of the
colleges. The hypothesis formulated for this report was:
H0: There is no link between retention rate and graduation rate

Association Between Retention Rate And Graduation Rate 5
HA: There is a link between retention rate and graduation rate
The dependent variable (Y) was graduation rate while the independent variable (X) was
retention rate. To determine the association between retention rate and graduation rate a simple
regression was done on the data. A simple regression model examines the strength, shape and
direction between two variables by making use of scatter plot and correlation coefficient. In this
report the regression model was formulated as below:
Y = β0 + β1X+ Ɛ
Where: Y: Graduation rate
Β0: is the y intercept
Β1: is the regression (beta) coefficient
Ɛ: Error term
Ɛ: Error term - Regression standard error (Std. Error of the Estimate) is the average
forecast error (difference between actual and values predicted by the estimated equation). Small
values indicate that the estimated model closely fits the observed data.
Results
The section below shows the results obtained from the analysis that was carried out to
determine the association between retention rate and graduation rate of the 29 sampled virtual
colleges in US. It includes the descriptive analysis (mean, standard deviation, coefficient of
variation, minimum and maximum), scatter plot and inferential statistics. The inferential
statistics section includes the regression results, Analysis of Variance (ANOVA) and the
regression equation that would be used to determine or forecast the graduation rate based on
retention rate parameter.

Association Between Retention Rate And Graduation Rate 6
Descriptive Analysis
Descriptive statistics were used to test for normality of the data. Dispersion and measures
of central tendency like mean and standard deviation were computed to see if it concurred with
the research hypothesis.
Table 1: Descriptive Statistics
Retention
Rate
Graduation
Rate
Mean 57.41 41.76
Stdev 23.24 9.87
Coefficient of
variation
40.48 23.63
Minimum 4 25
Maximum 100 61
According to the descriptive statistics in table 1 above the average retention rate was
57.41% associated with a standard deviation from the mean of 23.24%. In terms of graduation
rate, the average rate of graduation for the online colleges sampled was 41.76% associated with a
standard deviation of 9.87%. This implies that slightly over forty per cent of students who enroll
in virtual learning eventually graduate. In this report, it was also important to determine the
coefficient of variation. This would reveal the degree of variability and as such a low variability
is preferred. By comparison, retention rate revealed a higher variability (40.48%) than graduation
rate (9.87%). These results implied that it would be expected that the retention rate would vary at
a higher rate given a different sample compared with graduation rate. The graduation rate would
be expected to vary at less than ten per cent of the time. In addition, the results revealed a
maximum retention rate of one hundred per cent while the maximum graduation rate was sixty-
one per cent.

Association Between Retention Rate And Graduation Rate 7
Figure 1: Scatter Diagram
The scatter diagram was used to test for the linearity and homoscedasticity assumptions
of the regression model. This was done by plotting the values of retention rate against those of
graduation rate. The graph of the RR and GR in figure 1 above revealed a random array of dots
along the line of best fit and there was no curve in this graph therefore the assumption of
linearity was not violated (Hair et al., 2011). The graph did not reveal unequal variances hence
the assumption of homoscedasticity was not violated. According to the scatter diagram the line
of best fit revealed some form of positive linear relationship between rate of retention and rate of
graduation. This implied that the higher the retention rate the higher the graduation rate.
Inferential Statistics
Inferential statistics was used to draw implications from the data. The hypothesis was
achieved by calculating the Pearson product moment correlation coefficient of the variables. This

Association Between Retention Rate And Graduation Rate 8
established whether the findings indicate a strong or weak, positive or negative correlation.
According to table 2 below, the results revealed an R square or coefficient of determination of
0.449 (44.9%) that translates to a correlation coefficient (r) of 0.6702 (67.02%). This suggested a
positive relationship between retention rate and graduation rate.
Table 2: Regression Statistics
Regression Statistics
Multiple R 0.67024
5
R Square 0.44922
8
Adjusted R Square 0.42882
9
Standard Error 7.45610
5
Observations 29
It was also important to determine whether the regression equation would be adequate to
predict graduation rate based on retention rate parameter. This was done by assessing the
ANOVA.
Table 3: ANOVA
ANOVA
df SS MS F Significance F
Regression 1 1,224.2
9
1,224.2
9
22.0
2
0.0
0
Residual 27 1,501.0
2
55.5
9
Total 28 2,725.3
1
The ANOVA table above revealed an F statistics of 22.02 of the regression that was
associated with a p- value of p< .01. This suggested that the regression model would be used to
predict graduation rate since the alpha level was less than 5%.

Association Between Retention Rate And Graduation Rate 9
Table 4: Regression Analysis
Coefficients Standard Error t Stat P-value
Intercept 25.42 3.75 6.79 0.00
RR (%) 0.28 0.06 4.69 0.00
The p-value of the regression was less than .05 hence the decision was to reject the null
hypothesis and conclude that there is a link between retention rate and graduation rate (p < .05).
Regression analysis revealed the estimated equation for predicting graduation rate based on the
single parameter retention rate. To substitute with the equation stated earlier in this report (Y = β0
+ β1X+ Ɛ), the equation to predict graduation rate was as below:
Y (Graduation rate) = 25.42 + 0.28 (retention rate)
The intercept (25.42) which is the population intercept revealed that when retention rate
is zero, it would be expected the graduation rate to be 25.42 per cent. However, this result may
have no particular meaning in the current report. To interpret the regression (beta) coefficient or
slope of the graph showed an ascending straight line (β1 < 0) suggesting a positive linear
relationship between the two variables. According to the slope of the graph, it would be expected
that when retention rate increases by one per cent graduation rate would increase by 0.28 per
cent. This is rather a minimal increase rate that would suggest that other variables may exist that
predict graduation rate hence the regression does not provide a good fit.
As the president of South University, I would have major concerns on the performance of
my college. This is because after reviewing the sample data although my institution recorded a
retention rate of slightly over fifty per cent compared with overall minimum of 4%, the
university only achieved a graduation rate of 7% better than the rest of the universities.
Conversely, as president of University of Phoenix I would not have major concerns on
graduation rate since although the institution recorded the worst or lowest retention rate (4%) it

Association Between Retention Rate And Graduation Rate 10
was still slightly better than South University in terms of graduation rate percentile having done
better than 10% of other universities.
Discussion
Results in this report revealed that the average retention rate from the sample was 57 %
and a standard of 23%. The average graduation rate was 41%. These results were a bit worrying
since they suggested that less than half of the students that enrol in online programs actually
graduate. The degree of variability tested using the coefficient of determination suggested that
42% of the variance in graduation rate can be explained using retention rate. The other 58% can
be explained using other parameters such as social economic status, marital status, age or
employment status. Previous research has shown that these dimensions have a cause and effect
on the graduation rate of students who undergo online programs. This suggests there are other
variables that can be used to forecast graduation rate. This showed a limitation in the analysis
that had only one independent variable. Although the regression model was found to be
statistically significant, the unit change in retention rate could only be explained by 0.28 changes
in retention rate. This situation was another limitation. In addition, there was deficiency in
finding recent empirical review that accessed graduation rate based on retention rate. Most recent
studies focussed on retention rate as the dependent variable
Recommendations
It is recommended that another report be prepared that includes other independent
variables so as to improve on the results of the current report on analysis. It is further
recommended that a larger sample size than the one used in this report as well as an insight into a
possible moderating variable that may influence the predictability of graduation rate be examined
in future reports.

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References
Allen, I. E., & Seaman, J. (February. 2015). Grade Level: Tracking Online Education in the
United States. Babson Survey Research Group.
Jaggars, S. S. (2011, January). Online learning: Does it help low income and underprepared
students? (CCRC Working Paper No. 26) Retrieved from http://ccrc.tc.columbia.edu/media/k2/
attachments/online-learning-help-students.pdf
Levy, Y. (2007). Comparing dropouts and persistence in e-learning courses. Computers &
Education, 48, 185-204. Retrieved from
http://www.qou.edu/arabic/researchProgram/eLearningResearchs/ eLDropout.pdf
Mansfield, M., O’Leary, E., & Webb, S. (2011). Retention in Higher Education: Faculty and
Student Perceptions of Retention Programs and Factors Impacting Attrition Rates. A Research
Report Presented to the School of Education Indiana University. South Bend. Retrieved from
http://files.eric.ed.gov/fulltext/ED521416.pdf