Estimation Model for Graduation Success – A Perspective with Student Retention in Online Courses
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Study on the relationship between student retention and graduation rates in online courses. Analysis of data from 29 colleges in the USA shows a positive impact of higher retention on graduation rate.
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Estimation Model for Graduation Success – A Perspective with Student Retention in Online Courses 1
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Abstract With rapid growth of online programs, fears of retention rates are increasing. Models have been developed to understand persistence of students in face-to-face situations, but many of these structures do not exist for an online environment. Since the dropout is much higher in online courses compared to face-to-face programs, the development of models to explain online retention is considered a priority. This study moved in this direction by studying the relationship between student retention and graduation rates for 29 colleges in the USA. Data analysis shows an important and positive impact of higher retention on graduation rate of the colleges. 2
Introduction The emphasis on higher education is increasingly focused on results rather than on structure. Increased retention is thus objective of many institutions to assess and improve the quality of its work. The dearth in a high percentage of retention has always challenged the education system and this problem appears to be particularly acute in online courses. This article creates a successful graduation percentage estimation model that takes retention rate in colleges as the only predictor. The scholar believes that the model can serve as a useful guide to choose the best university for the students in terms of successful completion of courses. Literature Review This document outlines an estimation model to analyse the success percentage of graduation in American colleges and universities. When it comes to online learning, the average number seems of attrition seems to be higher than the traditional courses (Allen, & Seaman, 2010, p.1-29).Although national statistics on distance learning are available, some claim that the retention rate is 10 to 20% higher in online courses than on-campus education (Boston & Ice, 2010, p. 1593–1599). E-learning is advancing from a marginal level in general education to an integrated part.In thehighereducationsector,lackofresilienceforastudentisacomplexand multidimensional problem. Strategies for students' success should be considered as an individual, institutional or program level (Cress, 2014, p. 294). Subsequent surveys have been extended with various questions and factors that affect the retention of the students and their 3
impact on the successful completion of programs (Halawa, Greene, & Mitchell, 2014, pp. 58– 65). This study discusses the straight impact of retention rate on graduation rate in colleges and universities of the USA (Talbert, 2012, p.22). Supplementary factors that affect student performance, and support the student to succeed in formal education have been excluded from the scope of this article (Xu, & Jaggars, 2013, p.5-25). A thorough review and validity of the regression model in the context of e-learning suggest a moderately fit exemplary that demonstrates the link between graduation rate and retention rate of the colleges (Tovar, 2014, p. 766–782). Methodology A total of 29 colleges and universities in the USA were selected for the present research. The sample size was less than 30, and this is an important limitation of the research (Schönbrodt, & Perugini, 2013, p. 609–612). Among the surveyed institutes, the average rate of retention was roughly 57.41%. The average rate of students successfully completing their graduation was approximately 41.76%. This indicated that a large majority (58.24%) of the students failed to successfully complete their programs to obtain graduation degree. Retention rate as an independent factor was used to estimate the graduation rate of students (dependent variable). A scatter plot was drawn for scrutinizing the linear relation between the variables. A linear regression model was constructed and the validity, as well as statistical significance, was investigated at a 5% level of significance (Montgomery, Peck, & Vining, 2012, p. 80- 100). 4
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Results a)Themeanrateofretentionoftheinstitutionsinthesamplewasassessedat approximately 57.41% with a standard deviation of 23.24%. The least percentage of retention was noted to be 4% and the maximum was 100% retention. The average graduation rate was estimated at 41.76% with a standard deviation of 9.86%. Minimum graduation rate was 25% and a maximum of 61% graduation rate was noted in the sample. b)A scatter diagram was constructed with graduation rate as the dependent and retention rate as the independent variable. Figure 1 presents the constructed scatter diagram. Figure1: Scatter Diagram with the graduation rate as the dependent and retention rate as the independent variable The scatter diagram indicates that the graduation rate in the colleges increased with retention rate. Pearson's Correlation coefficient between retention and graduation rate was 0.67, which indicated a moderately high positive linear relation. The relation was also found to be statistically significant. 5
c)The estimated regression equation was GRADUATION RATE = A*RETENTION RATE+B The intercept and the slope of the regression were calculated as below. A=n∗(∑xi∗yi)−(∑xi)∗(∑yi) n(∑xi 2)−(∑xi) 2=29∗(73831)−(1665)∗(1211) 29∗(110717)−(1665)2=124784 438568=0.2845 B=(∑yi)∗(∑xi 2)−(∑xi)∗(∑xi∗yi) n(∑xi 2)−(∑xi)2=(1211)∗(110717)−(1665)∗(73831) 29∗(110717)−(1665)2=11149672 438568=25.423 =>GRADUATION RATE = 0.2845*RETENTION RATE+24.423 The detailed calculation was done in excel and has been provided in the Appendix section of the report. d)The regression equation was GRADUATION RATE = 0.2845*RETENTION RATE+24.423 Theslopecoefficient=0.2845impliedthatfor1%alterationinretentionwill significantly alter the graduation rate by approximately 0.28 percentage. e)To answer this problem, a regression model was constructed in MS Excel. The retention rate was found to be a statistically significant predictor(t = 4.693, p < 0.05)of graduation rates of the institutes. The linear association of these two variables was also indicated a moderately high correlation(r = 0.67, p < 0.05). f)The residual plot and linear fit plot of the regression model have been presented in Figure 2. The Coefficient of determination or the R-square(r2=0.449)value of the regression modelindicatesthepercentageof variabilityin graduationpercentages explained by retention rates of the colleges. A restrained 44.9% variation in graduation rate was explained by the retention rate of the colleges. 6
Figure2: Residual plot and Line fit plot of the regression model The residual plot indicated a well spread pattern of residuals. Also, the Line of fit indicated that the regression model was a good fit. g)Considering the estimation results, 51% retention rate of the South University was estimated to produce a graduation rate of GRADUATION RATE = 0.2845*51%+24.423=38.93%. But, the actual rate of graduation at South University was 25%. As a president of the South University, the scholar should be deeply worried. h)From the estimation results, 4% retention rate of the University of Phoenix was expected to produce a graduation rate of GRADUATION RATE = 0.2845*4%+24.423=25.56%. But, the actual rate of graduation at South University was 28%. As a president of the University of Phoenix, the scholar should be very happy about the above par graduation rate. 7
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Discussion The key results were:The average retention rate of the mechanism in the sample was estimated at about 27.41%. The average graduation rate was estimated at 41.76% and the standard deviation was 9.86%. Scatter chart shows that the graduation rate of colleges and universities increases as the retention rate increases. The correlation coefficient between Pearson retention rate and the graduation rate was 0.67. The estimated regression equation wasGRADUATION RATE = 0.2845*4%+24.423=25.56%. Retention rate was noted to be statistically significant predictor of graduation completion rates in the institutions(t = 4,693, p < 0.05). The study has certain limitations: demographic factors such as age and gender were not consideredhere.Externalfactors,such asmotivationalsupport orindividuallearning preferences were also ignored in the study. The strengthof the regression model was that the model was statistically significant and retention rate alone was able to explain a 44.9% variation in graduation rates. The positive and statistically significant impact of retention rate on graduation rate was earlier noted inprevious pieces of literature (Tsinidou, Gerogiannis, & Fitsilis, 2010, p. 227–244).Here,thescholarestablishedalinearandpositiveimpactofretentionon graduation. A majorpolicy implicationwas to recognize the extent of average retention and graduation rates. Also, a subsidiary implication was to assess the impact of drop out students on the graduation percentage of the colleges. 8
Recommendations The three recommendations are as follows. 1.Universities should try to increase the retention rates up to a point of inflection to improve their graduation rates. 2.Demographic and external predictors should be used as mediators to estimate the graduation percentage in universities. 3.Future studies should work on a larger sample for better validity and generalization of the results. 9
References Allen, IE & Seaman, J 2010,Learning on Demand: Online Education in the United States, 2009, Sloan Consortium, pp.1-29 retrieved February 17, 2019, from <https://eric.ed.gov/? id=ED529931>. Boston, W & Ice, P 2010, ‘Comprehensive Assessment of Student Retention in Online Learning Environments’, in Association for the Advancement of Computing in Education (AACE),pp.1593–1599,retrievedFebruary16,2019,from <https://www.learntechlib.org/primary/p/35779/>. Cress, U 2014, ‘Proceedings of the European MOOC Stakeholder Summit 2014’, , pp. 294. Halawa, S, Greene, D & Mitchell, J 2014, ‘Dropout prediction in MOOCs using learner activity features’,Proceedings of the 2nd European MOOCs Stakeholders Summit, pp. 58– 65. Montgomery,DC, Peck, EA & Vining, GG2012,Introduction to LinearRegression Analysis, John Wiley & Sons. pp. 80-100 Schönbrodt, FD & Perugini, M 2013, ‘At what sample size do correlations stabilize?’, Journal of Research in Personality, vol. 47, no. 5, pp. 609–612, retrieved February 17, 2019, from <http://www.sciencedirect.com/science/article/pii/S0092656613000858>. Talbert, PY 2012, ‘Strategies to Increase Enrollment, Retention, and Graduation Rates’, Journal of Developmental Education, vol. 36, no. 1, p. 22, retrieved February 17, 2019, from <https://eric.ed.gov/?id=EJ1035683>. 10
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Tovar, E 2014, ‘Student Engagement and Institutional Graduation Rates: Identifying High- Impact Educational Practices for Community Colleges AU- Price, Derek V.’,Community College Journal of Research and Practice, vol. 38, no. 9, pp. 766–782, retrieved February 17, 2019, from <https://naspa.tandfonline.com/doi/abs/10.1080/10668926.2012.719481>. Tsinidou, M, Gerogiannis, V & Fitsilis, P 2010, ‘Evaluation of the factors that determine quality in higher education: an empirical study’,Quality Assurance in Education, vol. 18, no. 3,pp.227–244,retrievedFebruary17,2019,from <https://www.emeraldinsight.com/doi/abs/10.1108/09684881011058669>. Xu, D & Jaggars, S 2013, ‘Adaptability to Online Learning: Differences Across Types of StudentsandAcademicSubjectAreas’,pp.5-25retrievedFebruary17,2019,from <https://doi.org/10.7916/D82N59NB>. 11
Appendices Data used in the study Descriptive Statistics 12
Correlation matrix RR(%)GR(%) RR(%)1 GR(%)0.6702451 Hand calculation for regression 13
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