1. Progression and Attrition Rate: Overview of Undergraduate and Masters Cohort Study
T Zewotir, D North and M Murray
School of Statistics and Actuarial Science,
UKZN

2. Introduction
University is open only to a fraction of the young talented citizens.
Problem: not all of this group successfully goes through the university system of education.
Attrition rate: the proportion of students who discontinue their studies on account of academic dismissal or voluntary dropout.

3. Why do we study attrition rate?
Relevant issue for the assessment of the overall learning environment and its operational efficiency.
The magnitude of attrition rate reflects selection procedures and/or social and academic integration and/or the quality of instructional process.
Key element for planners and administrators to predict the number of possible admissions and throughputs.

4. Part I
Undergraduate students progression rate

5. Dampening effect
There is a dampening effect of the rates of attrition as the students progress from year/semester to year/semester.
students entering at a later year have completed more prerequisites.
Students are generally acquainted with the environment.

6. Layout: Suppose a program requires K semesters/years of study.1 2 … K
Students enrolled N1 N2 Nk
Attrition y1 y2 yk
Remaining
N1-y1
N2-y2
Nk-yk
Attrition rate P1 P2 Pk
Dampening
P1  P2  …  Pk

7. Statistical Problem: Modelling the progression of the cohort.
Estimating the initial attrition rate and the dampening (or progression) rate. Criteria: KISS Dampening effect parameter, β, is close to 0  the attrition rate is the same as in the initial attrition throughout the K semesters/years. Dampening effect parameter, β, far from 0  negative showing the decaying of the attrition rate and positive indicating that the attrition rate gets worse as the students progress.

8. Demonstration: Initial attrition rate=0.40 and K=5
Log/exponential type: Fast dampening effect
β=-0.10, exp(-0.10)=0.904 (9.6%): , 0.362, 0.327, 0.296, 0.267;
β=-0.50, exp(-0.50)=0.607(39.3%): , 0.243, 0.147, 0.089,0.054;
β=-1.00, exp(-1.00)=0.368 (63.2%): 0.400, 0.147, 0.054, 0.019,
Logit type: Slow dampening effect
β=-0.10, exp(-0.10)=0.904 =OR: , 0.372, , 0.308;
β=-0.50, exp(-0.50)=0.607=OR: , 0.288, 0.197, 0.130, 0.083;
β=-1.00, exp(-1.00)=0.368 =OR: , 0.197, 0.083, 0.032,

9. More than one dampening effect
A constant dampening effect over the K years/semesters may not be a proper assumption.
For example wish to model an attrition rate that slows down after semester/year 2. Here we have two dampening effects.

10. Data Faculty Entry batch 1st year 2nd year 3rd year Humanities 2005
0.277
0.116
0.096
2006
0.266
0.103
0.075
2007
0.243
0.084
0.077
2008
0.229
0.086
0.072
Management
0.195
0.123
0.175
0.080
0.137
0.167
0.078
0.105
0.166
0.063
0.089
Science
0.308
0.101
0.053
0.225
0.067
0.188
0.094
0.034
0.164
0.031

11. Interest
Developing the best fitting model. Thereby answer the following:
Do the faculties have identical initial attrition rate?
Is there identical dampening effect as the students progress?
Is the initial attrition rate stable within the faculty?

12. Result
The initial attrition rates differ between the faculties (2= and p<0.0001).
The dampening effect from first year to second year, the dampening effect differs from faculty to faculty (2= and p<0.0001).

13. ... Result...
The progression/dampening rate after year 2 showed that all the faculties have different dampening effect (2= and p<0.0001).
All the faculties have different dampening/progression rate from second to third year.
Unlike others, in the Faculty of Management the attrition rate appreciates after year 2.

14. ...result
Since 2005 the first year attrition rate shows a decreasing linear trend in all the faculties.
The decreasing rate in Science is significantly higher than that of Management and Humanities.
The decreasing rate difference between Humanities and Management is insignificant (t= , p= ).

15. Part II
Masters students time-to-degree
Note: Only Research Masters

16. Why do we study the Masters level throughput?
It is crucial to meet the demands of high level skills .
It is important to assess the overall learning and research environment and its operational efficiency of the university.
Research on Masters throughput is motivated by economic and psychosocial costs of Masters attrition.

17. What are we going to examine?
The Masters entrants and graduates by demographic characteristics.
The success/failure rate of Masters students in a given cohort.
The time-to-degree for Masters students in different faculties.

18. The Data Cohort of the Masters program intake at UKZN.
The Performance of the 2004, 2005, …, cohorts of Masters program entrants is tracked.
The demographic and academic characteristics of these students were extracted from the University database.

22. Entrants by Race and Gender
Entrance year
2004
2005
2006
2007
2008
2009
2010
2011
African
Male 40 46 63 86 82 84
102
Female 29 36 34 49 44 71 98
Colored 4 2 1 3 5 10
Indian 43 39 42 30 45 33 47 37 54 57 59 50 81 70
Other
White 64 58 61 41 67 53 60 52

28. Time to Degree (in year)
Percentage of successful full-time students by duration and admission year
Admission
year
Time to Degree (in year)
Currently
Active (with no
interruption) 1 2 3 4 5 6 7
2004
2.0
18.2
11.3
5.4
4.4
3.3
2.0 (2.0)
2005
19.4
14.7
10.3
6.0 -
2.0 (1.2)
2006
3.8
15.3
21.1
17.2
3.4
2.3 (1.9)
2007
3.2
21.8
9.6
7.5 (7.1)
2008
20.3
20.0
19.0(19.0)
2009
17.8
41.6 (39.9)
2010
4.2
77.3

29. Successful full-time students average time-to-degree by Faculty
Entry Year
2004
2005
2006
2007
Education
3.25
3.50 -
3.00
Engineering
2.15
2.57
2.30
2.75
Health Sciences
2.29
2.22
2.00
Humanities
2.90
2.25
1.68
2.68
Law
1.00
Management
1.33
1.87
2.42
2.54
NRM Sch Med
4.70
4.00
3.38
Science & Agr
3.24
3.23
3.03
University
2.70
2.37
2.79

30. Summary
The admission rate of Masters degree students is increasing every year by about 6.6%.
Race and gender differences on the success rate are not significant.
Completing a full-time Masters in one year, although not impossible, it is not practically achievable by more than 95% of the students.