4.ANALYSIS

4: Analysis

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The movement of students through the higher education system is likely to vary by the characteristics of the students and by field and level of study. Aggregate models provide useful information towards the understanding of the dynamics of the system. However, they alone cannot provide the details necessary to understand the behaviour of particular groups of students. Thus, whenever possible a separate input-output model is estimated for each group of students defined by sex, field of study and level of course. The disaggregation is limited by the need to ensure that there are sufficient number of student movements from one state of the system to another from which transition proportions can be estimated.

The general model building procedure is described in Section 4.2. The results from fitting and estimating input-output models to various groups of students at the undergraduate and postgraduate level are given in Section 4.3 and Section 4.4. The groups at the undergraduate level are defined by field of study, and that at the postgraduate level by level of course. For each of these groups three models are estimated, one for all persons in the group and one each for males and females.

Two sets of results are reported. The first set contains the summary statistics that emanate from approximating the input-output model as a regular Markov chain. For example, estimates are derived of the probability of a student completing a course given the student's age at course commencement and the average time to completion. The second set of results are a summary of the projections of the number of students at various stages of the system until the year 2001. Only projections based on one set of assumptions are included. Future work will include sensitivity analysis and alternate models for projecting the number of commencing students.

4.2 Model Building

The procedure described below is general in nature and applies to all the input-output models that are developed and estimated. As a first step to constructing an input-output model the transient states must be defined. We define these states by age and year of enrolment in course. To ensure that all transition proportions are defined there must be at least one student in each transient state in 1993.

Next, tables showing the age of students by the time, in years, that they have been enrolled are extracted from each of the DEET course enrolment files of 1993 and 1994 and the course completions file for 1993. Data in these three cross-tabulations provide the basis for constructing the input-output matrix.

Students in a given transient state in 1993 move to another transient state in 1994, complete the course or drop out. The only unknown quantity is the number who drop out. However, this can be calculated because the other two quantities are known. Careful attention has to be paid when considering movements to and from states defined by grouped ages and multiple year of enrolment, such as being between 25 and 29 years of age and in the sixth or higher year of enrolment.

In theory the above process should result in an input-output matrix with a non-negative quantity in each cell. In practice, it was found that some of the movements into the dropout absorbing state were negative. This means that the compilation of the enrolment and completions data files is not consistent. There are two possible causes for these negative values. First, it could be a data recording error, and resources are not available, at this stage, to confirm whether indeed this is the case. The second possibility, which is more likely, is that there is a variation across institutions in the way completions data are recorded. Anecdotal evidence suggests that some institutions record a student as having completed a course when that student has satisfied all the requirements for the course, while others only record a completion when the student applies for graduation. There may also be other reasons why there is a lack of consistency between the enrolment and completions data.

The negative dropout values are a nuisance because they prevent a complete analysis of the dynamics of the system. In general, the negative values were very small in absolute terms and were more often than not associated with movement from transient states defined by an older age group and year of enrolment which was usually more than 3. It was decided to perturb some of the completions figures in order to eliminate the negative dropout numbers. The procedure for perturbing, which is ad hoc in nature, is described in the appendix to this report. A consequence of the perturbation is that the time to completion statistics may be slightly deflated. Since the magnitude and the number of perturbation is small, we assume the bias will be negligible.

The next step in the model building involves the calculation of the matrix of transition proportions, Q, and the matrix R of proportions moving into the absorbing states. The model can now be estimated as outlined in Chapter 2.

4.3 Undergraduates

Students were divided into eleven age groups. Associated with each age group are up to six year of enrolment categories. The resulting model consists of 51 transient states. These are marked by a cross in Table 4.1.

Although a typical state such as being a 20-year-old and in the second year of enrolment means precisely that, the last state in each row in Table 4.1 is to be interpreted differently. For example, being under 18 years of age and in the first year of enrolment means being under 18 years old and in the first or higher year of enrolment, and being a 22-year-old and in the sixth year of enrolment means being 22 years old and in the sixth or higher year of enrolment. This sort of aggregation is necessary to contain the size of the input-output model. It is unlikely that there will be many under 18-year-olds in their second year of enrolment, and even less likely that there will be many in the third or higher year of enrolment.

Table 4.1 Transient States of the Model for Undergraduates Defined Using Age and Year of Enrolment as Criteria

	Year of Enrolment in Course
Age	1	2	3	4	5	6
Under 18	_X
18	_X	_X
19	_X	_X	_X
20	_X	_X	_X	_X
21	_X	_X	_X	_X	_X
22	_X	_X	_X	_X	_X	_X
23	_X	_X	_X	_X	_X	_X
24	_X	_X	_X	_X	_X	_X
25-29	_X	_X	_X	_X	_X	_X
30-34	_X	_X	_X	_X	_X	_X
Over 34	_X	_X	_X	_X	_X	_X
Note: Across indicates that the transient state is included in the model

Three models, one each for males, females and persons, were estimated for each of the following groups of undergraduates:

all students;
Australian students (includes permanent residents); and
Australian students by nine fields of study.

Models for students doing Agriculture, Education (O) and Medicine could not be estimated satisfactorily as there was too much inconsistency between the course enrolment and completions data. The consequence of the inconsistency was that the movement between 1993 and 1994 of a large number of students could not be reconciled. Australian students were considered on their own because they make up the bulk of the students and they are also the primary concern of this study. Models for all students were estimated for use as a benchmark for other models.

Probability of Completing Course

Table 4.2 shows the estimates of the probability of a student completing a course given his/her age at course commencement. For example, an Australian male student who starts as an undergraduate at the age of 18 years has a 58 percent chance of eventually completing the course, while an Australian female student of the same age has a 66 percent chance of completing. There is considerable variation in these probabilities between males and females, across age groups and fields of study. However, there is hardly any difference in the estimated probabilities for all students and just Australian students. This may be due to the behaviour of the overseas fee-paying students not being significantly different to that of Australian students, and even if the behaviour was different the number of overseas fee-paying students is relatively small to have much impact on the estimated probabilities.

If we concentrate on the results for the Australian group, there is a clear indication that females have a higher chance of completing a course than males irrespective of what age the course is commenced at. However, the difference in the probabilities between male and female completion of a course varies with the age at which the course is commenced. This difference can be as high as 10 percentage points, for example, if the course is commenced at an age of 20 years. In general, as the age at which a course is commenced increases, the chances of completing the course diminish for both gender groups. For both males and females the highest chance of completing a course is if the commencement age is 20 years, at which age the probability for a female completing is 79 percent and that for a male 69 percent. Among the females, those aged between 25 and 29 years have the least chance of completing the course, while the corresponding age for males is 30 to 34 years.

Table 4.2 Probability of Completing an Undergraduate Course by Age at Course Commencement

Age at Course	All			Australian			Architecture			Arts			Business
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 18	0.62	0.66	0.64	0.62	0.66	0.64	0.68	0.69	0.69	0.55	0.64	0.61	0.64	0.63	0.64
18	0.59	0.66	0.63	0.58	0.66	0.62	0.69	0.73	0.71	0.54	0.63	0.61	0.60	0.66	0.62
19	0.64	0.73	0.69	0.63	0.72	0.68	0.56	0.64	0.60	0.65	0.69	0.68	0.63	0.66	0.64
20	0.69	0.78	0.73	0.69	0.79	0.74	0.65	0.74	0.71	0.67	0.81	0.77	0.78	0.73	0.76
21	0.67	0.73	0.70	0.67	0.73	0.70	0.72	0.87	0.72	0.62	0.74	0.70	0.65	0.64	0.63
22	0.60	0.69	0.65	0.59	0.69	0.64	0.56	0.87	0.60	0.63	0.62	0.62	0.53	0.54	0.54
23	0.59	0.67	0.63	0.57	0.66	0.62	0.62	0.72	0.70	0.56	0.62	0.59	0.52	0.50	0.51
24	0.57	0.64	0.61	0.56	0.63	0.60	0.65	0.79	0.64	0.56	0.60	0.59	0.49	0.44	0.47
25-29	0.54	0.61	0.58	0.54	0.61	0.58	0.52	0.58	0.52	0.55	0.56	0.56	0.46	0.43	0.45
30-34	0.51	0.62	0.58	0.52	0.62	0.58	0.37	0.64	0.42	0.58	0.59	0.59	0.40	0.39	0.40
Over 34	0.51	0.63	0.59	0.53	0.63	0.60	0.36	0.64	0.42	0.55	0.60	0.59	0.36	0.32	0.34

	Education (I)			Engineering			Health			Law			Science
	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 18	0.50	0.67	0.64	0.54	0.55	0.54	0.63	0.65	0.65	0.83	0.80	0.81	0.61	0.61	0.61
18	0.52	0.66	0.63	0.50	0.60	0.52	0.61	0.64	0.63	0.95	0.95	0.95	0.57	0.65	0.61
19	0.47	0.69	0.63	0.60	0.70	0.62	0.64	0.83	0.79	1.00	1.00	1.00	0.57	0.62	0.59
20	0.54	0.68	0.63	0.54	0.66	0.55	0.72	0.86	0.83	0.95	0.91	0.91	0.71	0.85	0.76
21	0.56	0.64	0.62	0.60	0.42	0.58	0.82	0.81	0.80	0.81	0.80	0.81	0.74	0.88	0.80
22	0.48	0.68	0.64	0.44	0.48	0.45	0.70	0.74	0.72	1.00	1.00	1.00	0.65	0.83	0.72
23	0.52	0.69	0.64	0.54	0.59	0.55	0.61	0.78	0.75	0.88	0.75	0.83	0.58	0.61	0.59
24	0.52	0.60	0.56	0.53	0.27	0.50	0.61	0.75	0.72	0.52	0.75	0.62	0.53	0.61	0.56
25-29	0.58	0.62	0.60	0.48	0.33	0.47	0.68	0.72	0.71	0.67	0.71	0.69	0.50	0.56	0.52
30-34	0.68	0.61	0.63	0.50	0.42	0.50	0.56	0.73	0.70	0.58	0.68	0.62	0.42	0.52	0.45
Over 34	0.68	0.73	0.71	0.41	1.00	0.44	0.60	0.73	0.71	0.64	0.66	0.65	0.37	0.46	0.40

The comparison of the probabilities across fields of study reveal that, in general, Engineering students have the least chance of completing and Law the highest. If it was possible to model the behaviour of students in Medicine, then we would expect them to also have a very high chance of completing a course. Some estimates of the probabilities, if calculated on the basis of movements of only a small number of students, may not be all that reliable. For example, there are not all that many older females doing Engineering or Architecture, and hence, the estimates relating to these groups may be unstable.

In general, females have a higher chance than males of completing a course in Architecture, Arts, Education (I), Health and Science. In the other fields of study this pattern is not nearly as uniform across different course commencement ages. In Business the differences between the male and female chances are relatively small, with the maximum of only 5 percentage points for students commencing the course at the age of 20 years.

A person commencing a course in Business or Engineering at an age of 24 years or more has a 50 percent or less chance of completing it, and a person commencing a course in Architecture or Science at an age over 29 years has a less than even chance of completing it. In all other fields of study a person has better than even chance of completing a course, irrespective of the age of the student when the course was commenced.

Time in the System

The estimates of the mean and the standard deviation of the time spent in the system (number of years of enrolment in a particular course) by a student is given in Tables 4.3 and 4.4, respectively. A number of factors affect these estimates, but at this stage it is not possible to isolate, or measure, the impact of any one of them because of lack of data. The factors which are likely to have an impact are:

the number of part-time students enrolled in the course;
the length of the course;
the number of students with credit for prior subjects or qualification; and
the attrition rate from the course, though this is considered separately below.

Table 4.3 shows that the mean time in the system varies by the age of the student when he/she commenced a course, gender and field of study. The mean time is 3.2 years for persons starting a course when they are 18 years old. In general, there is a steady decline in the mean time as the age at which a course is commenced increases, until around a course commencement age of 21 to 22 years when the minimum mean time in the system of 2.6 years is reached. A steady increase in the mean time can be observed as course commencement age increases above 23 years. This pattern repeats, more or less, for each field of study.

Australian male students spend, on average, a longer time in the system than females. This pattern of variation is not uniform across all fields of study. For example, the mean time in the system for male students in Arts who commence a course at the age of 23 years or more is shorter than that for females who commence at the same age. Architecture, Engineering and Law courses are of longer duration and this is reflected in the higher mean time in the system for students doing these courses.

The standard deviation of the time in the system also varies with course commencement age and fields of study. In general, the standard deviation is higher for students who begin their courses at an older age. A possible reason for this is that there are likely to be a relatively higher number of part-time students in the older age groups.

Time to Completion

The factors which are likely to have an impact on the mean time to complete a course are:

the number of part-time students enrolled in the course;
the length of the course; and
the number of students with credit for prior subjects or qualifications.

The mean and the standard deviation of the time taken by a student to a complete a course is given in Table 4.5 and Table 4.6, respectively. For example, it takes, on average, 4.4 years for an Australian male, commencing studies at the age of 18 years, to finish a bachelor's course, while for a female of the same age this time is 3.9 years.

For both male and female Australian students the minimum average time to course completion is achieved if the course is commenced at the age of 21 years. Overall, females take less time on average to complete a course than males, with the difference for some age groups, such as those commencing a course at the age of 21 years, being as much as 0.7 years.

Females who commence a course in Health at an age between 21 and 23 years take, on average, the shortest time to complete an undergraduate degree, while females who commence an Engineering course at the age of over 34 years take the longest time. However, there may not be all that many females over 34 studying a course in Engineering.

The standard deviation of the time to complete a course follows a pattern similar to that for the standard deviation of the time in the system-that is, it is higher for students who begin their courses at an older age.

Table 4.3 Mean Number of Years in the System for Undergraduates by Age at Course Commencement

Age at Course	All			Australian			Architecture			Arts			Business
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 18	3.4	3.1	3.2	3.4	3.1	3.2	3.7	3.5	3.6	3.0	2.9	3.0	3.2	3.0	3.1
18	3.3	3.1	3.2	3.3	3.1	3.2	3.6	3.6	3.6	3.0	3.0	3.0	3.2	3.1	3.2
19	3.2	3.0	3.1	3.2	3.0	3.0	3.6	3.7	3.6	3.0	2.9	2.9	3.0	2.9	2.9
20	2.9	2.7	2.8	2.9	2.6	2.7	3.4	3.8	3.5	2.6	2.8	2.7	2.9	2.7	2.8
21	2.8	2.4	2.6	2.8	2.4	2.6	3.9	3.6	3.8	2.6	2.6	2.6	2.9	2.7	2.8
22	2.7	2.5	2.6	2.7	2.5	2.6	2.6	3.0	2.8	2.7	2.7	2.7	2.8	2.9	2.8
23	2.8	2.5	2.7	2.8	2.6	2.7	3.2	2.9	3.1	2.7	2.9	2.8	3.0	3.0	3.0
24	2.8	2.6	2.7	2.9	2.7	2.8	3.3	2.5	3.0	2.7	3.1	2.9	3.1	3.0	3.1
25-29	2.8	2.6	2.7	2.9	2.7	2.8	3.1	2.9	3.0	2.8	3.0	3.0	3.1	3.0	3.1
30-34	2.9	2.9	2.9	3.0	2.9	2.9	2.7	3.5	2.8	3.1	3.4	3.3	3.1	3.1	3.1
Over 34	2.8	2.9	2.8	2.8	2.9	2.9	2.7	2.9	2.7	3.0	3.6	3.4	2.9	2.8	2.9

	Education (I)			Engineering			Health			Law			Science
	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 18	2.9	2.9	2.9	3.7	3.6	3.7	3.1	3.0	3.0	4.6	4.2	4.4	3.1	3.0	3.1
18	2.9	2.9	2.9	3.7	3.7	3.7	3.0	2.9	2.9	4.5	4.5	4.5	3.0	3.0	3.0
19	2.6	2.9	2.8	3.7	3.8	3.7	2.8	2.7	2.7	4.5	4.2	4.3	2.9	2.9	2.9
20	2.5	2.2	2.3	3.3	3.0	3.2	2.7	2.3	2.4	3.1	3.4	3.3	2.7	2.7	2.7
21	2.4	2.2	2.2	3.1	2.6	3.1	2.8	2.1	2.2	2.8	2.8	2.8	2.5	2.4	2.5
22	2.5	2.4	2.4	2.9	3.0	2.9	2.3	2.0	2.0	2.7	3.0	2.8	2.7	2.6	2.6
23	2.5	2.5	2.4	3.4	3.3	3.4	2.4	2.1	2.1	2.9	2.8	2.9	2.7	2.5	2.6
24	2.3	2.4	2.3	3.4	2.2	3.3	2.5	2.1	2.2	2.9	3.4	3.1	2.7	2.8	2.7
25-29	2.4	2.5	2.4	3.3	2.4	3.2	2.5	2.3	2.3	3.6	3.5	3.5	2.9	2.9	2.9
30-34	2.4	2.5	2.4	3.4	3.1	3.3	2.3	2.4	2.4	3.4	3.7	3.5	3.0	3.2	3.1
Over 34	2.2	2.4	2.4	2.8	5.5	3.0	2.1	2.4	2.3	3.6	4.0	3.8	2.9	3.2	3.0

Table 4.4 Standard Deviation of the Number of Years in the System for Undergraduates by Age at Course Commencement

Age at Course	All			Australian			Architecture				Arts				Business
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male		Female	Person	Male		Female	Person
Under 18	1.8	1.6	1.7	1.8	1.6	1.7	2.1	1.8	2.0	1.7		1.7	1.7	1.7		1.5	1.6
18	1.8	1.6	1.7	1.8	1.6	1.7	2.0	2.0	2.0	1.8		1.7	1.7	1.7		1.6	1.6
19	1.8	1.6	1.7	1.9	1.7	1.8	2.1	2.2	2.2	1.8		1.8	1.8	1.7		1.6	1.6
20	1.8	1.7	1.8	1.8	1.7	1.8	2.1	2.4	2.1	1.7		2.0	1.9	1.8		1.7	1.7
21	1.8	1.7	1.8	1.9	1.7	1.8	2.5	1.9	2.2	1.9		2.1	2.0	2.0		1.8	2.0
22	1.9	1.8	1.8	1.9	1.8	1.9	1.8	1.8	1.8	2.0		2.2	2.2	2.1		2.1	2.1
23	2.0	1.9	1.9	2.1	1.9	2.0	2.1	2.0	2.0	2.1		2.5	2.3	2.3		2.2	2.3
24	2.0	2.0	2.0	2.1	2.0	2.1	2.1	2.1	2.0	2.1		2.5	2.4	2.3		2.3	2.3
25-29	2.1	2.0	2.0	2.1	2.1	2.1	2.1	2.4	2.0	2.2		2.6	2.4	2.3		2.3	2.3
30-34	2.1	2.2	2.2	2.2	2.2	2.2	1.9	3.3	2.0	2.3		2.8	2.6	2.4		2.4	2.4
Over 34	2.1	2.1	2.1	2.1	2.2	2.1	1.8	3.1	1.9	2.4		2.7	2.6	2.3		2.2	2.3

	Education (I)			Engineering			Health				Law				Science
	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male		Female	Person	Male		Female	Person
Under 18	1.7	1.3	1.4	2.0	1.9	1.9	1.5	1.2	1.2	1.9		2.0	2.0	1.7		1.6	1.7
18	1.5	1.4	1.4	2.1	1.8	2.1	1.5	1.2	1.3	1.6		1.6	1.6	1.7		1.6	1.7
19	1.5	1.6	1.5	2.1	1.8	2.1	1.5	1.2	1.3	1.4		1.5	1.5	1.8		1.7	1.8
20	1.5	1.4	1.4	2.0	1.5	1.9	1.4	1.3	1.3	1.8		1.7	1.8	1.9		1.7	1.8
21	1.3	1.6	1.4	2.0	1.6	2.0	1.4	1.3	1.3	1.6		1.6	1.6	1.7		1.7	1.7
22	1.5	1.6	1.5	2.1	1.9	2.1	1.4	1.2	1.3	1.7		1.9	1.8	1.9		1.9	1.9
23	1.3	1.6	1.5	2.2	2.4	2.3	1.4	1.3	1.3	2.0		1.9	1.9	2.0		1.9	2.0
24	1.3	1.6	1.5	2.3	1.9	2.3	1.4	1.3	1.3	2.1		2.0	2.1	2.1		2.1	2.1
25-29	1.4	1.6	1.5	2.4	2.0	2.3	1.4	1.3	1.3	2.1		2.0	2.0	2.1		2.2	2.1
30-34	1.4	1.5	1.4	2.5	2.7	2.5	1.4	1.4	1.4	2.1		2.2	2.2	2.3		2.6	2.4
Over 34	1.3	1.4	1.4	2.4	3.7	2.5	1.3	1.4	1.3	2.1		2.3	2.2	2.3		2.7	2.4

Table 4.5 Mean Number of Years to Complete an Undergraduate Course by Age at Course Commencement

Age at Course	All			Australian			Architecture			Arts			Business
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 18	4.4	3.9	4.1	4.4	3.9	4.1	4.7	4.2	4.5	4.1	3.9	3.9	4.1	3.9	4.0
18	4.4	3.9	4.1	4.4	3.9	4.1	4.5	4.4	4.4	4.1	3.8	3.9	4.2	3.9	4.1
19	4.1	3.6	3.8	4.1	3.6	3.8	4.9	4.9	4.9	3.9	3.6	3.7	3.7	3.6	3.7
20	3.6	3.1	3.3	3.5	3.0	3.2	4.3	4.6	4.4	3.3	3.2	3.2	3.3	3.2	3.2
21	3.5	2.9	3.2	3.5	2.8	3.1	4.8	3.8	4.5	3.4	3.1	3.2	3.7	3.5	3.7
22	3.6	3.0	3.3	3.6	3.1	3.3	3.6	3.3	3.6	3.5	3.6	3.6	4.0	4.2	4.1
23	3.8	3.2	3.5	3.9	3.3	3.6	4.2	3.5	3.8	3.8	4.0	4.0	4.5	4.6	4.5
24	3.9	3.4	3.6	4.1	3.5	3.8	4.2	3.0	3.8	3.9	4.3	4.1	4.8	5.0	4.9
25-29	4.1	3.5	3.8	4.2	3.7	3.9	4.5	4.0	4.3	4.0	4.5	4.3	4.9	5.0	5.0
30-34	4.2	3.8	4.0	4.3	3.9	4.0	4.5	4.8	4.5	4.2	4.9	4.7	5.3	5.4	5.3
Over 34	4.1	3.8	3.9	4.1	3.8	3.9	4.4	3.9	4.3	4.4	5.0	4.8	5.3	5.4	5.3

	Education (I)			Engineering			Health			Law			Science
	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 18	4.2	3.6	3.7	5.1	4.9	5.1	3.9	3.6	3.6	5.3	5.0	5.1	4.2	4.0	4.1
18	4.1	3.7	3.8	5.3	4.8	5.2	3.8	3.5	3.6	4.7	4.7	4.7	4.2	3.9	4.1
19	3.8	3.5	3.5	4.9	4.7	4.8	3.6	3.0	3.1	4.5	4.2	4.3	4.0	3.8	3.9
20	3.5	2.7	2.9	4.4	3.8	4.4	3.3	2.5	2.6	3.2	3.6	3.4	3.3	3.0	3.1
21	3.2	2.8	2.8	4.2	3.9	4.1	3.2	2.3	2.5	3.3	3.3	3.3	3.0	2.6	2.8
22	3.5	2.9	3.0	4.6	4.4	4.6	2.8	2.3	2.4	2.7	3.0	2.8	3.4	2.9	3.2
23	3.2	3.0	3.1	4.7	4.6	4.7	3.0	2.3	2.4	3.2	3.4	3.2	3.8	3.3	3.6
24	3.1	3.2	3.2	4.9	4.5	4.9	3.2	2.5	2.6	4.4	4.1	4.2	4.0	3.8	3.9
25-29	3.1	3.2	3.2	5.0	4.4	5.0	3.0	2.7	2.7	4.6	4.3	4.5	4.3	4.1	4.2
30-34	2.9	3.2	3.1	5.1	5.3	5.1	3.0	2.8	2.9	4.7	4.7	4.7	4.9	4.9	4.9
Over 34	2.7	2.9	2.8	4.9	5.5	4.9	2.7	2.8	2.8	4.6	5.1	4.8	5.1	5.3	5.2

Table 4.6 Standard Deviation of Number of Years to Complete an Undergraduate Course by Age at Course Commencement

Age at Course	All			Australian			Architecture			Arts			Business
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 18	1.4	1.2	1.3	1.4	1.2	1.3	1.9	1.7	1.8	1.5	1.4	1.5	1.4	1.2	1.3
18	1.5	1.3	1.4	1.5	1.3	1.4	1.8	1.9	1.8	1.7	1.5	1.6	1.5	1.2	1.4
19	1.7	1.5	1.6	1.7	1.6	1.7	2.0	2.1	2.0	1.7	1.8	1.8	1.7	1.5	1.6
20	1.9	1.8	1.8	1.9	1.8	1.9	2.0	2.7	2.1	1.9	2.1	2.0	1.9	1.7	1.8
21	2.0	1.8	1.9	2.1	1.9	2.0	2.4	2.2	2.3	2.3	2.2	2.2	2.2	2.0	2.1
22	2.1	2.0	2.0	2.2	2.0	2.1	2.2	2.1	2.1	2.1	2.5	2.4	2.4	2.3	2.3
23	2.2	2.1	2.1	2.2	2.1	2.2	2.3	2.3	2.2	2.3	2.6	2.5	2.5	2.4	2.5
24	2.2	2.1	2.2	2.3	2.2	2.2	2.4	2.5	2.4	2.3	2.7	2.5	2.4	2.4	2.4
25-29	2.2	2.2	2.2	2.3	2.2	2.2	2.3	2.9	2.3	2.3	2.7	2.5	2.4	2.4	2.4
30-34	2.4	2.3	2.4	2.4	2.4	2.4	2.4	3.6	2.5	2.5	2.8	2.7	2.4	2.5	2.5
Over 34	2.4	2.3	2.3	2.4	2.3	2.4	2.4	3.5	2.5	2.6	2.7	2.7	2.4	2.6	2.5

	Education (I)			Engineering			Health			Law			Science
	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 18	1.3	0.9	1.0	1.5	1.4	1.5	1.1	0.8	0.9	1.1	1.4	1.3	1.3	1.2	1.2
18	1.1	1.0	1.0	1.7	1.4	1.6	1.1	0.9	1.0	1.5	1.5	1.5	1.4	1.3	1.4
19	1.2	1.6	1.4	1.9	1.6	1.8	1.3	1.2	1.2	1.4	1.5	1.5	1.8	1.6	1.8
20	1.4	1.5	1.5	2.0	1.4	2.0	1.2	1.3	1.4	1.8	1.7	1.8	2.1	1.8	2.0
21	1.3	1.7	1.5	2.1	1.8	2.1	1.3	1.4	1.4	1.5	1.5	1.5	2.0	1.9	1.9
22	1.5	1.7	1.5	2.3	2.1	2.3	1.4	1.3	1.3	1.7	1.9	1.8	2.3	2.1	2.2
23	1.3	1.7	1.5	2.4	2.4	2.4	1.4	1.4	1.4	2.1	1.8	2.0	2.4	2.3	2.4
24	1.4	1.7	1.5	2.5	2.4	2.5	1.4	1.4	1.4	1.9	1.9	1.9	2.5	2.4	2.5
25-29	1.4	1.7	1.5	2.5	2.5	2.5	1.5	1.4	1.4	1.8	1.8	1.8	2.6	2.4	2.5
30-34	1.4	1.5	1.5	2.8	3.0	2.9	1.5	1.4	1.4	1.9	2.0	1.9	2.8	2.8	2.8
Over 34	1.4	1.4	1.4	3.1	3.7	3.1	1.4	1.4	1.4	2.0	2.0	2.0	2.9	2.9	2.9

Projections

Projections by age and field of study were made of:

the number of commencing students, 1995 to 2001;
the total enrolment, 1995 to 2001;
the number of course completions, 1994 to 2001; and
the number of dropouts, 1994 to 2001.

It should be noted that for 1994 the number of commencing students and the total enrolment are actual figures. For 1995, the projections of the number of commencing students were adjusted to approximate the preliminary 1995 commencing numbers (see DEET 1995b). Thereafter they are based on the method as set out in Section 2.2. This method is driven by demographic changes and school enrolment changes only. In brief, this method assumes:

a constant school retention rate as calculated from the 1993 and 1994 school enrolment data;
a constant proportion, based on the 1994 data, of Year 12 students continuing into higher education;
a constant proportion, based on the 1994 data, of non-school-leavers entering higher education; and
the demographic changes projected to occur between 1995 and 2001.

In this report only aggregate projections by field of study are included because of the constraint of space. Projections by age are available on request.

Table 4.7 contains the projections of the number of commencing students from 1995 to 2001. Between 1995 and 2001 course commencement numbers are projected to increase by 0.8 percent. Fee-paying overseas students make up half of this growth because the growth in the number of Australian students is only 0.4 percent for this period. Moreover, female course commencement numbers are projected to increase by 1.2 percent compared to only 0.4 percent for males.

The number of commencing students are projected to decline from 1995 to 1998, and then to slowly increase until the year 2001. The 1995 levels are projected to be reached by the year 2000. The average annual growth in commencement numbers is 0.15 percent over the six year period. There is considerable variation in the growth by field of study. The Education (I) and Health commencement numbers are projected to increase most, while those for courses in Architecture, Engineering and to a lesser extent Science are projected to decline.

Among Australian students female commencement numbers are projected to grow by 0.9 percent between 1995 and 2001 compared to a decline in male numbers by 0.3 percent over the same period. These projections are plotted as time series in Figure 4.1. Female numbers are projected to grow across all fields of study, but males numbers are projected to grow in only Education (I) and Law.

Table 4.7 Projections of Undergraduate Commencements, 1995 to 2001

	Year																Percentage Change
	1994			1995	1996		1997		1998		1999		2000		2001			1995-2001		Average
Males
All	66391			70648	69413		68829		68792		69492		70098		70910			0.4		0.06
Australians	60032			64173	62862		62185		62045		62685		63240		64011			-0.3		-0.04
Architecture	1845			1970	1927		1903		1895		1912		1928		1950			-1.0		-0.17
Arts	11339			12141	11925		11809		11779		11875		11964		12090			-0.4		-0.07
Business	14119			15108	14805		14650		14624		14779		14913		15098			-0.1		-0.01
Education (I)	2874			3079	3029		3006		3003		3032		3058		3094			0.5		0.08
Engineering	8840			9386	9138		9012		8987		9111		9209		9344			-0.5		-0.08
Health	2961			3176	3120		3089		3081		3104		3126		3157			-0.6		-0.10
Law	2215			2386	2352		2335		2333		2350		2368		2394			0.3		0.06
Science	12482			13306	12995		12832		12794		12940		13060		13231			-0.6		-0.09
Females
All	84883			91034	89698		89355		89124		90196		91265		92144			1.2		0.20
Australians	79210			85208	83815		83393		83084		84107		85123		85976			0.9		0.15
Architecture	1051			1122	1098		1090		1083		1098		1113		1125			0.3		0.05
Arts	25475			27413	26978		26853		26766		27095		27425		27705			1.1		0.18
Business	12447			13334	13091		13012		12953		13115		13276		13408			0.6		0.09
Education (I)	8217			8814	8651		8601		8563		8677		8792		8888			0.8		0.14
Engineering	1395			1486	1449		1438		1429		1456		1480		1499			0.9		0.14
Health	13328			14436	14267		14227		14199		14355		14509		14637			1.4		0.23
Law	2350			2522	2484		2471		2462		2488		2516		2542			0.8		0.13
Science	9856			10541	10306		10231		10170		10331		10481		10602			0.6		0.10
Persons
All		151274	161682			159111		158184		157915		159688		161364		163054			0.8		0.14
Australians		139242	149381			146677		145578		145129		146792		148363		149986			0.4		0.07
Architecture		2896	3092			3025		2993		2979		3010		3041		3075			-0.6		-0.09
Arts		36814	39555			38903		38662		38544		38970		39390		39795			0.6		0.10
Business		26566	28442			27896		27663		27577		27893		28189		28506			0.2		0.04
Education (I)		11091	11893			11681		11606		11567		11709		11850		11982			0.8		0.12
Engineering		10235	10872			10587		10450		10416		10567		10689		10843			-0.3		-0.05
Health		16289	17612			17387		17317		17280		17459		17636		17794			1.0		0.17
Law		4565	4908			4836		4806		4795		4839		4884		4936			0.6		0.09
Science		22338	23847			23301		23063		22964		23271		23541		23833			-0.1		-0.01

Notes: (a) Commencements for 1994 are actual numbers

(b) Commencements for 1995 have been adjusted to approximate preliminary DEET (1995b) estimates

Figure 4.1 Projections of Australian Undergraduate Commencements, 1995 to 2001 (Commencements for 1994 are Actual Numbers and Projections for 1995 are Adjusted to Approximate Preliminary DEET (1995b) Estimates)

The projections of the total number of students in the system by field of study are given in Table 4.8. Overall student numbers are projected to increase by 5.2 percent between 1995 and 2001, with male numbers projected to increase by 4.7 percent and female numbers by 5.6 percent.

The total number of Australian students is projected to increase by 4.6 percent between 1995 and 2001, with male numbers by 3.9 percent and female numbers by 5.1 percent. In the year 2001 female students are projected to make up 55.6 percent of all Australian enrolment. The projections of male and female Australian students are plotted in Figure 4.2.

Total enrolment in all fields of study, except Education (I), are projected to increase between 1995 and 2001, with the growth in female numbers more than that for males. Both male and female enrolment in Education (I) are projected to decline, with male numbers declining by 3.6 percent and female numbers by only 0.7 percent. Enrolment in Law show an increase of 13.2 percent which is the highest of any field of study. Female Law enrolment are projected to increase by 15.7 percent and that for males by 10.6 percent.

Table 4.8 Projections of Total Undergraduate Enrolments, 1995 to 2001

	Year																								Percentage Change
	1994			1995			1996			1997			1998			1999			2000			2001			1995-2001			Average
Males
All	199960			205789			209070			210905			211697			212537			213744			215562			4.7			0.8
Australians	184498			189261			191727			192991			193387			193946			194916			196551			3.9			0.6
Architecture	6020			6251			6394			6469			6499			6526			6563			6610			5.7			0.9
Arts	31801			33031			33765			34154			34257			34367			34547			34838			5.5			0.9
Business	44380			45006			45379			45530			45473			45521			45731			46119			2.5			0.4
Education (I)	8561			8249			8024			7919			7874			7861			7889			7951			-3.6			-0.6
Engineering	30344			31330			31745			31943			32053			32181			32339			32623			4.1			0.7
Health	8106			8265			8320			8335			8317			8316			8337			8394			1.6			0.3
Law	7764			8171			8458			8657			8819			8913			8967			9036			10.6			1.7
Science	35885			37023			37563			37796			37836			37939			38134			38485			3.9			0.6
Females
All		241649			248616			252891			255689			256566			257856			259924			262537			5.6			0.9
Australians		228348			234450			238091			240469			241074			242155			244031			246487			5.1			0.8
Architecture		3377			3532			3640			3697			3713			3741			3772			3812			7.9			1.3
Arts		71831			75806			78324			79843			80467			81133			81943			82883			9.3			1.5
Business		36832			37687			38231			38557			38605			38753			39032			39408			4.6			0.7
Education (I)		24958			24052			23595			23483			23413			23460			23630			23892			-0.7			-0.1
Engineering		4696			4935			5017			5065			5087			5114			5157			5219			5.8			0.9
Health		36617			36512			36461			36670			36702			36828			37099			37477			2.6			0.4
Law		7909			8493			8951			9304			9530			9660			9743			9830			15.7			2.5
Science		27327			28622			29299			29729			29845			29999			30256			30596			6.9			1.1
Persons
All			441609			454405			461961			466594			468263			470393			473668			478099			5.2			0.9
Australians			412846			423711			429818			433460			434461			436101			438947			443038			4.6			0.7
Architecture			9397			9783			10034			10166			10212			10267			10335			10422			6.5			1.1
Arts			103632			108837			112089			113997			114724			115500			116490			117721			8.2			1.3
Business			81212			82693			83610			84087			84078			84274			84763			85527			3.4			0.6
Education (I)			33519			32301			31619			31402			31287			31321			31519			31843			-1.4			-0.2
Engineering			35040			36265			36762			37008			37140			37295			37496			37842			4.3			0.7
Health			44723			44777			44781			45005			45019			45144			45436			45871			2.4			0.4
Law			15673			16664			17409			17961			18349			18573			18710			18866			13.2			2.1
Science			63212			65645			66862			67525			67681			67938			68390			69081			5.2			0.9

Note: Enrolments for 1994 are actual numbers

Figure 4.2 Projections of Total Australian Undergraduate Enrolments, 1995 to 2001 (Enrolments for 1994 are Actual Numbers)

The actual number of course completions for 1994 are not available, and therefore, had to be projected. Table 4.9 shows that total number of course completions are projected to increase by 6.3 percent over the period 1995 to 2001. This consists of an increase of 6.1 percent for males and 6.5 percent for females.

Course completions by Australian students is projected to increase by 5.2 percent between 1995 and 2001, with male course completions by 4.6 percent and female by 5.7 percent. Female course completions are projected to be nearly 60 percent of all Australian course completions. The projections for males and females are plotted in Figure 4.3.

Once again there is considerable variation in the growth in completions across fields of study. There are projected to increase across all fields of study except Education (I) and Health where they are projected to decrease by 7.5 percent and 0.1 percent, respectively, between 1995 and 2001. Course completions in Law are projected to increase by 20 percent over this period, with male completions increasing by 14.8 percent and female completions by 25 percent.

Table 4.9 Projections of Undergraduate Course Completions, 1994 to 2001

	Year								Percentage Change
	1994	1995	1996	1997	1998	1999	2000	2001	1995-2001	Average
Males
All	38405	38519	39086	40064	40666	40769	40762	40878	6.1	1.0
Australians	35357	35257	35579	36356	36834	36866	36809	36879	4.6	0.8
Architecture	1055	1072	1108	1144	1165	1172	1174	1180	10.1	1.6
Arts	6189	6219	6395	6649	6731	6723	6714	6743	8.4	1.4
Business	8482	8224	8255	8435	8490	8431	8396	8423	2.4	0.4
Education (I)	2001	1857	1755	1703	1705	1690	1680	1686	-9.2	-1.6
Engineering	4298	4439	4507	4579	4691	4736	4713	4702	5.9	1.0
Health	1940	1946	1945	1979	1991	1979	1965	1969	1.2	0.2
Law	1567	1617	1674	1712	1789	1845	1853	1857	14.8	2.3
Science	7029	7072	7154	7337	7435	7417	7382	7397	4.6	0.8
Females
All	55959	55849	56721	58337	59001	59076	59101	59467	6.5	1.1
Australians	52576	52253	52878	54321	54891	54911	54889	55216	5.7	0.9
Architecture	684	687	719	752	762	765	764	771	12.2	1.9
Arts	14473	14828	15593	16395	16696	16791	16838	16995	14.6	2.3
Business	7414	7239	7328	7534	7613	7605	7597	7653	5.7	0.9
Education (I)	6847	6193	5808	5767	5771	5740	5719	5758	-7.0	-1.2
Engineering	686	769	795	804	828	830	829	826	7.4	1.2
Health	10493	10148	9882	10021	10074	10048	10047	10108	-0.4	-0.1
Law	1579	1646	1718	1844	1960	2029	2050	2057	25.0	3.8
Science	5762	5929	6099	6350	6479	6485	6475	6508	9.8	1.6
Persons
All	94364	94368	95807	98401	99667	99845	99863	100345	6.3	1.0
Australians	87933	87510	88457	90677	91725	91777	91698	92095	5.2	0.9
Architecture	1739	1759	1827	1896	1927	1937	1938	1951	10.9	1.7
Arts	20662	21047	21988	23044	23427	23514	23552	23738	12.8	2.0
Business	15896	15463	15583	15969	16103	16036	15993	16076	4.0	0.7
Education (I)	8848	8050	7563	7470	7476	7430	7399	7444	-7.5	-1.3
Engineering	4984	5208	5302	5383	5519	5566	5542	5528	6.1	1.0
Health	12433	12094	11827	12000	12065	12027	12012	12077	-0.1	0.0
Law	3146	3263	3392	3556	3749	3874	3903	3914	20.0	3.1
Science	12791	13001	13253	13687	13914	13902	13857	13905	7.0	1.1

Figure 4.3 Projections of Australian Undergraduate Course Completions, 1994 to 2001

Finally, Table 4.10 shows projections of the number of dropouts from the system between 1994 and 2001. Once again, 1994 figures for the number of dropouts are projected. The total number of dropouts is projected to increase by 3.7 percent between 1995 and 2001, with the male percentage slightly lower than this and that for the females slightly higher.

The number of Australian dropouts is projected to grow by 3.1 percent between 1995 and 2001. This represents a growth of 2.7 percent in the number of male dropouts and 3.5 percent that for females. The projected Australian male and female dropout numbers are plotted in Figure 4.4. Females are projected to make up 52.8 percent of all Australian dropouts by the year 2001.

The number of dropouts too show variation by field of study. Only male dropout numbers in Education (I) are projected fall between 1995 and 2001. Overall, the growth in the number of dropouts is highest in Law during this period, and unlike all other fields of study in Law the female growth in dropout numbers is lower than that for males.

Table 4.10 Projections of Undergraduate Dropouts, 1994 to 2001

	Year								Percentage Change
	1994	1995	1996	1997	1998	1999	2000	2001	1995-2001	Average
Males
All	26415	27618	27907	27934	27976	28129	28322	28588	3.5	0.6
Australians	24053	25140	25343	25293	25289	25406	25571	25815	2.7	0.4
Architecture	685	717	718	720	720	722	724	734	2.4	0.4
Arts	4722	4973	5022	5029	5034	5057	5083	5130	3.2	0.5
Business	6000	6207	6250	6247	6245	6272	6310	6370	2.6	0.4
Education (I)	1391	1389	1362	1339	1337	1342	1348	1364	-1.8	-0.3
Engineering	4102	4285	4305	4290	4285	4317	4350	4390	2.5	0.4
Health	1081	1128	1127	1123	1121	1124	1130	1139	1.0	0.2
Law	411	447	459	462	467	470	473	474	6.0	1.0
Science	5141	5384	5442	5410	5410	5448	5497	5553	3.1	0.5
Females
All	28107	29578	29841	29903	29911	30119	30430	30723	3.9	0.6
Australians	26531	27921	28135	28153	28140	28334	28628	28907	3.5	0.6
Architecture	286	303	308	313	310	314	320	325	7.3	1.2
Arts	8964	9637	9737	9745	9732	9818	9928	10028	4.1	0.7
Business	5069	5302	5356	5369	5362	5392	5436	5480	3.4	0.6
Education (I)	2875	2917	2893	2872	2861	2879	2908	2940	0.8	0.1
Engineering	565	593	601	604	601	609	610	622	4.9	0.8
Health	4052	4169	4141	4143	4157	4182	4214	4254	2.0	0.3
Law	359	388	392	394	395	400	403	406	4.6	0.8
Science	3484	3697	3705	3698	3698	3741	3789	3837	3.8	0.6
Persons
All	54522	57196	57748	57837	57887	58248	58752	59311	3.7	0.6
Australians	50584	53061	53478	53446	53429	53740	54199	54722	3.1	0.5
Architecture	971	1020	1026	1033	1030	1036	1044	1059	3.8	0.6
Arts	13686	14610	14759	14774	14766	14875	15011	15158	3.8	0.6
Business	11069	11509	11606	11616	11607	11664	11746	11850	3.0	0.5
Education (I)	4266	4306	4255	4211	4198	4221	4256	4304	0.0	0.0
Engineering	4667	4878	4906	4894	4886	4926	4960	5012	2.7	0.5
Health	5133	5297	5268	5266	5278	5306	5344	5393	1.8	0.3
Law	770	835	851	856	862	870	876	880	5.4	0.9
Science	8625	9081	9147	9108	9108	9189	9286	9390	3.4	0.6

Figure 4.4 Projections of Australian Undergraduate Dropouts, 1994 to 2001

4.4 Postgraduates

A different model is required for postgraduate students because their age profile is different to that for undergraduates. Postgraduate students' age profile is more uniform between the 22 to 45 year range. Ten age groups are considered. Associated with each age group there are up to six year of enrolment categories. The resulting model consists of 45 transient states. These are marked by a cross in Table 4.11. The states in this model are to be interpreted in the same way as that for the undergraduates' model.

Table 4.11 Transient States for the Model for Postgraduates Defined Using Age and Year of Enrolment as Criteria

	Year of Enrolment in Course
Age	1	2	3	4	5	6
Under 23	X
23-24	X	X
25-26	X	X	X
27-28	X	X	X	X
29-30	X	X	X	X	X
31-32	X	X	X	X	X	X
33-34	X	X	X	X	X	X
35-39	X	X	X	X	X	X
40-44	X	X	X	X	X	X
Over 44	X	X	X	X	X	X
Note: A Cross indicates that the transient state is included in the model

Three models, one each for males, females and persons, were estimated for the following three groups of postgraduate students defined by the level of the course:

Research (includes Higher Doctorate, Doctorate by Research and Master's by Research);
Master's by Coursework; and
Other Postgraduate (includes Postgraduate Qualifying, Graduate/Postgraduate Diploma new and extension area, Graduate Certificate and Bachelor's Postgraduate).

Analysis by fields of study is not contemplated at this stage as the number of students in some fields of study are unlikely to be sufficient for reliable estimates of the model parameters to be made.

Probability of Completing Course

Table 4.12 gives the probability of a student completing one of the three levels of course given his/her age at course commencement. For example, a male who commences a Research degree at the age of 23 or 24 years has a 61 percent chance of completing the degree, while a female of the same age has a 56 percent chance of completing it. In general, the chances of completing an Other Postgraduate course are the best and those of completing a Research degree the worst.

It is estimated that a person starting a Research degree at the age of 23 or 24 years has the best chance of completing it. However, there are some big differences between the chances for males and females who commence a course at the same age. For example, females commencing a course at the age of 31 or 32 years have only a 49 percent chance of completing the degree while males commencing at the same age have a 59 percent chance. Among those who are under 40 years old, males have a better chance of completing the course than females who commence at the same age. Only females who commence a degree at the age of 23 or 24 years have a better than even chance of completing it. Among males only those who commence a course at an age less than 23 years, or 40 years or more, have a worse than even chance of completing it.

A person's chances of completing a Master's by Coursework degree are approximately 67 percent irrespective of the age at which the course is commenced, except those who commence at an age of over 44 years have a 70 percent chance of completion. The difference between the male and female chances of completing a course vary by the age at which the course is commenced. Amongst those starting a course at an age of 25 or 26 years, the difference in the chances of completing the course are 7 percentage points in favour of the males. However, the difference is nearly 10 percentage points in favour of females among those who commence a course at an age of 40 years or more.

The probability of completing an Other Postgraduate course vary between 67 percent and 79 percent depending on the age at which a person commences the course. A female has a better chance of completing a course than a male who commences the course at the same age. The difference between the male and female chances of completing a course vary by the age at which the course is commenced, and is between 1 and 12 percentage points. For both males and females the chances of completing a course are best if the course is commenced at an age of 24 years or less.

Table 4.12 Probability of Completing an Postgraduate Course by Age at Course Commencement

Age at Course	Research			Master's by Coursework			Other Postgraduate
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 23	0.40	0.39	0.40	0.63	0.66	0.66	0.71	0.83	0.79
23-24	0.61	0.56	0.60	0.65	0.67	0.66	0.73	0.82	0.78
25-26	0.54	0.46	0.52	0.69	0.62	0.66	0.63	0.75	0.70
27-28	0.58	0.45	0.53	0.67	0.64	0.66	0.61	0.72	0.67
29-30	0.61	0.48	0.56	0.66	0.71	0.68	0.63	0.74	0.68
31-32	0.59	0.49	0.55	0.69	0.68	0.69	0.63	0.70	0.67
33-34	0.55	0.44	0.50	0.66	0.66	0.66	0.62	0.73	0.67
35-39	0.52	0.45	0.49	0.68	0.64	0.66	0.67	0.74	0.71
40-44	0.49	0.49	0.49	0.62	0.73	0.67	0.68	0.72	0.70
Over 44	0.46	0.46	0.46	0.65	0.74	0.70	0.68	0.69	0.69

Time in the System

Table 4.13 and Table 4.14 contain the mean and the standard deviation, respectively, of the time in the system for postgraduates. Factors which are likely to affect the estimates are:

the field of study;
the number of part-time students;
the length of the course;
number of students with credit for prior subjects or qualifications; and
the attrition rate from the course.

The mean time in the system for a person doing a Research degree varies by the age at which the course is commenced. The minimum mean time is 3.1 years for a person commencing at an age of 25 or 26 years, and the maximum mean time is 3.9 years for a person commencing at an age of 23 or 24 years. There is not much difference between the mean times for males and females. In general the standard deviation of the time in the system is least for those who commence a course when they are around the age of 25 to 28 years.

The mean time in the system tends to increase, but only very slightly, as the course commencement age increases for those doing Master's by Coursework. The mean time varies between 2.1 and 2.5 years. Although females stay in the system longer, on average, than males who commence the course at the same age, the difference in the times is small. The standard deviation of the time in the system is slightly higher, and more variable with course commencement age, for females than it is males.

For a person doing an Other Postgraduate course, the mean time in the system increases from mean of 1.4 years for someone who commences the course at an age of under 23 years to an average of 1.8 years for one who commences at an age of over 44 years. In general, females are in the system for a slightly longer time than males. In general, the standard deviation of the time in the system is slightly higher for males than females.

Table 4.13 Mean Number of Years in the System for Postgraduates by Age at Course Commencement

Age at Course	Research			Master's by Coursework			Other Postgraduate
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 23	3.4	3.5	3.4	2.1	2.2	2.1	1.4	1.4	1.4
23-24	3.9	3.8	3.9	2.2	2.3	2.2	1.6	1.6	1.6
25-26	3.2	3.1	3.1	2.2	2.2	2.2	1.7	1.6	1.6
27-28	3.2	3.1	3.2	2.3	2.3	2.3	1.6	1.7	1.7
29-30	3.4	3.3	3.4	2.3	2.5	2.4	1.7	1.8	1.7
31-32	3.4	3.5	3.4	2.3	2.4	2.4	1.7	1.8	1.7
33-34	3.4	3.2	3.3	2.3	2.4	2.3	1.7	1.8	1.7
35-39	3.5	3.4	3.4	2.3	2.4	2.4	1.7	1.8	1.8
40-44	3.6	3.6	3.6	2.3	2.7	2.5	1.7	1.8	1.8
Over 44	3.7	3.7	3.7	2.4	2.5	2.4	1.7	1.8	1.8

Table 4.14 Standard Deviation of the Number of Years in the System for Postgraduates by Age at Course Commencement

Age at Course	Research			Master's Coursework			Postgraduate Diploma
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 23	2.7	2.7	2.7	1.5	1.7	1.6	1.0	0.8	0.9
23-24	2.3	2.4	2.3	1.5	1.7	1.5	1.2	1.0	1.1
25-26	1.8	1.9	1.8	1.5	1.6	1.5	1.3	1.0	1.1
27-28	2.0	1.9	2.0	1.5	1.7	1.6	1.3	1.0	1.1
29-30	2.1	2.0	2.1	1.5	1.9	1.6	1.3	1.0	1.1
31-32	2.2	2.1	2.1	1.5	1.8	1.6	1.3	1.1	1.1
33-34	2.2	2.2	2.2	1.5	1.7	1.6	1.1	1.1	1.1
35-39	2.2	2.2	2.2	1.5	1.7	1.6	1.1	1.1	1.1
40-44	2.2	2.3	2.3	1.5	1.9	1.7	1.0	1.0	1.0
Over 44	2.2	2.4	2.3	1.6	1.8	1.7	1.0	1.0	1.0

Time to Completion

The mean and the standard deviation of the time to complete a postgraduate course are given in Table 4.15 and Table 4.16. Factors which are likely to affect the estimates are:

the field of study;
the number of part-time students;
the length of the course; and
number of students with credit for prior subjects or qualifications.

The mean time to complete a Research degree varies from 4.4 years for those who commence the course at the age of 25 or 26 years to 6 years for those who commence under the age of 23 years. The mean time sharply decreases as the age at which the course is commenced increases until a minimum is reached for those who commence at an age around 25 to 26 years, and then the mean time gradually increases with commencement age. A female's mean time to complete a course is longer than that for a male who commences at the same age with the maximum difference of half a year for those who commence at the age of 31 or 32 years. The pattern in the standard deviations of the time to complete a course is very similar to that for the standard deviations for the time in the system. We would expect the mean time to completion for doctorate students to be higher than the figures reported here, and the mean time to completion for Master's by Research to be lower.

In general, the mean time to complete a Master's by Coursework degree increases with the age at which the course is commenced, and varies between 2.7 and 3.1 years. A female's mean time to complete a course is slightly longer than that of a male commencing the course at the same age. Once again, the pattern of the standard deviations of the time to complete a course follow that for the time in the system although they are marginally higher.

There is an increase in the average time to complete an Other Postgraduate course as the age at which a course is commenced increases. The shortest mean time of 1.5 years is taken by a person who commences at an age of under 23 years, while those who commence at an age of 29 years or more take, on average, 2.1 years. In general females mean time is marginally shorter than that for males. The standard deviation of the time to complete a course does not vary much with course commencement age for females and persons. However, the standard deviation for males show considerable variation with course commencement age, and it is also higher than that for females who commence the course at the same age.

Table 4.15 Mean Number of Years to Complete a Postgraduate Course by Age at Course Commencement

Age at Course	Research			Master's by Coursework			Other Postgraduate
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 23	6.0	6.1	6.0	2.7	2.8	2.7	1.6	1.5	1.5
23-24	4.9	5.0	4.9	2.7	2.9	2.8	1.8	1.7	1.7
25-26	4.4	4.6	4.4	2.7	2.9	2.8	2.0	1.8	1.9
27-28	4.4	4.7	4.5	2.8	3.0	2.8	2.0	2.0	2.0
29-30	4.5	4.9	4.6	2.9	3.1	2.9	2.1	2.0	2.1
31-32	4.6	5.1	4.8	2.8	3.1	2.9	2.1	2.1	2.1
33-34	4.8	5.1	4.9	2.8	3.0	2.9	2.1	2.1	2.1
35-39	5.0	5.1	5.0	2.9	3.1	3.0	2.1	2.1	2.1
40-44	5.2	5.3	5.2	3.0	3.2	3.1	2.0	2.1	2.1
Over 44	5.4	5.6	5.5	3.0	3.0	3.0	2.0	2.1	2.1

Table 4.16 Standard Deviation of Number of Years to Complete a Postgraduate Course by Age at Course Commencement

Age at Course	Research			Master's Coursework			Other Postgraduate
Commencement	Male	Female	Person	Male	Female	Person	Male	Female	Person
Under 23	2.8	2.8	2.8	1.8	1.9	1.8	1.1	0.9	1.0
23-24	2.2	2.2	2.2	1.5	1.7	1.6	1.4	1.1	1.2
25-26	1.7	1.7	1.7	1.5	1.8	1.6	1.6	1.1	1.2
27-28	1.8	1.7	1.8	1.6	1.9	1.7	1.6	1.1	1.2
29-30	2.0	1.9	1.9	1.6	1.9	1.7	1.6	1.1	1.2
31-32	2.0	2.0	2.0	1.6	1.9	1.7	1.4	1.1	1.2
33-34	2.1	2.2	2.1	1.6	1.8	1.7	1.3	1.1	1.2
35-39	2.1	2.2	2.1	1.6	1.8	1.7	1.2	1.1	1.1
40-44	2.2	2.3	2.2	1.6	1.9	1.8	1.1	1.0	1.1
Over 44	2.3	2.2	2.3	1.7	1.9	1.8	1.1	1.0	1.1

Projections

Projections by age and level of course were made of:

the number of commencing students, 1995 to 2001;
the total enrolments, 1995 to 2001;
the number of course completions, 1994 to 2001; and
the number of dropouts, 1994 to 2001.

The 1994 intake and the total enrolment of students are actual figures. The 1995 projections of the intake are adjusted to approximate the preliminary DEET (1995b) estimates. Thereafter they are based on the method as set out in Section 2.2. In brief, this method assumes:

a constant proportion, based on the 1994 data, of the population in a given age group commencing postgraduate courses; and
the demographic changes projected to occur between 1995 and 2001.

In this report only aggregate projections by course level are included. Projections by age are available on request. The projections of intake by level of course and gender for 1995 to 2001 are given in Table 4.17. It shows that the highest growth in course commencements between 1995 and 2001 is projected to be 2.6 percent for Master's by Coursework. Students commencing Research degrees show a growth of 1.8 percent and those commencing Other Postgraduate courses 1.3 percent. Projections of the total postgraduate course commencements by gender are plotted in Figure 4.5.

Although female course commencements in Research degrees is projected to be 2 percent compared to 1.6 percent for males, the proportion of females commencing these courses goes down from 46.9 percent of all commencements in 1995 to only 42.4 percent in 2001. The growth in the Other Postgraduate course commencements for males is projected to be double the growth of that for females over this period. However, females are still projected to make up 58.5 percent of all Other Postgraduate course commencements in 2001.

Table 4.17 Projections of Postgraduate Commencements, 1995 to 2001

	Year								Percentage Change
	1994	1995	1996	1997	1998	1999	2000	2001	1995-2001	Average
Males
Research	5975	6606	6638	6661	6673	6685	6698	6714	1.6	0.3
Master's Coursework	9497	10494	10555	10616	10661	10699	10733	10763	2.6	0.4
Other Postgraduate	13685	15130	15208	15277	15312	15339	15369	15402	1.8	0.3
Total	29157	32230	32401	32555	32647	32723	32801	32880	2.0	0.3
Females
Research	4373	4854	4880	4897	4909	4922	4937	4952	2.0	0.3
Master's Coursework	8353	9279	9350	9405	9444	9476	9505	9524	2.6	0.4
Other Postgraduate	19406	21489	21560	21598	21616	21633	21656	21677	0.9	0.1
Total	32132	35622	35790	35899	35970	36031	36097	36152	1.5	0.2
Persons
Research	10348	11460	11517	11558	11582	11607	11635	11666	1.8	0.3
Master's Coursework	17850	19773	19904	20021	20106	20175	20238	20287	2.6	0.4
Other Postgraduate	33091	36619	36769	36875	36928	36972	37025	37079	1.3	0.2
Total	61289	67852	68190	68454	68616	68754	68898	69032	1.7	0.3

Notes: (a) Commencements for 1994 are actual numbers

(b) Commencements for 1995 have been adjusted to approximate preliminary DEET (1995b) estimates

Figure 4.5 Projections of Postgraduate Commencements, 1995 to 2001 (Enrolments for 1994 are Actual Numbers and Projections for 1995 are Adjusted to Approximate Preliminary DEET (1995b) Estimates)

Table 4.18 contains the projections of the total postgraduate enrolments by level of course and gender. Research degree enrolments are projected to increase by 16.1 percent between 1995 and 2001. The corresponding increases for Master's by Coursework and Other Postgraduate courses are 14.6 and 6.7 percent, respectively. The growth in female enrolments in Research and Master's by Coursework is projected to be higher than that for males. Figure 4.6 shows the projections of total postgraduate enrolments by gender.

Table 4.18 Projections of Total Postgraduate Enrolments, 1995 to 2001

	Year								Percentage Change
	1994	1995	1996	1997	1998	1999	2000	2001	1995-2001	Average
Males
Research	18344	19935	21014	21726	22210	22506	22682	22799	14.4	2.3
Master's Coursework	19952	21773	22892	23529	23907	24145	24314	24442	12.3	1.9
Other Postgraduate	22336	23941	24710	25062	25261	25386	25481	25564	6.8	1.1
Total	60632	65649	68616	70317	71378	72037	72477	72805	10.9	1.7
Females
Research	12640	13989	14946	15595	16029	16296	16459	16584	18.6	2.9
Master's Coursework	17216	19451	20832	21641	22117	22427	22649	22810	17.3	2.7
Other Postgraduate	31471	34256	35532	36001	36218	36346	36436	36509	6.6	1.1
Total	61327	67696	71310	73237	74364	75069	75544	75903	12.1	1.9
Persons
Research	30984	33924	35960	37321	38239	38802	39141	39383	16.1	2.5
Master's Coursework	37168	41224	43724	45170	46024	46572	46963	47252	14.6	2.3
Other Postgraduate	53807	58197	60242	61063	61479	61732	61917	62073	6.7	1.1
Total	121959	133345	139926	143554	145742	147106	148021	148708	11.5	1.8

Figure 4.6 Projections of Total Postgraduate Enrolments, 1995 to 2001 (Enrolments for 1994 are Actual Numbers)

Projections of postgraduate completions for the period 1994 to 2001 are given in Table 4.19. Research degree completions are projected to increase by a massive 38.1 percent over this period and that for Master's by Coursework by 22.2 percent. By comparison the increase in Other Postgraduate completions is a modest 8.8 percent. The growth in completions of Research and Master's by Coursework degrees is higher for females than for males. However, the female share of Research degree completions is projected to be only 39.2 percent of all Research degree completions in 2001. The projections of the total postgraduate completions by gender are plotted in Figure 4.7.

Table 4.19 Projections of Postgraduate Course Completions, 1994 to 2001

	Year								Percentage Change
	1994	1995	1996	1997	1998	1999	2000	2001		1995-2001	Average
Males
Research	2291	2605	2869	3063	3237	3359	3436	3484		33.7	5.0
Master's Coursework	5548	5993	6434	6724	6890	6984	7056	7107		18.6	2.9
Other Postgraduate	8987	9430	9847	10017	10108	10174	10225	10272		8.9	1.4
Total	16826	18028	19150	19804	20235	20517	20717	20863		15.7	2.5
Females
Research	1338	1544	1736	1888	2022	2129	2196	2245		45.4	6.4
Master's Coursework	4438	5050	5578	5925	6127	6251	6328	6390		26.5	4.0
Other Postgraduate	13957	15035	15785	16053	16176	16244	16292	16337		8.7	1.4
Total	19733	21629	23099	23866	24325	24624	24816	24972		15.5	2.4
Persons
Research	3629	4149	4605	4951	5259	5488	5632	5729		38.1	5.5
Master's Coursework	9986	11043	12012	12649	13017	13235	13384	13497		22.2	3.4
Other Postgraduate	22944	24465	25632	26070	26284	26418	26517	26609		8.8	1.4
Total	36559	39657	42249	43670	44560	45141	45533	45835		15.6	2.4

Figure 4.7 Projections of Postgraduate Course Completions, 1994 to 2001

Table 4.20 contains the projections of the number of postgraduate dropouts at the disaggregated level. The growth in the number of Research degree dropouts is projected to be 11.1 percent between 1995 and 2001, but it is only less than half this for Master's by Coursework degree. The growth in female dropouts from Research degrees is higher than that for males. From Master's by Coursework and Other Postgraduate courses the growth in the number of dropouts is higher for males. Finally, Figure 4.8 shows the projections of the number of postgraduate dropouts by gender for 1994 to 2001.

Table 4.20 Projections of Postgraduate Dropouts, 1994 to 2001

	Year								Percentage Change
	1994	1995	1996	1997	1998	1999	2000	2001	1995-2001	Average
Males
Research	2692	2890	2997	3070	3111	3141	3160	3175	9.9	1.6
Master's Coursework	3136	3443	3544	3563	3582	3604	3624	3645	5.9	1.0
Other Postgraduate	4577	5012	5078	5106	5133	5160	5181	5202	3.8	0.6
Total	10405	11345	11619	11739	11826	11905	11965	12022	6.0	1.0
Females
Research	2157	2352	2460	2541	2590	2611	2631	2647	12.5	2.0
Master's Coursework	2624	2923	2998	3022	3039	3054	3059	3065	4.9	0.8
Other Postgraduate	4759	5252	5315	5344	5370	5393	5409	5425	3.3	0.5
Total	9540	10527	10773	10907	10999	11058	11099	11137	5.8	0.9
Persons
Research	4849	5242	5457	5611	5701	5752	5791	5822	11.1	1.8
Master's Coursework	5760	6366	6542	6585	6621	6658	6683	6710	5.4	0.9
Other Postgraduate	9336	10264	10393	10450	10503	10553	10590	10627	3.5	0.6
Total	19945	21872	22392	22646	22825	22963	23064	23159	5.9	1.0

Figure 4.8 Projections of Postgraduate Dropouts, 1995 to 2001

4.5 A Summary of Projections

Table 4.21 summarises the projections for the whole higher education sector. It also includes projections for the Others category. This category is made up of Associate Diploma, Other Award, Enabling and Non-award courses together with students who were not included in the analysis for reasons stated in Section 3.2. The commencements and total enrolment projections for the Others category are held constant at the 1994 level, and the completions projections at the 1993 level, for sake of convenience. However, dropout numbers for any year are not available. As has been stated earlier these projections are based on a set of assumptions for undergraduates and another set for postgraduates. They are largely driven by demographic changes.

Table 4.21 Summary of Projections of Commencements, Total Enrolment, Completions and Dropouts, All Courses, 1994 to 2001

	Year								Percentage Change
Course Level	1994	1995	1996	1997	1998	1999	2000	2001	1995-2001	Average
Commencements
Undergraduate	151274	161682	159111	158184	157915	159688	161364	163054	0.8	0.1
Postgraduate	61289	67807	68172	68472	68771	69052	69298	69528	2.5	0.4
Others	12662	12662	12662	12662	12662	12662	12662	12662	0.0	0.0
Total	225225	242152	239946	239317	239348	241402	243323	245244	1.3	0.2
Total Enrolment
Undergraduate	441609	454405	461961	466594	468263	470393	473668	478099	5.2	1.3
Postgraduate	121959	133264	139898	143730	146180	147849	149050	149966	12.5	3.0
Others	21828	21828	21828	21828	21828	21828	21828	21828	0.0	0.0
Total	585396	609497	623687	632152	636271	640070	644546	649893	6.6	1.4
Completions
Undergraduate	94364	94368	95807	98401	99667	99845	99863	100345	6.3	1.0
Postgraduate	36559	39657	42249	43670	44560	45141	45533	45835	15.6	2.4
Others	3960	3960	3960	3960	3960	3960	3960	3960	0.0	0.0
Total	134883	137985	142016	146031	148187	148946	149356	150140	8.8	1.4
Dropouts
Undergraduate	54522	57196	57748	57837	57887	58248	58752	59311	3.7	0.6
Postgraduate	19945	21872	22392	22646	22825	22963	23064	23159	5.9	1.0
Others	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A
Total	74467	79068	80140	80483	80712	81211	81816	82470	4.3	0.7

Notes: (a) Commencements and total enrolment for 1994 are actual numbers

(b) Commencements for 1995 have been adjusted to approximate preliminary DEET (1995b) estimates

(c) Others include Associate Diploma, Other award, Enabling and Non-award courses, and those removed from the analysis as discussed in Section 3.2

(d) Completions for Others are set at the 1993 level for sake of convenience

4.6 Model Evaluation

The question of the stability over time of the estimated matrix of transition proportions, Q, is important. All projections that are made assume this matrix to remain invariant over the projection period. The calculation of the fundamental matrix, N, also assumes that that Q is invariant over time. If data for previous years with the necessary detail were available then it is possible to test statistically if Q, is stable over time. Data are available for 1989 to 1992, but without the detail necessary to re-estimate Q. However, we can assess the stability of the estimated Q indirectly by considering the accuracy of total enrolment predictions retrospectively. These predictions are made conditional on the actual intake of students for each year. If the accuracy of the predictions is high then it is not unreasonable to infer that Q is stable over this time period.

The total enrolment was predicted for each of the years 1990 to 1994 beginning each time with the actual 1989 enrolment distribution as the base and using the predicted intermediate enrolment values. In each case the intake vector was the actual intake for the prediction year. Thus five predictions are obtained: 1-step-ahead for 1990, 2-step-ahead for 1991, 3-step-ahead for 1992, 4-step-ahead for 1993 and 5-step-ahead for 1994. The procedure was repeated with each of the observed 1990 to 1992 enrolment distributions taken in turn as the base. Altogether four 1-step-ahead, four 2-step-ahead, three 3-step-ahead, two 4-step-ahead and one 5-step-ahead predictions were obtained.

Using the notation of chapter 2 the following recursive formulae generates all the predictions: for each

(4.1)

where denotes a prediction.

The accuracy of predictions was assessed by calculating the mean absolute percentage error (MAPE) and the mean percentage error (MPE) for each set of n-step-ahead predictions, for . Thus there were five MAPEs and five MPEs to assess accuracy and indirectly the stability of the matrix Q.

Similarly, the column representing transitions into the completion state in the matrix R was assessed for stability using the predictions for course completions. The procedure adopted was exactly as outlined above with the predictions conditional on the actual intake of students for each year.

The normal convention is to use the oldest data to estimate the model and the most recent data to evaluate the predictive power of the model. However, because of the lack of detail in the data for the earlier periods the above unconventional approach was adopted. A consequence of the above approach could be that the results may not have a pattern that is normally expected, such as that of the accuracy of predictions decreasing with a lengthening prediction horizon. The reason for this is that there are two opposing factors affecting accuracy of predictions. The first factor is the time period between 1993/1994 (data for these years were used to estimate the matrix of transition proportions) and the year for which the prediction is made. We can expect the accuracy of the predictions to be less as this time period increases. The second factor is the time period between the base year (the observed distribution of enrolment for the base year is used to initialise the recursive formula in equation (4.1)) and the year for which the prediction is made. Once again we can expect the accuracy of the predictions to deteriorate as this time period becomes longer.

The data for 1989 to 1992 that are available are in a more aggregated form than that for 1993 and 1994. In particular, they do not contain the course commencement date and students over 29 years in age are sorted in ten-year wide classes. A variable indicating the year of enrolment in a course by a student is given instead of the course commencement date. The value of this variable is one, two, three or four plus only. Thus, in order to conform with the structure of the input-output model a redistribution of students into the states of the model was done based on average proportions for 1993 and 1994. A summary of the data for 1989 to 1994 is described in Appendix B.

The calculations for the accuracy measures for predicting total enrolment for the years 1990 to 1994 are given in Table 4.22. The mean absolute percentage error (MAPE) for 1-step-ahead predictions for all undergraduates is 0.81 percent, with the figure for males 0.72 percent and that for females 0.91 percent. In general, the accuracy diminishes as the prediction horizon increases, although there are some exceptions to this rule when one looks at the results for some fields of study. This pattern of results is likely due to the factors affecting prediction accuracy that were discussed earlier in this section. It should be noted that the 5-step-ahead MAPE and MPE are based on a single prediction and as such are not really averages. Comparing just the 1-step-ahead MAPEs for males and females, overall male enrolment is more accurately predicted than that of females.

Three fields of study results, that of Business, Health and Law, stand out as not so accurate compared to the others. Part of the reason for the lack of accuracy may be due to the administrative adjustment in some fields of study classification in 1987 that affected just these three broad fields of study; see DEET (1995a). Other factors contributing to the lack of accuracy may be the volatility in the number of students commencing and the total number enrolled in courses in these fields of study. As indicated in Table B1 and Table B2 in Appendix B, there has been considerable increase in both the number commencing and the total enrolment of students taking courses in Law between 1989 and 1994. The corresponding data for Business show quite a bit of volatility in this period. The number of course commencements in Health has also been dropping since 1992. The growth in total enrolment in Health reached a peak of 13.7 percent in 1989, but since then the growth in numbers has been dropping, and, in fact, numbers declined by 3.7 percent in 1994.

Most of the values for MPE, a notable exception being Arts, are negative. This systematic pattern suggests possible bias in the predictions. The models consistently underestimate actual enrolment. However, as the absolute errors, in general, are not large this bias may not be significant.

Table 4.22 Prediction Accuracy for Undergraduate Enrolments, 1990 to 1994

	Mean Absolute Percentage Error					Mean Percentage Error
	1-step	2-step	3-step	4-step	5-step	1-step	2-step	3-step	4-step	5-step
Males
All	0.72	1.04	1.26	1.27	0.97	-0.68	-1.04	-1.26	-1.27	-0.97
Australian	0.74	0.95	1.17	1.19	0.92	-0.55	-0.95	-1.17	-1.19	-0.92
Architecture	0.77	1.00	1.35	1.52	1.16	-0.76	-1.00	-1.35	-1.52	-1.16
Arts	0.59	0.31	0.10	0.17	0.14	0.20	0.09	0.10	0.17	0.14
Business	1.79	2.50	3.07	3.21	2.62	-1.79	-2.50	-3.07	-3.21	-2.62
Education (I)	1.01	0.52	0.74	0.92	0.83	0.75	-0.25	-0.63	-0.92	-0.83
Engineering	0.61	0.76	1.11	1.29	1.13	-0.21	-0.76	-1.11	-1.29	-1.13
Health	2.90	3.75	4.31	4.39	3.17	-2.90	-3.75	-4.31	-4.39	-3.17
Law	5.07	6.05	6.79	6.68	5.27	-5.07	-6.05	-6.79	-6.68	-5.27
Science	0.87	0.77	0.63	0.51	0.34	-0.06	-0.41	-0.63	-0.51	-0.34
Females
All	0.91	1.56	2.01	1.98	1.58	-0.91	-1.56	-2.01	-1.98	-1.58
Australian	0.83	1.42	1.85	1.85	1.49	-0.75	-1.42	-1.85	-1.85	-1.49
Architecture	1.33	1.85	0.90	0.14	0.15	0.56	1.12	0.59	0.14	0.15
Arts	0.84	0.82	1.03	1.20	0.86	0.77	0.82	1.03	1.20	0.86
Business	2.59	3.67	4.56	4.70	3.58	-2.59	-3.67	-4.56	-4.70	-3.58
Education (I)	0.50	0.98	1.91	2.10	1.96	0.39	-0.98	-1.91	-2.10	-1.96
Engineering	0.34	0.53	0.87	1.16	1.09	-0.34	-0.53	-0.87	-1.16	-1.09
Health	3.54	4.73	5.24	4.69	3.20	-3.54	-4.73	-5.24	-4.69	-3.20
Law	5.33	6.21	7.10	7.29	5.65	-5.33	-6.21	-7.10	-7.29	-5.65
Science	0.28	0.20	0.12	0.17	0.18	0.14	-0.07	-0.12	-0.17	-0.18
Persons
All	0.81	1.33	1.67	1.66	1.30	-0.81	-1.33	-1.67	-1.66	-1.30
Australian	0.79	1.21	1.55	1.56	1.23	-0.66	-1.21	-1.55	-1.56	-1.23
Architecture	0.97	0.84	0.66	0.93	0.69	-0.30	-0.25	-0.66	-0.93	-0.69
Arts	0.71	0.59	0.74	0.88	0.64	0.59	0.59	0.74	0.88	0.64
Business	2.14	3.02	3.74	3.88	3.06	-2.14	-3.02	-3.74	-3.88	-3.06
Education (I)	0.59	0.79	1.59	1.80	1.67	0.48	-0.79	-1.59	-1.80	-1.67
Engineering	0.56	0.73	1.08	1.27	1.12	-0.22	-0.73	-1.08	-1.27	-1.12
Health	3.43	4.56	5.08	4.63	3.19	-3.43	-4.56	-5.08	-4.63	-3.19
Law	5.20	6.14	6.94	6.98	5.46	-5.20	-6.14	-6.94	-6.98	-5.46
Science	0.62	0.53	0.41	0.36	0.27	0.03	-0.26	-0.41	-0.36	-0.27

Table 4.23 contains the accuracy measures of predicting undergraduate course completions for the years 1989 to 1993. MAPE for 1-step-ahead predictions for all undergraduates is 3.54 percent, with the figure for males 2.68 percent and that for females 4.17 percent. For Australian students MAPE for 1-step-ahead predictions is 2.59 percent. However, just as in the case for total enrolment, there is considerable variation in this statistic across fields of study. It ranges from 1.7 percent for Science to just over 14.7 percent for Law. Also, the inaccuracy in predicting completions in Business, Health and Law is considerably above that for other fields of study. This may well be explained by the fact that the average annual increase in completions for these three fields of study between 1989 and 1993 was 12.7, 16.2 and 12.3 percent, respectively; see Table B3 in Appendix B.

The MPE results indicate possible bias in the predictions of completions generated from some of the models, but the direction of the bias is not as consistent as that evidenced for total enrolment predictions. Overall the models are less accurate in predicting completions than in predicting total enrolment.

Table 4.23 Prediction Accuracy for Undergraduate Completions, 1989 to 1993

	Mean Absolute Percentage Error					Mean Percentage Error
	1-step	2-step	3-step	4-step	5-step	1-step	2-step	3-step	4-step	5-step
Males
All	2.68	1.03	1.59	1.44	2.21	2.68	0.67	-0.40	-1.44	-2.21
Australian	1.93	0.87	1.70	1.36	1.93	1.76	0.60	-0.22	-1.36	-1.93
Architecture	3.82	4.43	4.38	3.84	2.28	-3.03	-4.43	-4.38	-3.84	-2.28
Arts	4.11	2.22	2.07	0.45	0.54	4.11	2.11	1.43	0.40	0.54
Business	11.74	5.11	4.29	3.40	5.32	11.74	4.34	1.00	-3.40	-5.32
Education (I)	16.65	6.70	4.87	0.38	0.48	-16.65	-5.88	-4.39	-0.38	0.48
Engineering	4.53	2.14	0.68	0.69	0.13	-4.37	-0.49	0.58	-0.01	-0.13
Health	6.64	2.24	3.82	6.46	8.07	6.64	-0.02	-3.82	-6.46	-8.07
Law	17.21	13.46	10.75	5.53	17.55	17.21	9.85	6.35	-4.60	-17.55
Science	1.34	1.54	1.90	1.82	0.62	-1.23	-1.31	-1.90	-1.82	-0.62
Females
All	4.17	2.84	1.91	1.44	2.86	4.17	2.80	0.58	-1.44	-2.86
Australian	3.19	2.59	1.73	1.27	2.54	3.19	2.59	0.60	-1.27	-2.54
Architecture	8.16	3.19	2.98	2.28	0.00	6.31	1.58	1.87	2.28	0.00
Arts	4.38	4.46	4.03	3.72	3.81	4.38	4.46	4.03	3.72	3.81
Business	13.43	6.68	5.12	4.65	9.19	13.43	4.84	0.17	-4.65	-9.19
Education (I)	8.97	4.94	3.68	2.04	0.49	-8.97	0.66	0.68	1.80	-0.49
Engineering	6.74	5.49	3.38	1.18	1.58	-4.83	-1.28	3.24	0.76	1.58
Health	13.62	8.19	7.65	8.94	9.58	13.62	4.50	-2.92	-8.94	-9.58
Law	12.54	13.45	8.39	5.17	18.22	12.04	5.26	3.91	-5.17	-18.22
Science	2.21	1.96	1.36	1.59	0.57	0.72	1.96	1.36	1.59	0.57
Persons
All	3.54	2.08	1.77	1.44	2.60	3.54	1.91	0.18	-1.44	-2.60
Australian	2.59	1.84	1.72	1.31	2.30	2.59	1.76	0.27	-1.31	-2.30
Architecture	3.38	2.35	2.06	1.51	1.40	0.08	-2.35	-2.06	-1.51	-1.40
Arts	4.29	3.74	3.24	2.71	2.81	4.29	3.74	3.24	2.71	2.81
Business	12.49	5.80	4.56	4.00	7.12	12.49	4.54	0.61	-4.00	-7.12
Education (I)	10.89	5.32	3.62	1.52	0.28	-10.89	-0.87	-0.50	1.30	-0.28
Engineering	4.76	2.39	0.96	0.46	0.09	-4.43	-0.57	0.86	0.09	0.09
Health	12.39	7.14	6.94	8.57	9.35	12.39	3.66	-3.11	-8.57	-9.35
Law	14.73	13.45	9.59	5.26	17.88	14.73	7.62	5.16	-4.88	-17.88
Science	1.70	1.05	0.84	0.49	0.10	-0.41	0.07	-0.50	-0.36	-0.10

Table 4.24 gives MAPE and MPE of predicting postgraduate enrolments for 1990 to 1994. The MAPE of 1-step-ahead predictions of the total enrolment is 1.79 percent, with the figure for males 2.36 percent and that for females 1.18 percent. Male enrolments for Research degrees are more accurately predicted than that for females while female enrolments are more accurately predicted for the other two course levels. A likely reason for large inaccuracies in predicting the total enrolment in Research and Master's by Coursework courses is the very high growth in the number of students commencing and the total enrolment in these courses that occurred between 1989 and 1994; see Table B4 and Table B5 in Appendix B. The MPE results suggest some bias in the results. The negative sign for MPE implies that the predictions are underestimates of the observed values.

Table 4.24 Prediction Accuracy for Postgraduate Enrolments, 1990 to 1994

	Mean Absolute Percentage Error					Mean Percentage Error
	1-step	2-step	3-step	4-step	5-step	1-step	2-step	3-step	4-step	5-step
Males
Research	3.22	3.67	3.83	2.95	2.16	-3.22	-3.67	-3.83	-2.95	-2.16
Master's by Coursework	2.92	3.14