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.
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.
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.
| 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:
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
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:
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 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
Table 4.5 Mean Number of Years to Complete an Undergraduate Course by Age at Course Commencement
Projections
Projections by age and field of study were made of:
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:
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
| All | |||||||||||||||||||||
| Australians | |||||||||||||||||||||
| Architecture | |||||||||||||||||||||
| Arts | |||||||||||||||||||||
| Business | |||||||||||||||||||||
| Education (I) | |||||||||||||||||||||
| Engineering | |||||||||||||||||||||
| Health | |||||||||||||||||||||
| Law | |||||||||||||||||||||
| Science | |||||||||||||||||||||
| All | |||||||||||||||||||||
| Australians | |||||||||||||||||||||
| Architecture | |||||||||||||||||||||
| Arts | |||||||||||||||||||||
| Business | |||||||||||||||||||||
| Education (I) | |||||||||||||||||||||
| Engineering | |||||||||||||||||||||
| Health | |||||||||||||||||||||
| Law | |||||||||||||||||||||
| Science | |||||||||||||||||||||
| All | |||||||||||||||||||||
| Australians | |||||||||||||||||||||
| Architecture | |||||||||||||||||||||
| Arts | |||||||||||||||||||||
| Business | |||||||||||||||||||||
| Education (I) | |||||||||||||||||||||
| Engineering | |||||||||||||||||||||
| Health | |||||||||||||||||||||
| Law | |||||||||||||||||||||
| Science | |||||||||||||||||||||
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
| All | ||||||||||||||||||||||||||||||
| Australians | ||||||||||||||||||||||||||||||
| Architecture | ||||||||||||||||||||||||||||||
| Arts | ||||||||||||||||||||||||||||||
| Business | ||||||||||||||||||||||||||||||
| Education (I) | ||||||||||||||||||||||||||||||
| Engineering | ||||||||||||||||||||||||||||||
| Health | ||||||||||||||||||||||||||||||
| Law | ||||||||||||||||||||||||||||||
| Science | ||||||||||||||||||||||||||||||
| All | ||||||||||||||||||||||||||||||
| Australians | ||||||||||||||||||||||||||||||
| Architecture | ||||||||||||||||||||||||||||||
| Arts | ||||||||||||||||||||||||||||||
| Business | ||||||||||||||||||||||||||||||
| Education (I) | ||||||||||||||||||||||||||||||
| Engineering | ||||||||||||||||||||||||||||||
| Health | ||||||||||||||||||||||||||||||
| Law | ||||||||||||||||||||||||||||||
| Science | ||||||||||||||||||||||||||||||
| All | ||||||||||||||||||||||||||||||
| Australians | ||||||||||||||||||||||||||||||
| Architecture | ||||||||||||||||||||||||||||||
| Arts | ||||||||||||||||||||||||||||||
| Business | ||||||||||||||||||||||||||||||
| Education (I) | ||||||||||||||||||||||||||||||
| Engineering | ||||||||||||||||||||||||||||||
| Health | ||||||||||||||||||||||||||||||
| Law | ||||||||||||||||||||||||||||||
| Science | ||||||||||||||||||||||||||||||
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
| All | ||||||||||
| Australians | ||||||||||
| Architecture | ||||||||||
| Arts | ||||||||||
| Business | ||||||||||
| Education (I) | ||||||||||
| Engineering | ||||||||||
| Health | ||||||||||
| Law | ||||||||||
| Science | ||||||||||
| All | ||||||||||
| Australians | ||||||||||
| Architecture | ||||||||||
| Arts | ||||||||||
| Business | ||||||||||
| Education (I) | ||||||||||
| Engineering | ||||||||||
| Health | ||||||||||
| Law | ||||||||||
| Science | ||||||||||
| All | ||||||||||
| Australians | ||||||||||
| Architecture | ||||||||||
| Arts | ||||||||||
| Business | ||||||||||
| Education (I) | ||||||||||
| Engineering | ||||||||||
| Health | ||||||||||
| Law | ||||||||||
| Science | ||||||||||
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
| All | ||||||||||
| Australians | ||||||||||
| Architecture | ||||||||||
| Arts | ||||||||||
| Business | ||||||||||
| Education (I) | ||||||||||
| Engineering | ||||||||||
| Health | ||||||||||
| Law | ||||||||||
| Science | ||||||||||
| All | ||||||||||
| Australians | ||||||||||
| Architecture | ||||||||||
| Arts | ||||||||||
| Business | ||||||||||
| Education (I) | ||||||||||
| Engineering | ||||||||||
| Health | ||||||||||
| Law | ||||||||||
| Science | ||||||||||
| All | ||||||||||
| Australians | ||||||||||
| Architecture | ||||||||||
| Arts | ||||||||||
| Business | ||||||||||
| Education (I) | ||||||||||
| Engineering | ||||||||||
| Health | ||||||||||
| Law | ||||||||||
| Science | ||||||||||
Figure 4.4 Projections of Australian Undergraduate Dropouts, 1994 to 2001
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.
| 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:
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
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 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
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 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
Projections
Projections by age and level of course were made of:
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:
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
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
Notes: (a) Commencements for 1994 are actual numbers
(b) Commencements for 1995 have been 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
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
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
| Research | |||||||||||
| Master's Coursework | |||||||||||
| Other Postgraduate | |||||||||||
| Total | |||||||||||
| Research | |||||||||||
| Master's Coursework | |||||||||||
| Other Postgraduate | |||||||||||
| Total | |||||||||||
| Research | |||||||||||
| Master's Coursework | |||||||||||
| Other Postgraduate | |||||||||||
| Total | |||||||||||
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
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
| Research | ||||||||||
| Master's Coursework | ||||||||||
| Other Postgraduate | ||||||||||
| Total | ||||||||||
Figure 4.8 Projections of Postgraduate Dropouts, 1995 to 2001
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.
| Course Level | ||||||||||
| Undergraduate | ||||||||||
| Postgraduate | ||||||||||
| Others | ||||||||||
| Total | ||||||||||
| Undergraduate | ||||||||||
| Postgraduate | ||||||||||
| Others | ||||||||||
| Total | ||||||||||
| Undergraduate | ||||||||||
| Postgraduate | ||||||||||
| Others | ||||||||||
| Total | ||||||||||
| Undergraduate | ||||||||||
| Postgraduate | ||||||||||
| Others | ||||||||||
| Total | ||||||||||
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
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
| All | |||||||||||
| Australian | |||||||||||
| Architecture | |||||||||||
| Arts | |||||||||||
| Business | |||||||||||
| Education (I) | |||||||||||
| Engineering | |||||||||||
| Health | |||||||||||
| Law | |||||||||||
| Science | |||||||||||
| All | |||||||||||
| Australian | |||||||||||
| Architecture | |||||||||||
| Arts | |||||||||||
| Business | |||||||||||
| Education (I) | |||||||||||
| Engineering | |||||||||||
| Health | |||||||||||
| Law | |||||||||||
| Science | |||||||||||
| All | |||||||||||
| Australian | |||||||||||
| Architecture | |||||||||||
| Arts | |||||||||||
| Business | |||||||||||
| Education (I) | |||||||||||
| Engineering | |||||||||||
| Health | |||||||||||
| Law | |||||||||||
| Science | |||||||||||
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
| All | |||||||||||
| Australian | |||||||||||
| Architecture | |||||||||||
| Arts | |||||||||||
| Business | |||||||||||
| Education (I) | |||||||||||
| Engineering | |||||||||||
| Health | |||||||||||
| Law | |||||||||||
| Science | |||||||||||
| All | |||||||||||
| Australian | |||||||||||
| Architecture | |||||||||||
| Arts | |||||||||||
| Business | |||||||||||
| Education (I) | |||||||||||
| Engineering | |||||||||||
| Health | |||||||||||
| Law | |||||||||||
| Science | |||||||||||
| All | |||||||||||
| Australian | |||||||||||
| Architecture | |||||||||||
| Arts | |||||||||||
| Business | |||||||||||
| Education (I) | |||||||||||
| Engineering | |||||||||||
| Health | |||||||||||
| Law | |||||||||||
| Science | |||||||||||
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
| Research | ||||||||||||||||||
| Master's by Coursework | ||||||||||||||||||