Appendix 1: 
Data
The Longitudinal Surveys of Australian Youth data
The primary source of data for this study is from the Longitudinal Surveys of Australian Youth (LSAY), a survey of young Australians interviewed annually on their school experiences, and post-school education, training and work activity. 
In 1998, a nationally representative sample of 14 118 Year 9 students was selected to form the second cohort of the Longitudinal Surveys of Australian Youth program. The initial sample was constructed by randomly selecting two to three Year 9 classes from a sample of schools designed to represent state and sector. Smaller states and territories were over-sampled to provide sufficient numbers to provide reliable state estimates on a number of key variables. This sample, termed the Y98 cohort, was surveyed in 1999 with a mail survey and in subsequent years with telephone surveys. In 2000, the sample was rebuilt (by contacting the cohort beyond those that responded to the 1999 survey), and hence the increase in the sample between 1999 and 2000.
Table 15:	Longitudinal Surveys of Australian Youth sample, collection methodology and attrition rates
	1998	1999	2000	2001	2002	
School year*	Year 9	Year 10	Year 11	Year 12/13	Left school	
No. students in the LSAY sample 	14 118	9 289	9 548	8 777	7 762	
Collection method	Numeracy & literacy tests and in-class interviews	Mail	Telephone	Telephone	Telephone	
Note:	* For majority of students.
The NCVER data
One of the NCVER Australian vocational education and training statistical collections contains the National VET Provider Collection. This collection of public VET students provides a more detailed picture of student VET activity to compliment the longitudinal surveys data for any given year. 
In 2002, Year 11 for our longitudinal surveys students, NCVER reported on the activity of 1.67 million students, 25% of which were aged less than 19 years (NCVER 2003).
The matching process
NCVER matched the longitudinal surveys data with the National VET Provider Collection for 1998, 1999, 2000, 2001, 2002 and 2003 years. The matching methodology used a combination of surrogate indicators which are most unlikely to occur unless it is the same person in both data sets (NCVER technical notes: Methodology used for monitoring student flows in the VET system 2001 [unpublished]). These included encrypted name, date of birth, sex, Indigenous status, postcode and the state where attended school. 
The matching is depicted in figure 3. It should be noted that while we were able to match the NCVER student data from 1998 through to 2003 with the longitudinal surveys data, the longitudinal surveys questionnaire only asked about school VET activity in Year 11 and Year 12 (2000 and 2001). Therefore we are only able to explore school VET activity on the matched NCVER data between 2000 and 2001. For data that matched outside these years, we cannot verify the nature of the school VET activity with the longitudinal surveys data as these questions were not asked.

Figure 3:	Data sets involved in the project

	

In total, 4562 records were matched from the longitudinal surveys data to the NCVER data. In some cases, there were one-to-many matches to the NCVER collections due to students enrolling and dropping a number of courses. These one-to-many matches were cleaned to include only the highest major qualification reported. As a result 3828 matches were achieved. Some 1385, or 36%, of these matches were continuing students, resulting in 2443 unique record matches.
Table 16:	Results of NCVER–Longitudinal Surveys of Australian Youth matching
	1998	1999	2000	2001	2002	2003	Total	
			School VET activity				
School Year*	Year 9	Year 10	Year 11	Year 12/13	Left school	Left school		
No. students in LSAY sample		14 118		9 289		9 548		8 777		7 762	N/A	N/A	
LSAY school VET program participants		Not 	asked		Not 	asked		2 144		1 603	N/A	N/A	N/A	
No. LSAY–NCVER matches		3	203		697		963		1 009		953		3 828	
Continuing students		–	–		70		336		380		599		1 385	
New students		3	203		627		627		629		354		2 443	
NCVER VET in Schools		0	1		15		284		14		5		319	
LSAY school VET program participants **		–	–		2 145		1 671		–		–		–	
Notes:	* For the majority of students; ** ‘No’ or ‘unknown’ VET status in original longitudinal surveys sample was updated if these students were reported as NCVER VET in Schools students.

Appendix 2: 
Factor analysis
Most of the control variables were readily available or could be easily derived from the Longitudinal Surveys of Australian Youth dataset except for engagement with school, perceived attitude of peers and self-perceived academic ability. To derive this information, factor analysis was conducted.
Engagement with school
‘Engagement’ in the Longitudinal Surveys of Australian Youth data is captured in the questionnaire administered to students while they were in Year 10, which asks about their participation in a range of extracurricular activities:
•	Sport
•	Music, band or orchestra
•	Debating
•	Drama, theatre, dance or school play
•	Community and support work at school (e.g. peer support, fundraising).
Responses to these items were re-coded from the original categories relating to frequency of participation into a four-point scale; with 0 representing no participation in the activity through to 3 representing participation in the activity on at least a weekly basis. The individual factor loadings for sport, music, debate, drama and support work were 0.425, 0.627, 0.687, 0.656 and 0.639, respectively. Each individual variable was then weighted proportionally by their actual contribution and summed up to give an engagement with school score.
Perceived attitude of peers
Perceived attitude of peers is measured in the longitudinal surveys data in Year 10, defined as a student’s perception of their classmates in terms of:
•	‘Students are eager to learn’
•	‘Students make good progress’
•	‘Students work hard’
•	‘Students are well behaved’.
Responses to these items were re-coded from the original categorical variable to a four-point scale with 0 representing strong disagreement to the statement through to 3 representing strong agreement to the statement. The individual factor loadings for eagerness to learn, making good progress, working hard and well behaved were 0.671, 0.652, 0.673 and 0.663, respectively. Each individual variable was then weighted proportionally by their actual contribution and summed up to give a perceived attitude of peers score.
Self-perceived academic ability
Self-perceived academic ability in the longitudinal surveys data is defined in terms of a student’s self-rated performance in the following subjects, which were captured in the questionnaire administered to students while they were in Year 10:
•	English
•	Mathematics
•	Science
•	Studies of society and environment (SOSE).
Responses to these items were re-coded from the original to a five-point scale, with 0 representing performing very poorly in the subject, through to 4 representing performing very well in the subject. The individual factor loadings for English, mathematics, science and SOSE were: 0.470, 0.474, 0.533 and 0.407, respectively. Each variable was then weighted proportionally by their actual contribution and summed to give a self-perceived academic ability score.

Appendix 3: 
Statistical modelling 
The quantitative analysis of the research report comprised of variants on four separate statistical models, described below:
1.	Prediction of who will participate in school VET programs in Year 11 (Model A) using the Longitudinal Surveys of Australian Youth data
2.	Prediction of apparent retention rates through a cross-sectional time series analysis of ABS apparent retention rates (Year 10 – Year 11 and Year 11 – Year 12) and Ministerial Council on Education, Employment, Training and Youth Affairs VET in Schools participation rates by state (see appendix 4)
3.	Prediction of retentions rates using the Longitudinal Surveys of Australian Youth data for: 
a.	Year 10 to Year 11 using the estimated school VET ‘dosage’ in 2000 with and without gender interaction (Model B and B1, respectively)
b.	Year 11 to Year 12 using the actual VET participation in Year 11 (Model C)
c.	Year 11 to Year 12 or other Year 12 equivalent studies using the actual VET participation in Year 11 (Model D)
4.	Prediction of successful outcomes using the Longitudinal Surveys of Australian Youth data for:
a.	2002 for all students (Model E)
b.	2001 for all students except those who were still at school in 2001 (Model F)
c.	2000 for all students except those who were still at school in 2000 (Model G).
School VET ‘dosage’ is defined as the proportion of Longitudinal Surveys of Australian Youth students who self-identified as participating in school vocational education and training in Year 11 (2000) at the school aggregate.
Year 12 equivalent studies include traineeship/apprenticeship, Year 12 at TAFE, TAFE/VET Certificates III and IV, other trade certificates, TAFE diploma, TAFE advanced diploma/associate degree or University diploma.
Successful outcomes are defined as being in full-time employment, at school, in higher education (full-time or part-time), in TAFE (full-time or part-time), in apprenticeships/traineeships, or in part-time employment and studies.
Table 17 summarises the outcome, control and treatment variables used in each of the models noted above in sections 1, 3 and 4. The majority of the variables are categorical unless otherwise stated. 
Table 18 describes the characteristics of the Longitudinal Surveys of Australian Youth Y98 cohort.
Please refer to appendix 1 for more detail on the longitudinal surveys data, and to appendix 4 for the cross-sectional time series analysis described in section 2 above.

Table 17:	The sample base, outcome, control and treatment variables used in models A–G
	Model A	Model B	Model B1	Model C	Model D	Model E, F, G	
Sample base							
All students						ü	
Students who did Year 10 in 1999		ü	ü				
Students who did Year 11 in 2000	ü			ü	ü		
Outcome variables							
Student participates in VET or not	ü						
Student participates in Year 11 or not		ü	ü				
Student participates in Year 12 or not				ü			
Student participates in Year 12 or other Year 12 equivalent studies or not					ü		
Student has successful outcomes or not						ü	
Control variables							
Gender	ü	ü	ü	ü	ü	ü	
School type	ü	ü	ü	ü	ü	ü	
State where attended school	ü	ü	ü	ü	ü	ü	
Area of residence	ü	ü	ü	ü	ü	ü	
Ethnicity	ü	ü	ü	ü	ü	ü	
Parental occupation	ü	ü	ü	ü	ü	ü	
Parental education	ü	ü	ü	ü	ü	ü	
Numeracy and literacy score (continuous)	ü	ü	ü	ü	ü	ü	
Aspiration	ü	ü	ü	ü	ü	ü	
Engagement with school (continuous)	ü	ü	ü	ü	ü	ü	
Perceived attitude of peers (continuous)	ü	ü	ü	ü	ü	ü	
Self-perceived academic ability (continuous)	ü	ü	ü	ü	ü	ü	
Treatment variables							
Actual VET participation in Year 11				ü			
School VET ‘dosage’		ü	ü		ü		
Highest school level completed by actual VET participation in Year 11						ü	
Gender interaction with treatment variable used		ü		ü	ü	ü	
In conducting the analysis noted in table 17, we used logistic regression modelling. Logistic regression was used because the outcome variables in each model were treated as 0, 1 variables. Each categorical control or treatment variable has a reference group in which the results of the modelling (beta values) can be easily compared to another group within the variable. These reference groups have been selected on the basis of having the highest proportion in the longitudinal surveys sample in each variable. However, the choice of reference characteristic does not change the relative differences in the logistic coefficients or odd ratios between groups. In this analysis, the reference groups are:
•	Male in gender
•	Government school in school type
•	NSW in state where attended school
•	Metropolitan in area of residence
•	English-speaking background in ethnicity
•	Manual in parental occupation
•	Completed secondary schooling or apprenticeship only in parental education level
•	Intended to do Year 12 in aspiration
•	Non-VET in actual VET participation in Year 11
•	Year 10 in highest school level completed by actual VET participation in Year 11
We used the log-likelihood ratio test to determine if a particular student characteristic needed to be included as interaction terms with the treatment variable. As a result, we included gender interaction for models C–G, as gender has a significant impact on student pathways. 
Table 18:	Longitudinal Surveys of Australian Youth Y98 cohort characteristics (unweighted)
	1998	1999	2000	2001	2002	
School year*	Year 9	Year 10	Year 11	Year 12	Left school	
Number of students in the LSAY sample	14 118	9 289	9 548	8 777	7 762	
Gender* (%)	
Female 	48.5	52.4	50.1	50.8	51.2	
Male	51.5	47.6	49.9	49.2	48.8	
School type* (%)	
Independent	14.9	15.9	15.4	15.6	16.0	
Catholic	22.1	22.5	24.0	24.6	24.7	
Government	63.0	61.6	60.5	59.7	59.3	
Location where attended school* (%)	
ACT	4.0	3.9	4.3	4.4	4.3	
NT	3.3	2.9	2.8	2.8	2.8	
TAS	5.1	5.9	5.3	5.5	5.8	
WA	12.0	11.9	11.9	11.9	11.7	
SA	8.8	9.4	9.1	9.1	9.2	
QLD	22.0	22.7	22.1	21.9	21.8	
VIC	20.9	20.0	20.7	20.5	20.7	
NSW	24.0	23.3	23.8	23.8	23.6	
Area of residence* (%)	
Rural/remote	18.5	19.7	19.5	19.4	19.3	
Regional	23.6	24.4	24.0	23.9	23.9	
Metropolitan	57.9	55.9	56.5	56.7	56.8	

Table 18:	Longitudinal Surveys of Australian Youth Y98 cohort characteristics (unweighted) (continued)
	1998	1999	2000	2001	2002	
School year*	Year 9	Year 10	Year 11	Year 12	Left school	
Number of students in the LSAY sample	14 118	9 289	9 548	8 777	7 762	
Ethnicity* (%)	
Non-English speaking background	9.0	8.1	8.0	7.9	7.7	
English-speaking background	91.0	91.9	92.0	92.1	92.3	
Parental occupation * (%)	
Professional	31.0	32.4	32.2	32.4	33.1	
Managerial	21.5	21.7	21.3	21.4	21.3	
Clerical/Personal service	9.9	10.0	10.1	10.2	10.0	
Manual	37.5	35.9	36.4	36.1	35.6	
Parental education level * (%)	
University	24.6	25.6	25.5	25.8	26.5	
TAFE	7.8	7.9	7.7	7.6	7.6	
Secondary school or apprenticeship	46.2	45.4	46.2	45.9	45.5	
Did not complete secondary school	21.4	21.1	20.7	20.6	20.4	
Aspiration (as asked in Year 10) * (%)	
Intended to leave before Year 12	n/a	20.0	20.7	19.8	18.8	
Intended to do Year 12	n/a	80.0	79.3	80.2	81.2	
Highest school level achieved * (%)	
Year 10	n/a	n/a	n/a	n/a	6.6	
Year 11 and did VET	n/a	n/a	n/a	n/a	3.1	
Year 11 but did not do VET	n/a	n/a	n/a	n/a	4.5	
Year 12 and did VET in Year 11	n/a	n/a	n/a	n/a	19.4	
Year 12 but did not do VET in Year 11	n/a	n/a	n/a	n/a	66.4	
Assessed achievement score (average) 	49.64	50.73	50.62	50.88	51.20	
Engagement with school (average) **	0.89	0.89	0.89	0.89	0.89	
Perceived attitude of peers (average) **	1.67	1.67	1.67	1.68	1.68	
Self-perceived academic ability (average) **	3.50	3.50	3.52	3.53	3.55	
Probability of doing VET in Year 11 (average)		n/a	0.27	n/a	n/a	n/a	
Notes:	* Exclude missing values; ** Refer to appendix 2 for further information on these variables.

Appendix 4: 
Time series analysis
This appendix describes the time series analysis as outlined in item 2 in the previous appendix. It predicts the apparent retention rates through a cross-sectional time series analysis of ABS apparent retention rates (Year 10 – Year 11 and Year 11 – Year 12) and Ministerial Council on Education, Employment, Training and Youth Affairs VET in Schools participation rates by state.
We used simple linear regression through the origin to conduct a cross-sectional time series analysis on: 
•	ABS Year 10 – Year 11 apparent retention rates by state from 1997–2003 with:
•	both VET in Schools participation rates and time trend (Model 1)
•	time trend only (Model 2)
•	VET in Schools participation rates only (Model 3) 
•	ABS Year 11 – Year 12 apparent retention rates by state from 1997–2003 with:
•	both VET in Schools participation rates and time trend (Model 4)
•	time trend only (Model 5)
•	VET in Schools participation rates only (Model 6).
The 1996 data was excluded from the analysis because the number of VET in Schools students was not attainable by state breakdown. ACT and NT were also excluded due to the very small bases. The apparent Year 12 retention rates are also problematic in ACT because of flows of NSW students to the ACT system.
We used data sourced from the ABS for the apparent retention rates, and from Ministerial Council on Education, Employment, Training and Youth Affairs for the VET in Schools participation rates for this analysis.
Table 19:	Year 10 – Year 11 apparent retention rates by state, 1996–2003
State	1996	1997	1998	1999	2000	2001	2002	2003	
	%	%	%	%	%	%	%	%	
NSW	81.6	82.0	81.6	82.1	80.8	82.8	83.8	84.7	
VIC	92.2	92.7	92.8	93.3	93.7	94.3	94.3	95.5	
QLD	86.4	86.9	87.6	89.2	89.3	90.2	91.1	91.6	
SA	92.1	92.1	91.7	92.7	91.0	93.9	93.6	94.9	
WA	86.5	87.4	86.3	88.3	86.4	87.9	88.9	89.1	
TAS	71.3	76.0	78.2	84.6	83.7	84.3	81.9	81.9	
NT	78.6	98.9	87.6	84.4	91.0	88.9	97.8	103.5	
ACT	103.4	105.5	103.1	103.0	104.7	101.5	104.0	103.2	
Australia	86.5	87.3	87.1	88.1	87.5	88.9	89.5	90.3	
Source: 	ABS 1996–2003, Schools, Australia, cat. no.4221.0

Table 20:	Year 11 – Year 12 apparent retention rates by state, 1996–2003
State	1996	1997	1998	1999	2000	2001	2002	2003	
	%	%	%	%	%	%	%	%	
NSW	86.4	86.0	85.2	85.8	85.0	87.0	87.5	86.7	
VIC	86.0	86.7	85.3	84.8	85.5	87.2	87.9	87.9	
QLD	89.6	90.2	89.4	89.4	88.2	89.3	89.9	89.5	
SA	77.7	77.1	77.3	78.0	74.9	76.5	75.1	75.6	
WA	83.7	84.2	82.1	82.9	81.0	83.3	84.0	79.4	
TAS	77.5	85.1	84.5	88.2	84.7	84.3	88.9	93.3	
NT	68.2	79.9	61.0	73.9	73.7	71.3	74.4	70.3	
ACT	89.0	88.9	87.7	89.7	86.2	89.1	88.5	86.9	
Australia	85.7	86.1	84.9	85.4	84.5	86.1	86.7	85.9	
Source: 	ABS 1996–2003, Schools, Australia, cat.no.4221.0
Table 21:	VET in Schools participation rates, 1996–2003
State	1996	1997	1998	1999	2000	2001	2002	2003	
	%	%	%	%	%	%	%	%	
NSW	n/a	35.8	38.5	39.3	39.8	44.6	50.6	52.3	
VIC	n/a	10.3	12.8	13.8	19.0	21.4	24.6	27.8	
QLD	n/a	41.4	41.1	49.4	53.6	57.0	58.6	69.0	
SA	n/a	15.0	46.5	61.0	74.8	72.5	70.3	75.2	
WA	n/a	5.8	12.5	20.8	21.3	29.6	30.2	31.0	
TAS	n/a	16.8	21.5	24.5	30.5	23.7	29.3	31.8	
NT	n/a	14.2	43.2	55.5	46.0	50.7	56.3	59.6	
ACT	n/a	22.0	36.3	48.1	45.2	43.7	43.6	42.2	
Australia	16.2	24.7	29.9	34.6	38.0	41.3	44.3	48.3	
Source: 	Ministerial Council on Education, Employment, Training and Youth Affairs (2004) 

The equation for Model 1 is:

Y10-11i,t = b1NSW + b2VIC + b3QLD + b4SA + b5WA + b6TAS + b7Y10-11i,t-1 + b8VETi,t + b9t
where 	Y10-11i,t = Year 10 – Year 11 apparent retention rate for state i at time t
			NSW	= 1 if i 	= NSW
					= 0 otherwise

			VIC	= 1 if i 	= VIC
					= 0 otherwise
			:
			:
			:
			TAS	= 1 if i 	= TAS
					= 0 otherwise

			Y10-11i,t-1 = Year 10 – Year 11 apparent retention rate for state i at time t-1
			VETi,t = VET in Schools participation rate for state i at time t
			i = NSW, VIC, QLD, SA, WA, TAS
			t = 0, 1, 2, ... 6 (for 1997, 1998, ..., 2003 respectively)
Table 22:	Regression results for Model 1
Control variables	Unstandardised 
coefficients	Standardised coefficients	t	Sig.	
	Value	Std. error	Value			
b1	NSW	0.510	0.091	0.236	5.628	0.000	
b2	VIC	0.580	0.101	0.269	5.754	0.000	
b3	QLD	0.554	0.099	0.257	5.616	0.000	
b4	SA	0.574	0.103	0.266	5.555	0.000	
b5	WA	0.542	0.095	0.251	5.732	0.000	
b6	TAS	0.507	0.087	0.235	5.845	0.000	
b7	Y10-11i,t-1	0.373	0.110	0.370	3.393	0.002	
b8	VETi,t	0.000	0.029	0.000	0.003	0.997	
b9	t	0.003	0.002	0.013	1.830	0.076	

ANOVA	
	Sum of squares	df	Mean square	F	Sig.	
Regression	32.605	9	3.623	26352.234	0.000	
Residual	0.005	33	0.000			
Total	32.609	42	 	 	 	

The equation for Model 2 is:

Y10-11i,t = b1NSW + b2VIC + b3QLD + b4SA + b5WA + b6TAS + b7Y10-11i,t-1 + b8t
where 	Y10-11i,t = Year 10 – Year 11 apparent retention rate for state i at time t
			NSW	= 1 if i  = NSW
					= 0 otherwise

			VIC	= 1 if i  = VIC
					= 0 otherwise
			:
			:
			:
			TAS	= 1 if i  = TAS
					= 0 otherwise

			Y10-11i,t-1 = Year 10 – Year 11 apparent retention rate for state i at time t-1
			i = NSW, VIC, QLD, SA, WA, TAS
			t = 0, 1, 2, ... 6 (for 1997, 1998, ..., 2003 respectively)
Table 23:	Regression results for Model 2
Control variables	Unstandardised 
coefficients	Standardised coefficients	t	Sig.	
	Value	Std. error	Value			
b1	NSW	0.510	0.085	0.236	6.020	0.000	
b2	VIC	0.580	0.096	0.269	6.018	0.000	
b3	QLD	0.554	0.092	0.257	6.050	0.000	
b4	SA	0.574	0.096	0.266	6.010	0.000	
b5	WA	0.542	0.090	0.251	6.010	0.000	
b6	TAS	0.507	0.082	0.235	6.153	0.000	
b7	Y10-11i,t-1	0.373	0.105	0.370	3.534	0.001	
b8	t	0.003	0.001	0.013	2.903	0.006	

ANOVA	
	Sum of squares	df	Mean square	F	Sig.	
Regression	32.605	8	4.076	30544.625	0.000	
Residual	0.005	34	0.000			
Total	32.609	42	 	 	 	

The equation for Model 3 is:

Y10-11i,t = b1NSW + b2VIC + b3QLD + b4SA + b5WA + b6TAS + b7Y10-11i,t-1  + b8VETi,t
where 	Y10-11i,t = Year 10 – Year 11 apparent retention rate for state i at time t
			NSW	= 1 if  i = NSW
					= 0 otherwise

			VIC	= 1 if  i = VIC
					= 0 otherwise
			:
			:
			:
			TAS	= 1 if  i = TAS
					= 0 otherwise

			Y10-11i,t-1 = Year 10 – Year 11 apparent retention rate for state i at time t-1
			VETi,t = VET in Schools participation rate for state i at time t
			i = NSW, VIC, QLD, SA, WA, TAS
			t = 0, 1, 2, ... 6 (for 1997, 1998, ..., 2003 respectively)
Table 24:	Regression results for Model 3
Control variables	Unstandardised 
coefficients	Standardised coefficients	t	Sig.	
	Value	Std. error	Value			
b1	NSW	0.411	0.075	0.190	5.469	0.000	
b2	VIC	0.479	0.087	0.222	5.499	0.000	
b3	QLD	0.444	0.081	0.206	5.496	0.000	
b4	SA	0.457	0.084	0.212	5.445	0.000	
b5	WA	0.446	0.081	0.207	5.485	0.000	
b6	TAS	0.418	0.074	0.193	5.637	0.000	
b7	Y10-11i,t-1	0.484	0.095	0.480	5.119	0.000	
b8	VETi,t	0.040	0.019	0.019	2.126	0.041	

ANOVA	
	Sum of squares	df	Mean square	F	Sig.	
Regression	32.604	8	4.076	27731.08	0.000	
Residual	0.005	34	0.000			
Total	32.609	42	 	 	 	

The equation for Model 4 is:

Y11-12i,t = b1NSW + b2VIC + b3QLD + b4SA + b5WA + b6TAS + b7Y10-11i,t-1  + b8Y11-12i,t-+ b9VETi,t + b10t
where 	Y11-12i,t = Year 11 – Year 12 apparent retention rate for state i at time t
			NSW	= 1 if  i = NSW
					= 0 otherwise

			VIC	= 1 if  i = VIC
					= 0 otherwise
			:
			:
			:
			TAS	= 1 if  i = TAS
					= 0 otherwise

			Y10-11i,t-1 = Year 10 – Year 11 apparent retention rate for state i at time t-1
			Y11-12i,t-1 = Year 11 – Year 12 apparent retention rate for state i at time t-1
			VETi,t = VET in Schools participation rate for state i at time t
			i = NSW, VIC, QLD, SA, WA, TAS
			t = 0, 1, 2, ... 6 (for 1997, 1998, ..., 2003 respectively)
Table 25:	Regression results for Model 4
Control variables	Unstandardised 
coefficients	Standardised coefficients	t	Sig.	
	Value	Std. error	Value			
b1	NSW	0.763	0.147	0.368	5.208	0.000	
b2	VIC	0.794	0.152	0.382	5.212	0.000	
b3	QLD	0.810	0.156	0.390	5.207	0.000	
b4	SA	0.760	0.149	0.366	5.087	0.000	
b5	WA	0.748	0.145	0.360	5.162	0.000	
b6	TAS	0.760	0.142	0.366	5.361	0.000	
b7	Y10-11i,t-1	-0.379	0.194	-0.391	-1.949	0.060	
b8	Y11-12i,t-1	0.485	0.204	0.483	2.383	0.023	
b9	VETi,t	-0.060	0.040	-0.029	-1.509	0.141	
b10	t	0.006	0.002	0.025	2.331	0.026	

ANOVA	
	Sum of squares	df	Mean square	F	Sig.	
Regression	30.163	10	3.016	11589.81	0.000	
Residual	0.008	32	0.000			
Total	30.172	42	 	 	 	

The equation for Model 5 is:

Y11-12i,t = b1NSW + b2VIC + b3QLD + b4SA + b5WA + b6TAS + b7Y10-11i,t-1  + b8Y11-12i,t-+ b9t
where 	Y11-12i,t = Year 11 – Year 12 apparent retention rate for state i at time t
			NSW	= 1 if  i = NSW
					= 0 otherwise

			VIC	= 1 if  i = VIC
					= 0 otherwise
			:
			:
			:
			TAS	= 1 if  i = TAS
					= 0 otherwise

			Y10-11i,t-1 = Year 10 – Year 11 apparent retention rate for state i at time t-1
			Y11-12i,t-1 = Year 11 – Year 12 apparent retention rate for state i at time t-1
			i = NSW, VIC, QLD, SA, WA, TAS
			t = 0, 1, 2, ... 6 (for 1997, 1998, ..., 2003 respectively)
Table 26:	Regression results for Model 5
Control variables	Unstandardised 
coefficients	Standardised coefficients	t	Sig.	
	Value	Std. Error	Value			
b1	NSW	0.694	0.142	0.334	4.893	0.000	
b2	VIC	0.735	0.150	0.354	4.898	0.000	
b3	QLD	0.732	0.150	0.353	4.895	0.000	
b4	SA	0.680	0.142	0.328	4.777	0.000	
b5	WA	0.691	0.143	0.333	4.847	0.000	
b6	TAS	0.702	0.139	0.338	5.048	0.000	
b7	Y10-11i,t-1	-0.344	0.197	-0.355	-1.749	0.090	
b8	Y11-12i,t-1	0.512	0.207	0.510	2.478	0.018	
b9	t	0.003	0.002	0.013	1.779	0.084	

ANOVA	
	Sum of squares	df	Mean square	F	Sig.	
Regression	30.163	9	3.351	12397.977	0.000	
Residual	0.009	33	0.000			
Total	30.172	42	 	 	 	

The equation for Model 6 is:

Y11-12i,t = b1NSW + b2VIC + b3QLD + b4SA + b5WA + b6TAS + b7Y10-11i,t-1  + b8Y11-12i,t-+ b9VETi,t
where 	Y11-12i,t = Year 11 – Year 12 apparent retention rate for state i at time t
			NSW	= 1 if  i = NSW
					= 0 otherwise

			VIC	= 1 if  i = VIC
					= 0 otherwise
			:
			:
			:
			TAS	= 1 if  i = TAS
					= 0 otherwise

			Y10-11i,t-1 = Year 10 – Year 11 apparent retention rate for state i at time t-1
			Y11-12i,t-1 = Year 11 – Year 12 apparent retention rate for state i at time t-1
			VETi,t = VET in Schools participation rate for state i at time t
			i = NSW, VIC, QLD, SA, WA, TAS
			t = 0, 1, 2, ... 6 (for 1997, 1998, ..., 2003 respectively)
Table 27:	Regression results for Model 6
	Control variables	Unstandardised 
coefficients	Standardised 
coefficients	t	Sig.	
		Value	Std. error	Value			
b1	NSW	0.613	0.140	0.295	4.373	0.000	
b2	VIC	0.635	0.145	0.306	4.376	0.000	
b3	QLD	0.640	0.146	0.308	4.373	0.000	
b4	SA	0.569	0.133	0.274	4.276	0.000	
b5	WA	0.598	0.138	0.288	4.325	0.000	
b6	TAS	0.625	0.138	0.301	4.535	0.000	
b7	Y10-11i,t-1	-0.151	0.179	-0.156	-0.845	0.404	
b8	Y11-12i,t-1	0.429	0.215	0.427	1.992	0.055	
b9	VETi,t	0.009	0.028	0.005	0.337	0.738	

ANOVA	
	Sum of squares	df	Mean square	F	Sig.	
Regression	30.162	9	3.351	11351.504	0.000	
Residual	0.010	33	0.000			
Total	30.172	42	 	 	 	
Dynamic simulation 
The dynamic simulation takes models 3 and 6 and models two scenarios based on actual data for the base period and predictions for the retention rates in subsequent periods. In the base case zero VET in Schools is assumed. By way of contrast, the VET in Schools scenario predicts retention rates after the base period, but this time using the actual VET in Schools proportions for Australia (that is the last row in table 21). The difference between the two scenarios gives the impact of VET in Schools, according to models 3 and 6.
Figure 4:	Dynamic simulation on Year 12 retention rate 

Appendix 5: 
Logistic regression results
This section contains the regression results for Models A–G.  Please refer to appendix 3, table 17, for details on the data used in each model. The following summarises the definition of each output measure:
•	b – These are the estimated beta coefficient for the logistic regression equation for predicting the dependent variable from the independent variables. The prediction equation is 
					p = 1/(1+ exp-z)
				where z = b0 + b1*x1 + b2*x2 + ... + bn*xn
•	S.E. – These are the standard errors associated with the coefficients. 
•	Wald and Sig. – These columns provide the Wald Chi-Square value and the 2-tailed p-value used in testing whether the coefficient is significantly different from 0.
•	df – This column lists the degrees of freedom for testing the coefficients.
•	Odds ratio – These are the odds ratios for predictors. They are the exponentiation of the coefficients.
Table 28:	Model A—Regression results for predicting VET participation in Year 11
	b	S.E.	Wald	df	Sig.	Odds ratio	
Gender							
Male	0	–	–	–	–	–	
Female	-0.121	0.065	3.509	1	0.061	0.886	
School type			6.713	2	0.035		
Government	0	–	–	–	–	–	
Catholic	-0.259	0.1	6.693	1	0.01	0.771	
Independent	-0.044	0.078	0.327	1	0.568	0.957	
State where attended school			45.37	7	0		
NSW	0	–	–	–	–	–	
VIC	-0.541	0.099	29.849	1	0	0.582	
QLD	-0.2	0.093	4.665	1	0.031	0.819	
SA	-0.179	0.119	2.256	1	0.133	0.836	
WA	-0.405	0.114	12.557	1	0	0.667	
TAS	-0.71	0.16	19.77	1	0	0.492	
NT	-0.164	0.349	0.221	1	0.638	0.849	
ACT	-0.472	0.187	6.361	1	0.012	0.624	
Area of residence			11.301	2	0.004		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	0.229	0.068	11.248	1	0.001	1.258	
Unknown residence	0.198	0.31	0.408	1	0.523	1.219	
Ethnicity			29.767	2	0		
ESB	0	–	–	–	–	–	
NESB	0.229	0.068	11.248	1	0.001	1.258	
Unknown ethnicity	0.198	0.31	0.408	1	0.523	1.219	

Table 28:	Model A—Regression results for predicting VET participation in Year 11 (continued)
	b	S.E.	Wald	df	Sig.	Odds ratio	
Parental occupation			29.767	2	0		
Manual	0	–	–	–	–	–	
Clerical	-0.135	0.113	1.435	1	0.231	0.874	
Managerial	-0.172	0.091	3.594	1	0.058	0.842	
Professional	-0.224	0.084	7.063	1	0.008	0.799	
Unknown parental occupation	0.056	0.146	0.149	1	0.7	1.058	
Parental education			21.992	4	0		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	0.067	0.088	0.58	1	0.446	1.069	
TAFE	0.002	0.127	0	1	0.985	1.002	
University	-0.382	0.093	16.792	1	0	0.683	
Unknown parental education	0.049	0.102	0.233	1	0.629	1.051	
Assessed achievement score	-0.04	0.004	87.134	1	0	0.96	
Engagement with school	-0.104	0.069	2.27	1	0.132	0.901	
Aspiration (asked in Year 10)			19.059	2	0		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	0.37	0.087	17.963	1	0	1.448	
Unknown aspiration	-0.236	0.33	0.511	1	0.475	0.79	
Perceived attitude of peers	-0.006	0.074	0.006	1	0.938	0.994	
Self-perceived academic ability	-0.388	0.05	61.314	1	0	0.679	
Constant	2.867	0.277	107.47	1	0	17.585	
In using the regression model, we get a resultant distribution of the probability of participating in school VET that is skewed to non-participation, as is illustrated in figure 5.
Figure 5:	Distribution of probability of participating in school VET programs in Year 11
The predicted probability of doing VET has a minimum value of 0.02 and a maximum value of 0.85. The standard deviation is 0.15, the mean value is 0.27, and the median value is 0.24. So, for our predicted probability of doing VET, the average probability is 27%, which is consistent with our actual VET participation, with 26.7% of Longitudinal Surveys of Australian Youth students indicating that they had participated in school VET programs in Year 11.
Table 29:	Model B—Regression results for predicting the Year 10 to Year 11 retention rates—using estimated school VET ‘dosage’ in 2000
	b	S.E.	Wald	df	Sig.	Odds ratio	
Gender	 						
Male	0	–	–	–	–	–	
Female	0.222	0.193	1.325	1	0.25	1.248	
School type	 		17.946	2	0		
Government	0	–	–	–	–	–	
Catholic	0.444	0.131	11.524	1	0.001	1.56	
Independent	0.568	0.183	9.604	1	0.002	1.765	
State where attended school	 		84.16	7	0		
NSW	0	–	–	–	–	–	
VIC	1.161	0.155	56.003	1	0	3.193	
QLD	0.8	0.137	33.846	1	0	2.225	
SA	1.218	0.205	35.222	1	0	3.381	
WA	0.703	0.165	18.265	1	0	2.021	
TAS	0.442	0.196	5.071	1	0.024	1.555	
NT	0.516	0.482	1.145	1	0.285	1.675	
ACT	0.957	0.314	9.285	1	0.002	2.603	
Area of residence	 		14.097	2	0.001		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	-0.395	0.106	13.96	1	0	0.674	
Unknown residence	-0.399	0.418	0.914	1	0.339	0.671	
Ethnicity	 		15.764	2	0		
ESB	0	–	–	–	–	–	
NESB	0.903	0.249	13.161	1	0	2.468	
Unknown ethnicity	-0.311	0.231	1.811	1	0.178	0.733	
Parental occupation	 		13.374	4	0.01		
Manual	0	–	–	–	–	–	
Clerical	0.268	0.182	2.163	1	0.141	1.307	
Managerial	-0.108	0.129	0.709	1	0.4	0.897	
Professional	0.333	0.14	5.635	1	0.018	1.395	
Unknown parental occupation	-0.25	0.182	1.891	1	0.169	0.779	
Parental education	 		13.131	4	0.011		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	-0.111	0.126	0.774	1	0.379	0.895	
TAFE	0.145	0.21	0.477	1	0.49	1.156	
University	0.541	0.171	9.973	1	0.002	1.718	
Unknown parental education	-0.021	0.142	0.021	1	0.884	0.979	
Assessed achievement score	0.038	0.006	35.428	1	0	1.039	
Engagement with school	0.041	0.108	0.143	1	0.706	1.041	
Aspiration	 		230.286	2	0		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	-1.491	0.1	222.717	1	0	0.225	
Unknown aspiration	0.377	0.44	0.734	1	0.391	1.458	
Perceived attitude of peers	0.404	0.107	14.338	1	0	1.498	
Self-perceived academic ability	0.618	0.077	64.97	1	0	1.855	
School VET ‘dosage’	0.211	0.412	0.261	1	0.609	1.235	
Female by school VET ‘dosage’	0.503	0.58	0.753	1	0.386	1.654	
Constant	-2.822	0.425	44.01	1	0	0.059	

Table 30:	Model B1—Regression results for predicting the Year 10 to Year 11 retention rates without gender interaction—using estimated school VET ‘dosage’ in 2000
	b	S.E.	Wald	df	Sig.	Odds ratio	
Gender	 						
Male	0	–	–	–	–	–	
Female	0.366	0.098	13.923	1	0	1.442	
School type	 		18.246	2	0		
Government	0	–	–	–	–	–	
Catholic	0.448	0.131	11.706	1	0.001	1.565	
Independent	0.573	0.183	9.77	1	0.002	1.774	
State where attended school	 		83.894	7	0		
NSW	0	–	–	–	–	–	
VIC	1.159	0.155	55.83	1	0	3.185	
QLD	0.797	0.137	33.629	1	0	2.218	
SA	1.216	0.205	35.166	1	0	3.374	
WA	0.702	0.165	18.169	1	0	2.017	
TAS	0.438	0.196	4.995	1	0.025	1.55	
NT	0.521	0.483	1.166	1	0.28	1.684	
ACT	0.95	0.314	9.161	1	0.002	2.586	
Area of residence	 		14.191	2	0.001		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	-0.396	0.106	14.029	1	0	0.673	
Unknown residence	-0.412	0.418	0.975	1	0.323	0.662	
Ethnicity	 		15.931	2	0		
ESB	0	–	–	–	–	–	
NESB	0.909	0.249	13.349	1	0	2.481	
Unknown ethnicity	-0.309	0.231	1.791	1	0.181	0.734	
Parental occupation	 		13.337	4	0.01		
Manual	0	–	–	–	–	–	
Clerical	0.263	0.182	2.09	1	0.148	1.301	
Managerial	-0.111	0.129	0.751	1	0.386	0.895	
Professional	0.331	0.14	5.57	1	0.018	1.392	
Unknown parental occupation	-0.252	0.182	1.919	1	0.166	0.777	
Parental education	 		13.181	4	0.01		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	-0.109	0.126	0.752	1	0.386	0.897	
TAFE	0.144	0.21	0.469	1	0.493	1.155	
University	0.543	0.171	10.063	1	0.002	1.722	
Unknown parental education	-0.021	0.142	0.022	1	0.882	0.979	
Assessed achievement score	0.038	0.006	35.378	1	0	1.039	
Engagement with school	0.039	0.108	0.134	1	0.714	1.04	
Aspiration	 		231.109	2	0		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	-1.493	0.1	223.585	1	0	0.225	
Unknown aspiration	0.374	0.441	0.722	1	0.396	1.454	
Perceived attitude of peers	0.401	0.107	14.164	1	0	1.494	
Self-perceived academic ability	0.618	0.077	64.938	1	0	1.854	
School VET ‘dosage’	0.443	0.315	1.971	1	0.16	1.557	
Female by school VET ‘dosage’	0	–	–	–	–	–	
Constant	-2.875	0.42	46.763	1	0	0.056	

Table 31:	Model C—Regression results for predicting the Year 11 to Year 12 retention rates for males and females—using actual VET participation in Year 11 
Males	b	S.E.	Wald	df	Sig.	Odds ratio	
School type			9.061	2	0.011		
Government	0	–	–	–	–	–	
Catholic	0.583	0.2	8.499	1	0.004	1.64	
Independent	0.336	0.241	1.938	1	0.164	1.399	
State where attended school			33.302	7	0		
NSW	0	–	–	–	–	–	
VIC	-0.003	0.257	0	1	0.992	0.997	
QLD	0.388	0.264	2.163	1	0.141	1.474	
SA	-0.907	0.261	12.033	1	0.001	0.404	
WA	-0.568	0.269	4.442	1	0.035	0.567	
TAS	-0.542	0.325	2.776	1	0.096	0.582	
NT	-1.016	0.698	2.123	1	0.145	0.362	
ACT	-0.349	0.449	0.603	1	0.437	0.705	
Area of residence			0.194	2	0.908		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	-0.058	0.166	0.124	1	0.725	0.943	
Unknown residence	0.123	0.588	0.044	1	0.834	1.131	
Ethnicity			1.151	2	0.563		
ESB	0	–	–	–	–	–	
NESB	0.292	0.308	0.901	1	0.342	1.339	
Unknown ethnicity	-0.152	0.379	0.161	1	0.688	0.859	
Parental occupation			3.47	4	0.482		
Manual	0	-	-	-	-	-	
Clerical	-0.112	0.261	0.185	1	0.667	0.894	
Managerial	0.157	0.217	0.521	1	0.47	1.17	
Professional	0.337	0.214	2.473	1	0.116	1.401	
Unknown parental occupation	0.056	0.296	0.036	1	0.85	1.058	
Parental education			5.303	4	0.258		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	-0.12	0.208	0.331	1	0.565	0.887	
TAFE	-0.086	0.324	0.07	1	0.792	0.918	
University	0.382	0.245	2.435	1	0.119	1.465	
Unknown parental education	-0.268	0.234	1.32	1	0.251	0.765	
Assessed achievement score	0.036	0.01	12.957	1	0	1.037	
Engagement with school	0.134	0.182	0.545	1	0.46	1.144	
Aspiration			15.729	2	0		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	-0.672	0.17	15.726	1	0	0.51	
Unknown aspiration	-0.332	0.596	0.31	1	0.578	0.717	
Perceived attitude of peers	0.367	0.17	4.645	1	0.031	1.443	
Self-perceived academic ability	0.718	0.121	35.149	1	0	2.05	
Participated in VET in Year 11	-0.34	0.16	4.489	1	0.034	0.712	
Constant	-2.371	0.654	13.144	1	0	0.093	

Table 31:	Model C—Regression results for predicting the Year 11 to Year 12 retention rates for males and females—using actual VET participation in Year 11 (continued)
Females	b	S.E.	Wald	df	Sig.	Odds ratio	
School type			4.666	2	0.097		
Government	0	–	–	–	–	–	
Catholic	0.405	0.221	3.348	1	0.067	1.499	
Independent	0.391	0.276	2.001	1	0.157	1.478	
State where attended school			40.961	7	0		
NSW	0	–	–	–	–	–	
VIC	0.013	0.263	0.002	1	0.962	1.013	
QLD	0.682	0.306	4.958	1	0.026	1.979	
SA	-0.648	0.283	5.226	1	0.022	0.523	
WA	-0.445	0.277	2.585	1	0.108	0.641	
TAS	-1.065	0.308	11.98	1	0.001	0.345	
NT	-2.297	0.775	8.775	1	0.003	0.101	
ACT	-0.032	0.477	0.004	1	0.947	0.969	
Area of residence			2.071	2	0.355		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	-0.215	0.177	1.475	1	0.225	0.807	
Unknown residence	0.412	0.768	0.287	1	0.592	1.51	
ETHNICITY			3.053	2	0.217		
ESB	0	–	–	–	–	–	
NESB	0.63	0.398	2.511	1	0.113	1.878	
Unknown ethnicity	0.485	0.597	0.659	1	0.417	1.624	
Parental occupation			9.689	4	0.046		
Manual	0	–	–	–	–	–	
Clerical	-0.036	0.259	0.019	1	0.891	0.965	
Managerial	0.558	0.244	5.206	1	0.023	1.747	
Professional	0.311	0.219	2.009	1	0.156	1.365	
Unknown parental occupation	-0.397	0.314	1.6	1	0.206	0.672	
Parental education			2.942	4	0.568		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	0.088	0.217	0.162	1	0.687	1.091	
TAFE	-0.051	0.304	0.028	1	0.868	0.951	
University	0.404	0.271	2.216	1	0.137	1.498	
Unknown parental education	-0.084	0.231	0.132	1	0.717	0.92	
Assessed achievement score	0.041	0.011	13.929	1	0	1.042	
Engagement with school	0.324	0.178	3.308	1	0.069	1.383	
Aspiration			12.888	2	0.002		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	-0.689	0.192	12.861	1	0	0.502	
Unknown aspiration	-0.115	0.843	0.019	1	0.891	0.891	
Perceived attitude of peers	0.346	0.179	3.754	1	0.053	1.414	
Self-perceived academic ability	0.305	0.122	6.204	1	0.013	1.356	
Participated in VET in year 11	-0.165	0.174	0.899	1	0.343	0.848	
Constant	-1.118	0.701	2.545	1	0.111	0.327	

Table 32:	Model D—Regression results for predicting the Year 11 to Year 12 equivalent retention* rates for males and females—using the actual VET participation in Year 11
Males	b	S.E.	Wald	df	Sig.	Odds ratio	
School type			9.009	2	0.011		
Government	0	–	–	–	–	–	
Catholic	0.573	0.21	7.468	1	0.006	1.774	
Independent	0.469	0.26	3.251	1	0.071	1.599	
State where attended school			29.327	7	0		
NSW	0	–	–	–	–	–	
VIC	-0.135	0.27	0.25	1	0.617	0.874	
QLD	0.356	0.282	1.599	1	0.206	1.428	
SA	-0.958	0.276	12.028	1	0.001	0.384	
WA	-0.556	0.289	3.712	1	0.054	0.573	
TAS	-0.575	0.344	2.785	1	0.095	0.563	
NT	-0.917	0.73	1.578	1	0.209	0.4	
ACT	-0.518	0.456	1.29	1	0.256	0.596	
Area of residence			0.019	2	0.991		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	-0.019	0.174	0.012	1	0.911	0.981	
Unknown residence	0.039	0.606	0.004	1	0.949	1.039	
Ethnicity			1.429	2	0.489		
ESB	0	–	–	–	–	–	
NESB	0.375	0.328	1.311	1	0.252	1.455	
Unknown ethnicity	0.193	0.433	0.199	1	0.656	1.213	
Parental occupation			2.491	4	0.646		
Manual	0	–	–	–	–	–	
Clerical	-0.038	0.276	0.019	1	0.892	0.963	
Managerial	0.212	0.231	0.842	1	0.359	1.236	
Professional	0.304	0.224	1.841	1	0.175	1.356	
Unknown parental occupation	0.102	0.307	0.111	1	0.739	1.108	
Parental education			6.873	4	0.143		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	-0.166	0.218	0.579	1	0.447	0.847	
TAFE	0.145	0.376	0.148	1	0.7	1.156	
University	0.337	0.258	1.704	1	0.192	1.401	
Unknown parental education	-0.421	0.239	3.091	1	0.079	0.657	
Assessed achievement score	0.039	0.01	14.041	1	0	1.04	
Engagement with school	0.116	0.191	0.372	1	0.542	1.123	
Aspiration			17.607	2	0		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	-0.732	0.176	17.3	1	0	0.481	
Unknown aspiration	-0.672	0.62	1.175	1	0.278	0.51	
Perceived attitude of peers	0.364	0.178	4.188	1	0.041	1.439	
Self-perceived academic ability	0.7	0.127	30.602	1	0	2.014	
Participated in VET in Year 11	-0.331	0.168	3.888	1	0.049	0.718	
Constant	-2.277	0.686	11.008	1	0.001	0.103	

Table 32:	Model D—Regression results for predicting the Year 11 to Year 12 equivalent retention* rates for males and females—using the actual VET participation in Year 11 (continued)
Females	b	S.E.	Wald	df	Sig.	Odds ratio	
School type			3.187	2	0.203		
Government	0	–	–	–	–	–	
Catholic	0.416	0.241	2.986	1	0.084	1.516	
Independent	0.204	0.284	0.517	1	0.472	1.226	
State where attended school			38.077	7	0		
NSW	0	–	–	–	–	–	
VIC	-0.026	0.285	0.008	1	0.928	0.975	
QLD	0.593	0.329	3.251	1	0.071	1.81	
SA	-0.632	0.307	4.232	1	0.04	0.532	
WA	-0.333	0.31	1.152	1	0.283	0.717	
TAS	-1.22	0.323	14.291	1	0	0.295	
NT	-2.18	0.805	7.341	1	0.007	0.113	
ACT	0.219	0.564	0.151	1	0.698	1.245	
Area of residence			1.832	2	0.4		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	-0.206	0.189	1.188	1	0.276	0.814	
Unknown residence	0.462	0.8	0.334	1	0.563	1.588	
Ethnicity			4.893	2	0.087		
ESB	0	–	–	–	–	–	
NESB	1.164	0.535	4.729	1	0.03	3.203	
Unknown ethnicity	0.295	0.596	0.244	1	0.621	1.343	
Parental occupation			12.159	4	0.016		
Manual	0	–	–	–	–	–	
Clerical	-0.082	0.27	0.092	1	0.761	0.921	
Managerial	0.928	0.297	9.73	1	0.002	2.529	
Professional	0.23	0.231	0.996	1	0.318	1.259	
Unknown parental occupation	-0.235	0.345	0.465	1	0.495	0.791	
Parental education			2.923	4	0.571		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	0.004	0.232	0	1	0.985	1.004	
TAFE	0.067	0.346	0.038	1	0.846	1.07	
University	0.426	0.293	2.111	1	0.146	1.531	
Unknown parental education	-0.136	0.247	0.304	1	0.581	0.873	
Assessed achievement score	0.037	0.012	9.552	1	0.002	1.038	
Engagement with school	0.419	0.195	4.599	1	0.032	1.521	
Aspiration			8.142	2	0.017		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	-0.595	0.209	8.142	1	0.004	0.551	
Unknown aspiration	-0.23	0.851	0.073	1	0.787	0.795	
Perceived attitude of peers	0.294	0.193	2.319	1	0.128	1.341	
Self-perceived academic ability	0.291	0.132	4.855	1	0.028	1.338	
Participated in VET in Year 11	-0.029	0.191	0.024	1	0.878	0.971	
Constant	-0.737	0.755	0.951	1	0.329	0.479	
Note:	* Equivalent studies include traineeship/apprenticeship, Year 12 at TAFE, TAFE/VET Certificates III-IV, other trade certificates, TAFE diploma, TAFE advanced diploma/associate degree and University diploma.

Table 33:	Model E—Regression results for predicting the successful outcomes in 2002
	b	S.E.	Wald	df	Sig.	Odds ratio	
Gender	 						
Male	0	–	–	–	–	–	
Female	-1.027	0.280	13.406	1	0	0.358	
School type	 		10.364	2	0.006		
Government	0	–	–	–	–	–	
Catholic	0.353	0.111	10.137	1	0.001	1.423	
Independent	0.165	0.133	1.539	1	0.215	1.179	
State where attended school	 		10.841	7	0.146		
NSW	0	–	–	–	–	–	
VIC	-0.046	0.132	0.121	1	0.728	0.955	
QLD	0.051	0.132	0.149	1	0.700	1.052	
SA	-0.157	0.161	0.959	1	0.327	0.854	
WA	-0.251	0.146	2.950	1	0.086	0.778	
TAS	-0.159	0.189	0.704	1	0.401	0.853	
NT	-0.684	0.474	2.088	1	0.148	0.504	
ACT	-0.473	0.220	4.626	1	0.031	0.623	
Residence	 		3.038	2	0.219		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	-0.147	0.092	2.573	1	0.109	0.863	
Unknown residence	0.207	0.440	0.222	1	0.638	1.231	
Ethnicity	 		0.986	2	0.611		
ESB	0	–	–	–	–	–	
NESB	0.061	0.174	0.123	1	0.725	1.063	
Unknown ethnicity	0.250	0.264	0.902	1	0.342	1.284	
Parental occupation	 		8.990	4	0.061		
Manual	0	–	–	–	–	–	
Clerical	-0.144	0.146	0.975	1	0.323	0.866	
Managerial	0.251	0.125	4.008	1	0.045	1.285	
Professional	-0.039	0.112	0.119	1	0.730	0.962	
Unknown parental occupation	-0.210	0.185	1.291	1	0.256	0.811	
Parental education	 		11.784	4	0.019		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	0.176	0.117	2.275	1	0.131	1.193	
TAFE	0.345	0.185	3.477	1	0.062	1.412	
University	0.388	0.125	9.692	1	0.002	1.474	
Unknown parental education	0.142	0.136	1.096	1	0.295	1.153	
Assessed achievement score	0.023	0.006	16.445	1	0	1.024	
Engagement with school	0.157	0.093	2.844	1	0.092	1.171	
Aspiration (asked in Year 10)	 		0.013	2	0.994		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	0.006	0.114	0.003	1	0.960	1.006	
Unknown aspiration	-0.041	0.424	0.009	1	0.922	0.960	
Perceived attitude of peers	0.113	0.096	1.386	1	0.239	1.120	
Self-perceived ability	0.239	0.066	13.275	1	0	1.270	
Highest school level completed	 		4.478	5	0.483		
Year 10	0	–	–	–	–	–	
Year 11, no VET in Year 11	-0.443	0.352	1.584	1	0.208	0.642	
Year 11, did VET in Year 11	-0.140	0.410	0.117	1	0.732	0.869	
Year 12, no VET in Year 11	-0.280	0.250	1.259	1	0.262	0.756	
Year 12, VET in Year 11	-0.499	0.265	3.549	1	0.060	0.607	
Unknown highest school level completed	-0.356	0.447	0.633	1	0.426	0.701	

Table 33:	Model E—Regression results for predicting the successful outcomes in 2002 (continued)
	b	S.E.	Wald	df	Sig.	Odds ratio	
Gender by highest school level completed	 						
Female and Year 10	0	–	–	–	–	–	
Female and Year 11 with no VET in Year 11	0.264	0.444	0.353	1	0.553	1.302	
Female and Year 11 with VET in Year 11	0.300	0.548	0.300	1	0.584	1.350	
Female and Year 12 with no VET in Year 11	0.888	0.302	8.650	1	0.003	2.430	
Female and Year 12 with VET in Year 11	1.008	0.332	9.210	1	0.002	2.739	
Female and unknown highest school level completed	0.233	0.577	0.163	1	0.687	1.262	
Constant	-0.015	0.410	0.001	1	0.971	0.985	

Table 34:	Model F—Regression results for predicting the successful outcomes in 2001 excluding those who were still at school in 2001
	b	S.E.	Wald	df	Sig.	Odds ratio	
Gender	 						
Male	0	–	–	–	–	–	
Female	-0.963	0.202	22.802	1	0	0.382	
School type	 		0.625	2	0.732		
Government	0	0	0	0	0	0	
Catholic	-0.086	0.197	0.191	1	0.662	0.917	
Independent	0.144	0.255	0.321	1	0.571	1.155	
State where attended school	 		2.752	7	0.907		
NSW	0	–	–	–	–	–	
VIC	0.213	0.237	0.806	1	0.369	1.237	
QLD	-0.143	0.223	0.414	1	0.520	0.866	
SA	-0.064	0.257	0.062	1	0.803	0.938	
WA	-0.124	0.236	0.277	1	0.599	0.883	
TAS	0.046	0.280	0.026	1	0.871	1.047	
NT	0.224	0.746	0.090	1	0.764	1.250	
ACT	0.194	0.455	0.182	1	0.670	1.214	
Residence	 		0.791	2	0.673		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	0.132	0.156	0.715	1	0.398	1.141	
Unknown residence	0.276	0.694	0.158	1	0.691	1.317	
Ethnicity	 		0.970	2	0.616		
ESB	0	–	–	–	–	–	
NESB	0.088	0.341	0.066	1	0.797	1.092	
Unknown ethnicity	0.371	0.383	0.937	1	0.333	1.449	
Parental occupation	 		2.032	4	0.730		
Manual	0	–	–	–	–	–	
Clerical	0.196	0.263	0.554	1	0.457	1.217	
Managerial	0.110	0.199	0.307	1	0.579	1.116	
Professional	-0.104	0.205	0.256	1	0.613	0.902	
Unknown parental occupation	-0.166	0.266	0.389	1	0.533	0.847	
Parental education	 		4.172	4	0.383		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	-0.321	0.187	2.936	1	0.087	0.726	
TAFE	0.008	0.323	0.001	1	0.981	1.008	
University	-0.228	0.242	0.887	1	0.346	0.796	
Unknown parental education	0.044	0.213	0.043	1	0.836	1.045	
Assessed achievement score	0.005	0.009	0.266	1	0.606	1.005	
Engagement with school	0.002	0.160	0	1	0.991	1.002	
Aspiration (asked in Year 10)	 		9.558	2	0.008		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	0.467	0.155	9.074	1	0.003	1.595	
Unknown aspiration	-0.241	0.638	0.143	1	0.705	0.785	
Perceived attitude of peers	0.349	0.155	5.092	1	0.024	1.418	
Self-perceived ability	0.196	0.112	3.049	1	0.081	1.216	
Highest school level completed	 		12.823	3	0.005		
Year 10	0	–	–	–	–	–	
Year 11, no VET in Year 11	-0.427	0.249	2.930	1	0.087	0.653	
Year 11, did VET in Year 11	0.156	0.296	0.279	1	0.597	1.169	
Unknown highest school level completed	1.056	0.414	6.491	1	0.011	2.874	
Table 34:	Model F—Regression results for predicting the successful outcomes in 2001 excluding those who were still at school in 2001 (continued)
	b	S.E.	Wald	df	Sig.	Odds ratio	
Gender by highest school level completed	 						
Female and Year 10	0	–	–	–	–	–	
Female and Year 11 with no VET in 
Year 11	0.182	0.334	0.295	1	0.587	1.199	
Female and Year 11 with VET in Year 11	0.207	0.416	0.248	1	0.619	1.230	
Female and unknown highest school level completed	0.962	0.589	2.662	1	0.103	2.616	
Constant	-0.470	0.602	0.609	1	0.435	0.625	

Table 35:	Model G—Regression results for predicting the successful outcomes in 2000 excluding those who were still at school in 2000

	b	S.E.	Wald	df	Sig.	Odds ratio	
Gender	 						
Male	0	–	–	–	–	–	
Female	-0.888	0.181	24.064	1	0	0.412	
School type	 		0.198	2	0.906		
Government	0	–	–	–	–	–	
Catholic	0.103	0.239	0.185	1	0.667	1.108	
Independent	0.058	0.327	0.031	1	0.860	1.059	
State where attended school	 		7.783	7	0.352		
NSW	0	–	–	–	–	–	
VIC	0.361	0.285	1.597	1	0.206	1.434	
QLD	-0.183	0.240	0.577	1	0.447	0.833	
SA	-0.635	0.354	3.209	1	0.073	0.530	
WA	0.042	0.285	0.021	1	0.884	1.043	
TAS	0.057	0.345	0.027	1	0.869	1.059	
NT	-0.523	0.963	0.295	1	0.587	0.593	
ACT	-0.443	0.553	0.640	1	0.424	0.642	
Residence	 		0.220	2	0.896		
Metropolitan	0	–	–	–	–	–	
Non-metropolitan	-0.089	0.189	0.220	1	0.639	0.915	
Unknown residence	-0.071	0.846	0.007	1	0.933	0.931	
Ethnicity	 		1.255	2	0.534		
ESB	0	–	–	–	–	–	
NESB	-0.442	0.430	1.053	1	0.305	0.643	
Unknown ethnicity	0.147	0.399	0.135	1	0.713	1.158	
Parental occupation	 		9.260	4	0.055		
Manual	0	–	–	–	–	–	
Clerical	-0.812	0.324	6.297	1	0.012	0.444	
Managerial	-0.130	0.226	0.329	1	0.566	0.878	
Professional	-0.521	0.249	4.365	1	0.037	0.594	
Unknown parental occupation	-0.409	0.308	1.764	1	0.184	0.664	
Parental education	 		2.523	4	0.641		
Completed sec. school/apprenticeship	0	–	–	–	–	–	
Did not complete secondary school	-0.017	0.226	0.005	1	0.941	0.984	
TAFE	-0.249	0.380	0.429	1	0.512	0.780	
University	-0.141	0.304	0.215	1	0.643	0.868	
Unknown parental education	-0.348	0.240	2.107	1	0.147	0.706	
Assessed achievement score	0.021	0.011	3.481	1	0.062	1.022	
Engagement with school	0.091	0.181	0.253	1	0.615	1.095	
Aspiration (asked in Year 10)	 		2.632	2	0.268		
Intended to do Year 12	0	–	–	–	–	–	
Intended to leave before Year 12	0.291	0.181	2.603	1	0.107	1.338	
Unknown aspiration	0.009	0.796	0	1	0.991	1.009	
Perceived attitude of peers	0.041	0.183	0.050	1	0.824	1.042	
Self-perceived ability	0.100	0.135	0.553	1	0.457	1.106	

Table 35:	Model G—Regression results for predicting the successful outcomes in 2000 excluding those who were still at school in 2000 (continued)

	b	S.E.	Wald	df	Sig.	Odds ratio	
Highest school level completed	 						
Year 10	0	–	–	–	–	–	
Unknown highest school level completed	2.911	0.418	48.468	1	0	18.377	
Gender by highest school level completed	 						
Female and Year 10	0	–	–	–	–	–	
Female and unknown highest school level completed	0.925	0.597	2.399	1	0.121	2.521	
Constant	-0.365	0.694	0.277	1	0.599	0.694	

Appendix 6: 
Overall impact on Year 12 retention (mind experiment)
This appendix describes the mind experiment (following table 4) conducted by looking at the overall impact on Year 10 to Year 12 retention for those students whom we observe undertaking school VET programs at Year 11, split by gender.  We start with the actual number of Year 11 students and divide them into those who did and did not participate in school VET programs.
Estimated number of students in Year 10
For those who participated in school VET programs, we consider the ith student in the sample of Year 11 and calculate the probability pi that a student with the same personal characteristics moves from Year 10 to Year 11 using model B1. For this exercise, we use a ‘school dosage’ of vocational education and training set at the national participation rate for 2003 (48%).  For each student i in Year 11, we calculate that there would have 1/pi students in Year 10. So we estimate that the observed sample in Year 11 has come from ∑(1/pi) students in Year 10. We then repeat this for the counterfactual and for non-VET students, with the ‘school dosage’ set at zero for both groups.
Estimated number of students in Year 12
For those who participated in school vocational education and training, we consider the ith student in the sample of Year 11 and calculate the probability pi that a student with the same personal characteristics moves from Year 11 to Year 12 using model C.  For the VET treatment we use actual VET participation.  We use zero again for the counterfactual and non-VET students. For each student i in Year 11, we calculate that the student has a probability pi of making it to Year 12. So we estimate the sample in Year 12 as ∑pi students. We then repeat this for the counterfactual and for non-VET students, with the ‘school dosage’ set at zero for both groups.

Figure 6:	Overall impact on Year 12 retention for males

n = 703

As observed

Counterfactual *

Males

n^ = 1922

No VET in Year 11

n^ = 745

n^ = 756

As observed

Counterfactual * 

As observed

As observed

n^ = 2127

n = 2,062

n^ = 604

n^ = 626

n^ = 1928

n^ = 601

n^ = 624

* Assumes no VET was offered in Year 11
n represents actual number
n^ represents estimated number

Males
n = 703

n = 2062

     Year 10	Year 11	Year 12	Year 12 equivalent

VET in Year 11

Figure 7:	Overall impact on Year 12 retention for females

As observed

Counterfactual *

Females

Year 10

Year 11

Year 12

n^ = 2322

No VET in Year 11

n^ = 804

n^ = 810

As observed

Counterfactual * 

As observed

As observed

n^ = 2508

n = 2,454

Year 12 equivalent

n^ = 724

n^ = 729

n^ = 2341

n^ = 706

n^ = 716

* Assumes no VET was offered in Year 11
n represents actual number
n^ represents estimated number

Females
n = 778

n = 2454

VET in Year 11

Appendix 7: 
Chi-Square analysis
In this section, we tested the null hypothesis that there is no relationship between courses students were studying in Year 11 and courses they were studying one-year post-school. To test this, we used the Chi-Square contingency table test for independence between the field of education studied in 2000 and the field of education studied in 2002 for those Longitudinal Surveys of Australian Youth  students who were matched to the NCVER provider collection.
Our observed values (O) are the numbers of students who participated in courses in 2000 and 2002 (see tables 12 and 13). We contrasted this with our expected values (E), split by gender. Our expected values are derived from the distribution of VET activity in 2000 and 2002 for all our matched students. Our null hypothesis is that there is no relationship between student VET courses in 2000 and 2002.
This test was conducted separately for males and females.

The test statistic is Q = ∑ ∑ [ (O – E)2 ]/E
where 
O = Observed value
E = Expected value	

Table 36:	Observed and expected number of male students in field of education studied, 2000 and 2002
Field of education 
in 2000 		Field of education in 2002	
	 	Information technology	Engineering & related technologies	Architecture & building	Agriculture, environment & related studies	Health	Management & commerce	Society & culture	Creative arts	Food, hospitality & personal services	Mixed field programmes	Total	
Information technology	O	1	0	0	0	0	0	0	0	0	1	2	
	E	0.027	0.378	0.054	0.054	0.135	0.405	0.378	0.108	0.297	0.162		
Engineering & related technologies	O	0	7	1	0	0	0	1	2	0	0	11	
	E	0.149	2.081	0.297	0.297	0.743	2.230	2.081	0.595	1.635	0.892		
Architecture & building	O	0	0	1	0	0	0	0	0	0	0	1	
	E	0.014	0.189	0.027	0.027	0.068	0.203	0.189	0.054	0.149	0.081		
Agriculture, environment & related studies	O	0	2	0	1	0	0	0	0	0	0	3	
	E	0.041	0.568	0.081	0.081	0.203	0.608	0.568	0.162	0.446	0.243		
Health	O	0	0	0	0	3	1	0	0	0	0	4	
	E	0.054	0.757	0.108	0.108	0.270	0.811	0.757	0.216	0.595	0.324		
Education	O	0	0	0	0	0	0	0	0	0	1	1	
	E	0.014	0.189	0.027	0.027	0.068	0.203	0.189	0.054	0.149	0.081		
Management & commerce	O	0	5	0	0	2	8	3	0	2	0	20	
	E	0.270	3.784	0.541	0.541	1.351	4.054	3.784	1.081	2.973	1.622		
Society & culture	O	0	0	0	0	0	3	4	0	1	0	8	
	E	0.108	1.514	0.216	0.216	0.541	1.622	1.514	0.432	1.189	0.649		
Creative arts	O	0	0	0	0	0	0	1	1	1	0	3	
	E	0.041	0.568	0.081	0.081	0.203	0.608	0.568	0.162	0.446	0.243		
Food, hospitality & 
personal services	O	0	0	0	0	0	1	2	0	6	1	10	
	E	0.135	1.892	0.270	0.270	0.676	2.027	1.892	0.541	1.486	0.811		
Mixed field programmes	O	0	0	0	1	0	2	3	1	1	3	11	
	E	0.149	2.081	0.297	0.297	0.743	2.230	2.081	0.595	1.635	0.892		
Total	 	1	14	2	2	5	15	14	4	11	6	74	

Null hypothesis: 	There is no relationship between field of education in 2000 and field of education in 2002 for male students

Alternative hypothesis:	There is a relationship between field of education in 2000 and field of education in 2002 for male students

Significance level:	0.05 (5%)

Test statistic:	Q = 212.688 (follows a Chi-Square distribution with 90 degrees of freedom)

Therefore:		P-value < 0.0001

Decision rule:		Reject null hypothesis if P-value < 0.05

Outcome:		Reject null hypothesis
In conclusion, there is enough evidence to suggest that there is a relationship between what male students were doing in school in Year 11 (2000) and what they were doing one-year post-school in 2002.

Table 37:	Observed and expected number of female students in field of education studied, 2000 and 2002
Field of education
in 2000		Field of education in 2002	
		Natural & physical sciences	Information technology	Engineering & related technologies	Architecture & building	Agriculture, environmental & related studies	Health	Education	Management & commerce	Society & culture	Food, hospitality & personal services	Mixed field programmes	Total	
Information technology	O	0	1	2	0	1	0	0	3	0	0	0	7	
	E	0.315	0.820	0.694	0.505	0.441	0.315	0.757	1.072	0.820	0.694	0.568		
Engineering & related technologies	O	0	3	0	1	0	0	0	2	0	4	2	12	
	E	0.541	1.405	1.189	0.865	0.757	0.541	1.297	1.838	1.405	1.189	0.973		
Architecture & building	O	0	0	0	1	1	0	0	2	0	0	0	4	
	E	0.180	0.468	0.396	0.288	0.252	0.180	0.432	0.613	0.468	0.396	0.324		
Agriculture, environmental & related studies	O	0	0	1	0	2	0	0	2	0	0	1	6	
	E	0.270	0.703	0.595	0.432	0.378	0.270	0.649	0.919	0.703	0.595	0.486		
Health	O	0	0	0	0	1	0	0	0	1	0	0	2	
	E	0.090	0.234	0.198	0.144	0.126	0.090	0.216	0.306	0.234	0.198	0.162		
Management & commerce	O	2	7	4	3	0	3	8	2	9	5	3	46	
	E	2.072	5.387	4.559	3.315	2.901	2.072	4.973	7.045	5.387	4.559	3.730		
Society & culture	O	0	0	0	1	0	0	0	1	1	0	0	3	
	E	0.135	0.351	0.297	0.216	0.189	0.135	0.324	0.459	0.351	0.297	0.243		
Creative arts	O	1	0	0	0	0	0	0	1	0	1	0	3	
	E	0.135	0.351	0.297	0.216	0.189	0.135	0.324	0.459	0.351	0.297	0.243		
Food, hospitality & personal services	O	1	2	1	2	1	1	3	1	2	0	3	17	
	E	0.766	1.991	1.685	1.225	1.072	0.766	1.838	2.604	1.991	1.685	1.378		
Mixed field programmes	O	1	0	3	0	1	1	1	3	0	1	0	11	
	E	0.495	1.288	1.090	0.793	0.694	0.495	1.189	1.685	1.288	1.090	0.892		
Total	 	5	13	11	8	7	5	12	17	13	11	9	111	

Null hypothesis: 	There is no relationship between field of education in 2000 and field of education in 2002 for female students

Alternative hypothesis:	There is a relationship between field of education in 2000 and field of education in 2002 for female students

Significance level:	0.05 (5%)

Test statistic:	Q = 103.388 (follows a Chi-Square distribution with 90 degrees of freedom)

Therefore:	P-value = 0.1583

Decision rule:	Reject null hypothesis if P-value < 0.05

Outcome:	Null hypothesis cannot be rejected
In conclusion, there is insufficient evidence to suggest that there is a relationship between what female students were doing in school in Year 11 (2000) and what they were doing one-year post-school in 2002.