6227.0 - Education and Work, Australia, May 2007  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 18/12/2007   
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TECHNICAL NOTE DATA QUALITY


RELIABILITY OF THE ESTIMATES

1 Since the estimates in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability. That is, they may differ from those estimates that would were produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate may have varied by chance because only a sample of dwellings was included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs.


2 Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.


Equation: RSE% = (SEestimate)100


3 RSEs for estimates from 2007 SEW are published for the first time in 'direct' form. Previously a statistical model was produced that related the size of estimates to their corresponding RSEs, and this information was displayed via an 'SE table'. From this point onwards, RSEs for SEW estimates were calculated for each separate estimate and are published. The Jackknife method of variance estimation is used for this process, which involves the calculation of 30 'replicate' estimates based on 30 different subsamples of the original sample. The variability of estimates obtained from these subsamples is used to estimate the sample variability surrounding the main estimate.


4 Tables 2, 7 and 22 contain estimates collected from previous Education and Work surveys. The spreadsheets associated with this release contain RSEs for these estimates. The RSEs for the years 1997, 1999, 2001 and 2003 were calculated using the previous statistical RSE models, which are available from each relevant issue of Education and Work, Australia (cat. no. 6227.0) available on the ABS web site <www.abs.gov.au>. For the 2005 and 2006 data, the RSEs were directly calculated. This method differs from that presented in their related publication, which describes the statistical model to calculate RSEs. While the direct method is more accurate, the difference between the two is negligible.


5 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication, only RSEs for Table 1 are included at the end of these Technical Notes (see Table 1 Relative Standard Errors in the section 'Relative Standard Error'). However, RSEs for all tables are available free-of-charge on the ABS web site <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Education and Work, Australia, 2007 (cat. no. 6227.0).


6 In the tables in this publication, only estimates (numbers, percentages, means and medians) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs were included and are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g. **2.1) to indicate that they are considered too unreliable for general use.



CALCULATION OF STANDARD ERROR

7 Standard errors can be calculated using the estimates (counts or means) and the corresponding RSEs. For example, Table 1 shows the estimated number of males in New South Wales enrolled in a course of study was 391,500. The RSE Table corresponding to the estimates in Table 1 (see Table 1 Relative Standard Errors in the 'Relative Standard Error' section at the end of these Technical Notes) shows the RSE for this estimate is 2.4%. The SE is calculated by:


Equation: SE of estimate = (RSE100)estimate= 0.024391,500 = 9,400 (rounded to the nearest hundred)


8 Therefore, there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall within the range 382,100 to 400,900 and about 19 chances in 20 that the value will fall within the range 372,700 to 410,300. This example is illustrated in the diagram below:

Diagram: Illustration of 66% and 95% confience intervals for estimate 391,500



PROPORTION AND PERCENTAGES

9 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y.


Equation: RSE(xy) = square root of (RSE(x) squared - RSE(y) squared)


10 As an example, using estimates from Table 1, of the 825,100 persons enrolled in a course of study in New South Wales, 391,500 are males, or 47.4%. The RSE for 391,500 is 2.4% and the RSE for 825,100 is 1.6% (see Table 1 Relative Standard Errors in the section 'Relative Standard Error' at the end of these Technical Notes). Applying the above formula, the RSE for the proportion of males in New South Wales enrolled in a course of study:


Equation: RSE = square root of ((2.4) squared - (1.6)squared) = 1.8%


11 Therefore, the SE for the proportion of males in New South Wales enrolled in a course of study is 0.9 percentage points (=(1.8/100) x 47.4). Hence, there are about two chances in three that the proportion of males in New South Wales enrolled in a course of study is between 46.5% and 48.3%, and 19 chances in 20 that the proportion is between 45.6% and 49.2%.



DIFFERENCES

12 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:


Equation: SE(x-y) = square root of (SE(x) squared + SE(y) squared)


13 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.



SIGNIFICANCE TESTING

14 The statistical significance test for any of the comparisons between estimates was performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 12. This standard error is then used to calculate the following test statistic:


Equation: (x-ySE(x-y))


15 If the value of this test statistic is greater than 1.96 then there is good evidence of a real difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations.


16 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error, and they occur in any enumeration, whether it be a full count or sample. Every effort is made to reduce non-sampling error to a minimum by careful design or questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.



RELATIVE STANDARD ERROR

17 Relative Standard Errors for Table 1 are included below. However, RSEs for all tables are available free-of-charge on the ABS web site <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Education and Work, Australia, 2007 (cat. no. 6227.0).

TABLE 1 RELATIVE STANDARD ERRORS, Persons enrolled in a course of study - Selected characteristics
NSW
Vic.
Qld
SA
WA
Tas.
NT(a)
ACT
Aust.
RSE OF ESTIMATE (%)
Sex
Males
2.4
2.5
4.3
4.7
4.1
5.3
23.0
11.0
1.4
Females
2.7
2.3
2.0
3.3
4.0
5.4
16.7
5.7
1.3
Age group (years)
15-19
2.3
1.9
2.5
3.0
2.3
3.2
21.9
5.8
1.2
20-24
4.2
5.0
6.7
6.6
8.4
11.1
30.9
8.0
2.1
25-34
5.0
5.6
5.6
9.4
9.4
10.0
23.1
18.9
2.5
35-44
8.1
8.6
8.2
8.3
9.2
13.4
31.7
11.5
4.4
45-54
8.1
11.5
10.6
16.4
12.9
17.6
34.7
13.6
4.2
55-64
15.2
11.5
16.2
17.9
21.1
13.9
55.2
26.6
6.6
Country of birth
Born in Australia
2.6
2.5
2.5
3.6
2.9
4.0
16.9
4.8
1.6
Born overseas
6.6
7.5
9.0
10.2
8.8
16.2
25.4
28.5
3.8
Area of usual residence
State capital city
1.9
2.5
3.0
3.2
3.0
5.7
. .
. .
1.2
Balance of state/Territory
3.5
4.7
3.0
7.1
7.0
4.6
15.0
7.3
2.2
Labour force status
In the labour force
2.6
2.8
2.7
3.9
3.3
5.3
15.0
4.9
1.4
Employed
2.7
2.8
2.6
3.9
3.2
5.7
14.7
5.1
1.4
Employed full-time
3.1
5.0
4.4
6.9
6.2
8.9
18.4
10.0
2.2
Employed part-time
5.4
3.3
4.1
5.6
4.4
8.7
18.9
6.3
2.0
Unemployed
7.8
13.0
15.8
19.5
17.7
27.0
81.9
26.0
6.3
Not in the labour force
4.7
4.3
4.6
5.8
7.5
7.4
26.7
23.6
2.2
Level of education of current study in May 2007
Study leading to a qualification
1.7
2.1
2.4
2.9
3.1
4.0
16.6
7.8
1.0
Postgraduate Degree
10.5
9.3
11.9
18.2
19.2
24.2
47.0
25.3
5.2
Graduate Diploma/Graduate Certificate
15.8
16.6
14.3
18.1
15.2
44.1
63.2
21.7
8.0
Bachelor Degree
7.2
4.7
5.6
6.6
7.3
11.9
30.1
17.0
3.4
Advanced Diploma/Diploma
8.6
7.9
7.6
10.5
12.4
18.5
36.7
13.8
3.6
Certificate III/IV
6.1
6.6
6.5
9.8
7.3
11.7
30.3
15.7
3.0
Certificate I/II
20.2
16.1
15.8
21.3
18.0
29.1
102.4
36.8
8.4
Certificate n.f.d.
11.4
15.6
10.4
18.2
17.1
28.8
47.7
24.9
7.4
Year 12
4.9
6.0
7.2
7.0
7.9
12.1
35.3
11.3
2.8
Year 11
6.1
4.8
4.6
8.1
7.0
9.4
34.1
13.2
2.9
Year 10 or below
5.2
3.8
8.7
7.2
13.0
7.3
31.0
13.6
2.9
Level not determined
15.8
17.8
49.2
37.9
25.9
60.6
101.7
51.7
9.7
Study not leading to a qualification
9.3
16.0
16.4
13.9
17.0
18.6
29.9
30.5
7.3
Type of educational institution attending
School
2.0
2.2
3.5
3.4
3.8
3.7
21.1
5.7
1.1
TAFE
4.6
6.4
5.6
7.9
5.6
9.5
44.5
12.5
2.9
Higher education
5.2
4.7
5.0
5.3
8.0
9.5
20.2
16.7
2.7
Other institution
7.4
6.6
6.2
12.6
9.5
10.8
27.2
15.1
4.4
Type of attendance
Full-time
2.4
2.2
3.3
4.0
4.6
4.7
18.2
11.8
1.2
Part-time
3.0
4.0
3.9
5.5
5.7
6.2
15.7
9.2
2.0
Total
1.6
1.9
2.2
2.9
2.8
3.6
15.0
7.3
1.0
. . not applicable
(a) Refers to mainly urban areas only. For more information see paragraph 9 of the Explanatory Notes.