TECHNICAL NOTE RELIABILITY OF ESTIMATES
ESTIMATES
1 Estimates provided in this report are based on information obtained from samples of households and persons. Estimates are subject to sampling and non-sampling error.
Non-sampling error
2 Non-sampling error may arise as a result of error in the reporting, recording or processing of data and can occur even if there is complete enumeration of the population. Non-sampling error can be introduced through inadequacies in the questionnaire, non-response, inaccurate reporting by respondents, error in the application of survey procedures, incorrect recording of answers and errors in data entry and processing.
3 It is not possible to measure the size of the non-sampling error. The extent of this error could vary considerably from survey to survey and from question to question. Every effort is made in the design of the survey and development of survey procedures to minimise the effect of this type of error.
Sampling error
4 Sampling error is the difference between the published estimates, derived from a sample of persons, and the value that would have been produced if all persons in scope of the survey had been included.
ESTIMATES OF SAMPLING ERROR
5 One measure of the variability of estimates which occurs as a result of surveying only a sample of the population is the standard error (SE).
6 There are about two chances in three that a sample estimate will differ by less than one SE from the figure that would have been obtained if all households had been included in the survey and about 19 chances in 20 that the difference will be less than two SEs.
7 Tables of standard errors of household and person estimates are provided for 2004-05 below. Standard estimates are provided to enable readers to determine the SE for an estimate from the size of that estimate. The SE is derived from a mathematical model, referred to as the 'SE model'. It should be noted that the SE model only gives an approximate value for the SE for any particular estimate, since there is some minor variation between SEs for different estimates of the same size.
STANDARD ERRORS OF HOUSEHOLD ESTIMATES - 2004-05 |
| |
| Size of estimate | Standard Error | Relative Standard Error | |
| no. | no. | % | |
| |
| 100 | 130 | 130.0 | |
| 200 | 220 | 110.0 | |
| 300 | 300 | 100.0 | |
| 500 | 420 | 84.0 | |
| 700 | 530 | 75.7 | |
| 1 000 | 670 | 67.0 | |
| 1 500 | 870 | 58.0 | |
| 2 000 | 1 050 | 52.5 | |
| 2 500 | 1 200 | 48.0 | |
| 3 000 | 1 350 | 45.0 | |
| 3 500 | 1 450 | 41.4 | |
| 4 000 | 1 600 | 40.0 | |
| 5 000 | 1 800 | 36.0 | |
| 7 000 | 2 150 | 30.7 | |
| 10 000 | 2 600 | 26.0 | |
| 15 000 | 3 250 | 21.7 | |
| 20 000 | 3 750 | 18.7 | |
| 30 000 | 4 550 | 15.1 | |
| 40 000 | 5 150 | 12.9 | |
| 50 000 | 5 700 | 11.4 | |
| 100 000 | 7 650 | 7.6 | |
| 150 000 | 8 950 | 5.9 | |
| 200 000 | 10 000 | 5.0 | |
| 300 000 | 11 550 | 3.8 | |
| 500 000 | 13 650 | 2.7 | |
| 1 000 000 | 16 750 | 1.7 | |
| 2 000 000 | 20 050 | 1.0 | |
| 5 000 000 | 24 400 | 0.5 | |
| |
STANDARD ERRORS OF PERSON ESTIMATES - 2004-05 |
| |
| Size of estimate | Standard Error | Relative Standard Error | |
| no. | no. | % | |
| |
| 100 | 200 | 200.0 | |
| 200 | 330 | 165.0 | |
| 300 | 450 | 150.0 | |
| 500 | 640 | 128.0 | |
| 700 | 810 | 115.7 | |
| 1 000 | 1 020 | 102.0 | |
| 1 500 | 1 320 | 88.0 | |
| 2 000 | 1 580 | 79.0 | |
| 2 500 | 1 800 | 72.0 | |
| 3 000 | 2 000 | 66.7 | |
| 3 500 | 2 200 | 62.8 | |
| 4 000 | 2 400 | 60.0 | |
| 5 000 | 2 700 | 54.0 | |
| 7 000 | 3 300 | 47.1 | |
| 10 000 | 3 950 | 39.5 | |
| 15 000 | 4 900 | 32.7 | |
| 20 000 | 5 650 | 28.3 | |
| 30 000 | 6 850 | 22.8 | |
| 40 000 | 7 850 | 19.6 | |
| 50 000 | 8 650 | 17.3 | |
| 100 000 | 11 600 | 11.6 | |
| 150 000 | 13 600 | 9.1 | |
| 200 000 | 15 150 | 7.6 | |
| 300 000 | 17 450 | 5.8 | |
| 500 000 | 20 650 | 4.1 | |
| 1 000 000 | 25 350 | 2.5 | |
| 2 000 000 | 30 350 | 1.5 | |
| 5 000 000 | 36 950 | 0.7 | |
| |
8 The standard error can also be expressed as a percentage of the estimate. This is known as the relative standard error (RSE). The RSE is determined by dividing the standard error of the estimate SE(x) by the estimate x and expressing it as a percentage. That is: RSE(x)=100*SE(x)/x (where x is the estimate). The RSE is a measure of the percentage error likely to have occurred due to sampling.
9 The tables below illustrate the RSE ranges for the size of estimates for tables in this report. Only estimates with RSEs less than 25% are considered sufficiently reliable for most purposes. Household and person estimates with an RSE between 25% and 50% are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Household and person estimates with an RSE greater than 50% are preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use.
PROPORTIONS AND PERCENTAGES
10 Proportions of a total and percentages formed from the ratio of two estimates are subject to sampling error. The size of the error depends on the accuracy of both the numerator and denominator. The formula for the relative standard error of a proportion or percentage for all four surveys is:
EDUCATIONAL CLASSIFICATIONS
11 In 2001, the Australian Standard Classification of Education (ASCED) (cat. no. 1272.0) replaced the ABS Classification of Qualifications (ABSCQ) (cat. no. 1261.0) . The ASCED is a new national standard classification which can be applied to all sectors of the Australian education system including schools, vocational education and training, and higher education.
12 The major groups of the ASCED classification have been aggregated to increase the reliability of estimates within each category.
13 The nine broad Levels of Education in ASCED are:
1 Postgraduate Degree Level
2 Graduate Diploma and Graduate Certificate Level
3 Bachelor Degree Level
4 Advanced Diploma and Diploma Level
5 Certificate Level
6 Secondary Education
7 Primary Education
8 Pre-primary Education
9 Other Education
14 These nine broad levels of ASCED have been collapsed into the following categories:
Year 12 or lower (ASCED groups 6, 7, 8 and 9)
Trade/other certificate (ASCED group 5)
Diploma/advanced diploma (ASCED group 4)
Bachelor degree or higher (ASCED groups 1, 2 and 3)
2003 SDAC HOUSEHOLD INCOME DATA
15 Due to the difference in household income data of the MPHS and previous surveys, household income data for 2003 have been suppressed due to unreliable estimates. These have been annotated as not to be published in this publication (np).