TECHNICAL NOTE DATA QUALITY
RELIABILITY OF ESTIMATES
1 Since the estimates in this publication are based on information obtained from selected occupants of a sample of dwellings, they are subject to sampling variability; that is, they may differ from those that would have been 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 might have varied by chance because only a sample of dwellings was included. There are about 2 chances in 3 (67%) that a sample estimate will vary 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.
3 Space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication. However, RSEs were calculated for each separate estimate and are available to download free-of-charge as Excel spreadsheets from the ABS website <www.abs.gov.au> as an attachment to this publication. The Jackknife method of variance estimation is used to calculate SEs, which involves the calculation of 30 replicate estimates based on 30 different sub samples of the original sample. The variability of estimates obtained from these sub samples is used to estimate the sample variability surrounding the main estimate.
4 In the tables in this publication, only estimates (numbers or percentages) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g.*3.4) to indicate they are subject to high SEs relative to their estimate 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.
CALCULATING STANDARD ERRORS FOR POPULATION ESTIMATES
5 Standard errors can be calculated using the estimates (counts or proportions) and their corresponding RSEs. For example, Table 3 shows the estimated number of people who had some paid involvement in organised sport and physical activity during the 12 months prior to interview was 122,500. The RSE Table corresponding to the estimates in Table 3, provided in the 'Relative Standard Error' section at the end of these Technical Notes, shows the RSE for this estimate is 10.6%. The SE is calculated by:
6 Therefore there are about 2 chances in 3 that the value that would have been produced if all persons had been included in the survey would fall within the range 109,500 and 135,500, and about 19 chances in 20 that the value will fall within the range 96,500 and 148,500. This example is illustrated in the diagram below:
In general, the size of the SE increases as the size of the estimate increases. Conversely, the RSE decreases as the size of the estimate increases (due to the number of people contributing to the estimate increasing). Very small estimates are thus subject to such high RSEs that their value for most practical purposes is unreliable.
CALCULATING STANDARD ERRORS FOR DIFFERENCES OF ESTIMATES
The difference between two survey estimates (numbers or percentages) is also 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 formula:
While this formula will only be exact for differences between separate and uncorrelated (unrelated) characteristics of sub-populations it is expected to provide a good approximation for all differences likely to be of interest in this publication.
The statistical significance test for any of the comparisons between estimates was performed to determine whether, with a certain level of confidence, there is a true 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 8. This standard error is then used to calculate the following test statistic:
If the value of this test statistic is greater than 2 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.
RELATIVE STANDARD ERROR
Relative Standard Errors for Table 3 are included below. However, RSEs for all tables are available free-of-charge on the ABS website <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication.
PERSONS INVOLVED IN PLAYING ROLE, Payment status, By selected characteristics: Relative Standard Errors
RSE of Some paid involvement(a)
RSE of Unpaid involvement only(b)
RSE of Total persons involved in playing role
RSE of Proportion with some paid involvement(a)
|State or territory of usual residence |
|New South Wales |
|South Australia |
|Western Australia |
|Northern Territory |
|Australian Capital Territory |
|Age group (years) |
|65 and over |
|Labour force status |
|Employed full-time |
|Employed part-time |
|Total employed |
|Not in the labour force |
|Area of usual residence |
|State capital cities |
|Balance of state/Territory |
|Country of birth |
|Main English-speaking countries |
|Non main English-speaking countries |
|Total born overseas(c) |
|(a) Paid involvement includes those who only received goods and services as payment. |
|(b) Includes those who did not know whether they would be paid for their involvement. |
|(c) Includes those with inadequate data for Country of birth. |
This page last updated 25 November 2010