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TECHNICAL NOTE DATA QUALITY
4 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication. However, RSEs for all these estimates are available free-of-charge on the ABS web site
<www.abs.gov.au>, released in spreadsheet format from the Downloads tab for this publication. As a guide, the population estimates and RSEs for selected data from table 2 are presented at a table in this Technical Note.
5 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 have been included and are preceded by an asterisk (e.g. *13.5) 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 AND RELATIVE STANDARD ERROR
6 RSEs are routinely presented as the measure of sampling error in this publication and related products. SEs can be calculated using the estimates (counts or means) and the corresponding RSEs.
7 An example of the calculation of the SE from an RSE follows. The table shows that the estimated number of males aged 18–24 years who did not prefer to work more hours is 226,900, and the RSE for this estimate was 9.5%. The SE is:
= (RSE / 100) x estimate
= 0.095 x 226,900
= 21,600 (rounded to the nearest 100)
Proportions 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 RSEs of proportions not provided in the spreadsheets is given below. This formula is only valid when x is a subset of y.
10 Considering the table, of the 1,021,300 males who worked 0–34 hours each week, 692,400 or 67.8% did not prefer to work more hours. The RSE of 692,400 is 4.6% and the RSE for 1,021,300 is 3.6%. Applying the above formula, the RSE for the proportion of males who did not prefer to work more hours is:
11 Therefore, the SE for the proportion of males who worked 0–34 hours per week who did not prefer more hours was 2.0 percentage points (= (67.8/100) x 2.9). Therefore, there are about two chances in three that the proportion of males who worked 0–34 hours per week who did not prefer more hours is between 65.8% and 69.8%, and 19 chances in 20 that the proportion was within the range 63.8% to 71.8%.
Sums or Differences between estimates
12 Published estimates may also be used to calculate the sum of, or difference between, two survey estimates (of numbers, means or percentages) where these are not provided in the spreadsheets. Such estimates are also subject to sampling error.
13 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:
14 The sampling error of the sum of two estimates is calculated in a similar way. An approximate SE of the sum of two estimates (x+y) may be calculated by the following formula:
15 An example follows. From paragraph 7 the estimated number of males aged 18–24 years who did not prefer to work more hours was 226,900 and the SE was 21,600. From the table, the estimate of males aged 25–34 years who did not prefer to work more hours was 78,600, and the SE was 11,554. The estimate of males aged 18–34 years who preferred not to work more hours is:
17 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 would fall within the range 281,000 to 330,000 and about 19 chances in 20 that the value would fall within the range 256,500 to 354,500.
18 While these formulae will only be exact for sums of, or differences between, separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all sums or differences likely to be of interest in this publication.
PERSONS AGED 18 YEARS AND OVER, USUALLY WORKED 0–34 HOURS PER WEEK OR NOT EMPLOYED, Whether wanted a job or more hours—By age
* estimate has a relative standard error of 25% to 50% and should be used with caution
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