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TECHNICAL NOTE DATA QUALITY
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 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 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.
3 RSEs for Work-related injuries estimates have been calculated using the Jackknife method of variance estimation. This process 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 RSEs for all estimates in this publication are available free-of-charge on the ABS website, released in spreadsheet format from the Downloads tab. As a guide, the population estimates and RSEs for selected data from tables 2 and 3 are presented at table T1 and table T2 in this Technical Note.
5 In the tables in this publication, only estimates (numbers, percentages and rates) 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 rates) and the corresponding RSEs.
7 An example of the calculation of the SE from an RSE follows. Table T1 shows that the estimated number of persons in Australia aged 15-19 who experienced a work-related injury or illness in the last 12 months is 38,200, and the RSE for this estimate is 18.3%. The SE is:
= (RSE%/100) x estimate
= 0.183 x 38,200
= 7,000 (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.
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, rates 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 persons aged 15-19 who experienced a work-related injury or illness in the last 12 months is 38,200 and the SE is 7,000. From table T1, the estimate of persons aged 20-24 who experienced a work-related injury or illness in the last 12 months is 53,100 and the SE is 9,300. The estimate of persons aged 15-24 who experienced a work-related injury or illness in the last 12 months is: 38,200 + 53,100 = 91,300
16 The SE of the estimate of persons aged 15-24 who experienced a work-related injury or illness in the last 12 months 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 will fall within the range 79,700 to 102,900 and about 19 chances in 20 that the value will fall within the range 68,100 to 114,500.
18 While this formula 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.
T1: PERSONS WHO WORKED AT SOME TIME IN THE LAST 12 MONTHS, Age—By whether experienced a work-related injury or illness (a)
* estimate has a relative standard error of 25% to 50% and should be used with caution
(a) In the last 12 months.
T2: PERSONS WHO EXPERIENCED A WORK-RELATED INJURY OR ILLNESS (a), Details of job where most recent work-related injury or illness occurred—By sex
– nil or rounded to zero (including null cells)
(a) In the last 12 months.
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