6324.0 - Work-Related Injuries, Australia, 2009-10 
Quality Declaration
Quality Declaration ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 13/12/2010
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TECHNICAL NOTE DATA QUALITY
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 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 website <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Work-Related Injuries (cat. no. 6324.0). 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 for an estimate of persons 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 39,200, and the RSE for this estimate is 17.9%. The SE is:
= (RSE%/100) x estimate = 0.179 x 39,200 = 7,000 (rounded to the nearest 100) 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 32,200 to 46,200 and about 19 chances in 20 that the value will fall within the range 25,200 to 53,200. This example is illustrated in the following diagram. 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 table T2, of the 284,300 females who experienced a work-related injury or illness in the last 12 months, 130,300 or 45.8% worked part-time in the job where the work-related injury or illness occurred. The RSE of 130,300 is 8.9% and the RSE for 284,300 is 7.1%. Applying the above formula, the RSE for the proportion of females who worked part-time hours in job where most recent work-related injury or illness occurred is as follows. Please note, due to the Jackknife method of variance estimation being used to calculate the RSEs reported in the spreadsheet attachments to this publication (including some proportions), the method of estimation used below will result in slightly different RSEs compared with those RSEs reported in the spreadsheets. 11 Therefore, the SE for the proportion of the 284,300 females who experienced a work-related injury or illness, who worked part-time hours in the job where the work-related injury or illness occurred is 2.5 percentage points (= 45.8/100 x 5.4). Therefore, there are about two chances in three that the proportion of females who experienced a work-related injury or illness who worked part time is between 43.3% and 48.3%, and 19 chances in 20 that the proportion is within the range 40.8% and 50.8%. 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, 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 39,200 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 85,200 and the SE is 9,800. The estimate of persons aged 15-24 who experienced a work-related injury or illness in the last 12 months is: 39,200 + 85,200 = 124,400 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 112,400 to 136,400 and about 19 chances in 20 that the value will fall within the range 100,400 to 148,400. 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. SELECTED ESTIMATES AND RSES
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