6324.0 - Work-Related Injuries, Australia, JUL 2013 TO JUN 2014 Quality Declaration 
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 19/11/2014   
   Page tools: Print Print Page Print all pages in this productPrint All

TECHNICAL NOTE DATA QUALITY

INTRODUCTION

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.

      RSE% = (SE/estimate) x 100

    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:

      SE of estimate
      = (RSE%/100) x estimate
      = 0.183 x 38,200
      = 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 31,200 to 45,200 and about 19 chances in 20 that the value will fall within the range 24,200 to 52,200. This example is illustrated in the following diagram.

      Standard error range

      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.

      Formula for RSEs

      10 Considering table T2, of the 208,100 females who experienced a work-related injury or illness in the last 12 months, 80,200 or 38.6% worked part-time in the job where the work-related injury or illness occurred. The RSE of 80,200 is 12.1% and the RSE for 208,100 is 7.8%. 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.

      Formula for RSE

      11 Therefore, the SE for the proportion of the 208,100 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 3.6 percentage points (= 38.6/100 x 9.3). 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 35.0% and 42.2%, and 19 chances in 20 that the proportion is within the range 31.4% and 45.8%.

      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:

      Formula for SE

      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:

      SE 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:


      Formula for SE

      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.

      SELECTED ESTIMATES AND RSES


      T1: PERSONS WHO WORKED AT SOME TIME IN THE LAST 12 MONTHS, Age—By whether experienced a work-related injury or illness (a)



      WHETHER EXPERIENCED A WORK-RELATED INJURY OR ILLNESS IN THE LAST 12 MONTHS
      Experienced a work-related injury or illness
      Did not experience a work-related injury or illness
      Total
      Rate with a work-related injury or illness
      ESTIMATES ('000)
      Age group (years)
      15–19
      38.2
      719.0
      757.1
      50.4
      20–24
      53.1
      1236.4
      1289.4
      41.1
      25–29
      62.0
      1394.9
      1456.9
      42.6
      30–34
      52.9
      1378.4
      1431.4
      37.0
      35–39
      52.4
      1231.6
      1283.9
      40.8
      40–44
      65.9
      1321.7
      1387.6
      47.5
      45–49
      53.0
      1242.6
      1295.6
      40.9
      50–54
      66.7
      1217.5
      1284.2
      51.9
      55–59
      49.3
      1018.1
      1067.4
      46.2
      60–64
      26.0
      687.0
      713.0
      36.4
      65 and over
      *12.5
      492.0
      504.4
      *24.8
      Total
      531.8
      11939.2
      12471.0
      42.6
      RSES OF ESTIMATES (%)
      Age group (years)
      15–19
      18.3
      2.0
      1.4
      18.7
      20–24
      17.6
      1.2
      0.9
      17.7
      25–29
      14.6
      1.1
      0.8
      14.6
      30–34
      12.4
      0.9
      0.7
      12.6
      35–39
      11.2
      0.6
      0.6
      11.0
      40–44
      12.5
      1.0
      0.6
      12.7
      45–49
      13.3
      0.9
      0.8
      13.2
      50–54
      11.7
      0.9
      0.6
      11.8
      55–59
      12.7
      1.1
      0.8
      12.7
      60–64
      16.9
      1.2
      1.0
      17.0
      65 and over
      26.2
      2.8
      2.7
      26.1
      Total
      4.9
      0.4
      0.3
      4.9

      * 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


      MALES
      FEMALES
      PERSONS
      '000
      %
      '000
      %
      '000
      %
      ESTIMATES
      Whether worked full-time or part-time in job where most recent work-related injury occurred
      Worked full-time
      283.4
      87.5
      127.8
      61.4
      411.2
      77.3
      Worked part-time
      40.4
      12.5
      80.2
      38.6
      120.6
      22.7
      Hours usually worked in job where most recent work-related injury or illness occurred
      Less than 16
      *11.7
      *3.6
      20.5
      9.9
      32.2
      6.1
      16–29
      *22.0
      *6.8
      45.6
      21.9
      67.6
      12.7
      30–34
      *6.7
      *2.1
      14.1
      6.8
      20.8
      3.9
      35–39
      89.5
      27.7
      63.8
      30.7
      153.4
      28.8
      40
      79.9
      24.7
      35.6
      17.1
      115.6
      21.7
      41–44
      *16.9
      *5.2
      *5.3
      *2.5
      22.1
      4.2
      45–49
      34.7
      10.7
      *10.0
      *4.8
      44.7
      8.4
      50–59
      37.1
      11.4
      *9.4
      *4.5
      46.5
      8.7
      60 or more
      25.3
      7.8
      *3.7
      *1.8
      29.0
      5.4
      Whether worked shift work in job where most recent work-related injury or illness occurred
      Worked under shift arrangements
      92.5
      28.6
      65.1
      31.3
      157.6
      29.6
      Did not work under shift arrangements
      231.3
      71.4
      142.9
      68.7
      374.2
      70.4
      Total
      323.7
      100.0
      208.1
      100.0
      531.8
      100.0
      RSES OF ESTIMATES (%)
      Whether worked full-time or part-time in job where most recent work-related injury occurred
      Worked full-time
      6.5
      2.0
      7.9
      4.6
      5.0
      2.3
      Worked part-time
      14.3
      13.8
      12.1
      7.3
      9.8
      7.8
      Hours usually worked in job where most recent work-related injury or illness occurred
      Less than 16
      26.2
      28.0
      20.5
      19.6
      15.4
      16.3
      16–29
      27.0
      26.4
      16.6
      12.5
      16.1
      14.2
      30–34
      31.9
      29.9
      19.7
      17.9
      16.7
      14.8
      35–39
      9.9
      7.9
      11.7
      10.4
      6.3
      4.7
      40
      13.1
      10.2
      20.3
      17.3
      10.0
      8.0
      41–44
      28.2
      26.8
      38.3
      39.8
      23.2
      22.6
      45–49
      15.3
      14.9
      30.7
      28.7
      12.7
      11.4
      50–59
      18.7
      18.5
      32.1
      35.2
      17.0
      17.7
      60 or more
      21.6
      21.7
      39.3
      38.0
      20.5
      20.2
      Whether worked shift work in job where most recent work-related injury or illness occurred
      Worked under shift arrangements
      11.7
      10.1
      13.4
      8.2
      9.1
      7.1
      Did not work under shift arrangements
      7.2
      4.0
      7.2
      3.7
      5.4
      3.0
      Total
      6.0
      –
      7.8
      –
      4.9
      –
      * estimate has a relative standard error of 25% to 50% and should be used with caution
      – nil or rounded to zero (including null cells)
      (a) In the last 12 months.