6324.0 - Work-Related Injuries, Australia, 2005-06
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 20/12/2006
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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. 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.

2 Due to space limitations, it is impractical to print the SE of each estimate in the publication. Instead, a table of SEs is provided to enable readers to determine the SE for an estimate from the size of that estimate (see table T1). The SE table is derived from a mathematical model, referred to as the 'SE model', which is created using the data collected in this survey. It should be noted that the SE model only gives an approximate value for the SE for any particular estimate, since there is some minor variation between SEs for different estimates of the same size.

CALCULATION OF STANDARD ERROR

3 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 1 shows that in 2005-06, the estimated number of women in Australia who worked at some time in the last 12 months was 4,944,300. Since this estimate is between 2,000,000 and 5,000,000, table T1 shows that the SE for Australia will lie between 25,000 and 32,700 and can be approximated by interpolation using the following general formula:

4 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 4,911,700 to 4,976,900 and about 19 chances in 20 that the value will fall within the range 4,897,100 to 5,009,500. This example is illustrated in the diagram below.

5 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. Very small estimates are thus subject to such high RSEs that their value for most practical purposes is unreliable. In the tables in this publication, only estimates with RSEs of 25% or less are considered reliable for most purposes. Estimates with RSEs greater than 25% but less than or equal to 50% are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs of greater than 50%, preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%.

PROPORTIONS AND PERCENTAGES

6 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 RSE of a proportion is given below. This formula is only valid when x is a subset of y.

7 Considering the example from the previous page, of the 4,944,300 women who worked at some time in the last 12 months, 251,900 or 5.1% experienced a work-related injury or illness. The SE of 251,900 may be calculated by interpolation as 12,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 12,000/251,900 = 4.8%. The SE for 4,944,300 was calculated previously as 32,600, which converted to an RSE is 32,600/4,944,300 = 0.7%. Applying the above formula, the RSE of the proportion is

8 Therefore, the SE for the proportion of women who worked at some time in the last 12 months and who experienced a work-related injury or illness is 0.2 percentage points (=(5.1/100)x4.7). Therefore, there are about two chances in three that the proportion of women who worked at some time in the last 12 months and who experienced a work-related injury or illness is between 4.9% and 5.3% and 19 chances in 20 that the proportion is within the range 4.7% to 5.5%.

DIFFERENCES

9 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is 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 following formula:

10 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.

STANDARD ERRORS

 T1 STANDARD ERRORS OF ESTIMATES AUST. NSW Vic. Qld SA WA Tas. NT ACT SE RSE Size of estimate (persons) no. no. no. no. no. no. no. no. no. % 100 250 280 260 180 250 120 120 110 170 170.0 200 390 420 390 260 360 190 200 180 270 135.0 300 500 520 490 330 440 250 260 250 350 116.7 500 670 690 650 430 570 330 360 350 490 98.0 700 820 820 790 510 680 400 440 430 610 87.1 1,000 1 000 990 950 610 800 490 540 530 760 76.0 1,500 1 250 1 210 1 170 750 970 610 660 670 970 64.7 2,000 1 460 1 390 1 350 850 1 110 700 760 780 1 150 57.5 2,500 1 650 1 550 1 500 950 1 200 800 850 850 1 300 52.0 3,000 1 800 1 700 1 650 1 050 1 300 850 900 950 1 450 48.3 3,500 1 950 1 800 1 750 1 100 1 400 900 950 1 000 1 600 45.7 4,000 2 100 1 950 1 900 1 150 1 500 1 000 1 000 1 100 1 700 42.5 5,000 2 350 2 150 2 100 1 300 1 650 1 100 1 100 1 200 1 900 38.0 7,000 2 750 2 500 2 450 1 500 1 900 1 250 1 250 1 350 2 300 32.9 10,000 3 250 2 900 2 850 1 750 2 200 1 450 1 400 1 550 2 800 28.0 15,000 3 900 3 450 3 350 2 050 2 600 1 750 1 550 1 750 3 400 22.7 20,000 4 450 3 900 3 800 2 300 2 900 1 950 1 650 1 900 3 950 19.8 30,000 5 300 4 600 4 450 2 700 3 350 2 250 1 750 2 050 4 800 16.0 40,000 6 000 5 150 4 950 3 000 3 700 2 450 1 850 2 200 5 500 13.8 50,000 6 550 5 600 5 350 3 250 4 050 2 650 1 900 2 300 6 100 12.2 100,000 8 600 7 300 6 850 4 150 5 100 3 300 2 000 2 500 8 250 8.3 150,000 10 000 8 400 7 800 4 750 5 800 3 700 2 000 2 550 9 800 6.5 200,000 11 050 9 250 8 550 5 200 6 350 3 950 2 000 2 600 11 000 5.5 300,000 12 700 10 600 9 650 5 850 7 200 4 350 15 400 2 550 12 950 4.3 500,000 14 950 12 500 11 150 6 800 8 300 4 850 . . 2 550 15 650 3.1 1,000,000 18 400 15 350 13 300 8 200 10 000 6 250 . . . . 20 000 2.0 2,000,000 22 200 18 600 15 550 9 700 11 850 . . . . . . 25 000 1.3 5,000,000 27 650 23 400 18 600 13 000 11 500 . . . . . . 32 700 0.7 10,000,000 . . 36 450 15 250 . . . . . . . . . . 39 200 0.4 20,000,000 . . . . . . . . . . . . . . . . 46 050 0.2 . . not applicable

 T2 LEVELS AT WHICH ESTIMATES HAVE RELATIVE STANDARD ERRORS OF 25% AND 50%(a) NSW Vic. Qld. SA WA Tas. NT ACT Aust. no. no. no. no. no. no. no. no. no. Estimate with 25% RSE 16 300 13 100 12 500 5 300 8 000 3 900 4 100 4 500 12 400 Estimate with 50% RSE 4 400 3 800 3 600 1 500 2 400 1 000 1 200 1 200 2 800 (a) Refers to the number of persons contributing to the estimate.