6359.0 - Forms of Employment, Australia, November 2010
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 29/04/2011
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TECHNICAL NOTE DATA QUALITY

INTRODUCTION

1 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 data from a number of past Labour Force Surveys. 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 ERRORS

3 An example of the calculation and the use of SEs in relation to estimates of people is as follows. Table 2 shows that the estimated number of persons in Australia who were other business operators was 1,047,000. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows the SE for Australia will be between 11,750 and 17,050 and can be approximated by interpolation using the following general formula:

4 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 in the range 1,035,000 to 1,059,000, and about 19 chances in 20 that the value will fall within the range 1,023,000 to 1,071,000. 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 that 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 25% or less.

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 formulae to approximate the RSE of a proportion is given below. This formulae is only valid when x is a subset of y:

7 Considering the example above, of the 1,047,000 persons who were other business operators, 398,900 or 38.1% were female. The SE of 398,900, may be calculated by interpolation as 7,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 7,500/398,000 = 1.9%. The SE for 1,047,000 was calculated previously as 12,000, which converted to an RSE is 12,000/1,047,000 = 1.1%. Applying the above formulae, the RSE of the proportion is:

8 The SE for the proportion of females who were other business operators, is 0.6 percentage points, calculated as (38.1/100)x1.5. There are about two chances in three that the proportion of female business operators is between 37.5% and 38.7% and 19 chances in 20 that the proportion is within the range 36.9% to 39.3%.

9 All other estimates produced from population estimates smaller than the values in T2 have RSEs larger than 25% and should be used with caution. T2 also indicates the size of the population estimates that would produce all other estimates with RSEs greater than 50% are considered too unreliable for general use.

DIFFERENCES

10 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 appropriate SE of the difference between two estimates (x-y) may be calculated by the following formulae:

11 While this formulae 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. % 100 290 290 220 180 220 110 80 100 110 110.0 200 400 380 320 240 290 160 120 170 190 95.0 300 470 440 390 280 340 190 150 210 260 86.7 500 580 540 500 340 420 240 190 270 380 76.0 700 660 620 580 390 480 270 230 300 480 68.6 1,000 760 710 680 450 550 310 260 330 610 61.0 1,500 900 830 810 530 640 360 310 360 780 52.0 2,000 1 010 930 910 590 710 390 340 390 920 46.0 2,500 1 100 1 000 1 000 650 800 400 350 400 1 050 42.0 3,000 1 200 1 100 1 050 700 850 450 400 450 1 150 38.3 3,500 1 250 1 150 1 100 700 900 450 400 450 1 250 35.7 4,000 1 300 1 200 1 200 750 900 500 450 450 1 350 33.8 5,000 1 450 1 300 1 250 800 1 000 500 450 500 1 500 30.0 7,000 1 650 1 500 1 450 900 1 150 600 550 600 1 700 24.3 10,000 1 850 1 700 1 600 1 050 1 300 700 700 700 2 000 20.0 15,000 2 150 1 950 1 800 1 200 1 500 850 1 000 850 2 350 15.7 20,000 2 400 2 200 1 950 1 350 1 650 1 000 1 250 1 000 2 550 12.8 30,000 2 800 2 550 2 250 1 550 1 900 1 250 1 750 1 250 2 900 9.7 40,000 3 100 2 800 2 500 1 800 2 100 1 500 2 250 1 500 3 150 7.9 50,000 3 350 3 050 2 750 2 000 2 300 1 700 2 650 1 650 3 400 6.8 100,000 4 250 4 000 3 750 3 000 3 400 2 400 4 650 2 250 4 300 4.3 150,000 5 000 4 850 4 600 3 850 4 450 2 850 6 400 2 500 5 000 3.3 200,000 5 750 5 650 5 400 4 550 5 350 3 200 7 950 2 650 5 600 2.8 300,000 7 250 7 250 6 850 5 550 6 750 3 700 10 900 2 800 6 650 2.2 500,000 10 150 10 050 9 250 7 000 8 600 4 250 . . 2 800 8 350 1.7 1,000,000 15 100 15 250 13 200 8 900 10 950 4 850 . . . . 11 750 1.2 2,000,000 20 350 22 550 17 700 10 600 12 700 . . . . . . 17 050 0.9 5,000,000 25 900 36 100 23 900 11 900 13 250 . . . . . . 28 450 0.6 10,000,000 27 750 49 750 27 950 . . . . . . . . . . 37 950 0.4 15,000,000 . . . . . . . . . . . . . . . . 42 850 0.3 . . not applicable

 T2 POPULATION LEVELS AT WHICH ESTIMATES HAVE RSES OF 25% AND 50% NSW Vic. Qld. SA WA Tas. NT ACT Aust. no. no. no. no. no. no. no. no. no. Relative Standard Error (RSE) of 25% 6 300 5 400 5 100 2 600 3 500 1 400 1 100 1 400 6 800 Relative Standard Error (RSE) of 50% 2 000 1 800 1 700 800 1 200 500 300 600 1 600