6359.0 - Forms of Employment, Australia, November 2013
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 07/05/2014  Final
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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 1,013,500. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows the SE for Australia will be between 13,600 and 19.750 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 999,800 to 1,013,500, and about 19 chances in 20 that the value will fall within the range 986,100 to 1,040,900. 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 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 above, of the 1,013,500 persons who were other business operators, 404,000 or 39.9% were female. The SE of 404,000, may be calculated by interpolation as 8,700. To convert this to an RSE we express the SE as a percentage of the estimate, or 8,700/404,000 = 2.2%. The SE for 1,013,500 was calculated previously as 13,700, which converted to an RSE is 13,700/1,013,500 = 1.4%. 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 (39.9/100)x1.7. There are about two chances in three that the proportion of female business operators is between 39.2% and 40.6% and 19 chances in 20 that the proportion is within the range 38.5% to 41.3%.

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 Size of estimate no. no. no. no. no. no. no. no. no. % 100 360 250 250 190 240 110 50 120 130 130.0 200 480 320 360 260 320 150 80 200 220 110.0 300 570 380 440 310 380 190 100 250 310 103.3 500 700 470 560 380 460 230 120 320 440 88.0 700 810 530 650 430 530 270 140 360 560 80.0 1000 930 610 760 490 610 310 170 400 700 70.0 1500 1 100 710 900 580 710 350 200 430 900 60.0 2000 1 230 800 1 010 640 790 390 220 460 1 070 53.5 2500 1 350 850 1 100 700 850 400 250 500 1 200 48.0 3000 1 450 950 1 200 750 900 450 250 500 1 350 45.0 3500 1 550 1 000 1 250 800 1 000 450 250 550 1 450 41.4 4000 1 600 1 050 1 300 850 1 050 500 250 550 1 550 38.8 5000 1 750 1 150 1 400 900 1 100 500 300 600 1 700 34.0 7000 2 000 1 300 1 600 1 000 1 250 600 350 700 2 000 28.6 10000 2 300 1 450 1 800 1 150 1 450 700 450 800 2 300 23.0 15000 2 650 1 700 2 000 1 300 1 650 850 650 1 000 2 700 18.0 20000 2 950 1 900 2 200 1 450 1 850 950 800 1 150 3 000 15.0 30000 3 400 2 200 2 500 1 700 2 100 1 250 1 150 1 500 3 350 11.2 40000 3 800 2 400 2 800 1 950 2 350 1 450 1 450 1 750 3 650 9.1 50000 4 100 2 600 3 050 2 200 2 550 1 650 1 700 2 000 3 950 7.9 100000 5 200 3 450 4 200 3 300 3 750 2 400 2 950 2 650 4 950 5.0 150000 6 100 4 150 5 150 4 250 4 950 2 850 4 050 3 000 5 800 3.9 200000 7 050 4 850 6 000 4 950 5 950 3 150 5 100 3 150 6 500 3.3 300000 8 850 6 250 7 650 6 100 7 500 3 650 6 950 3 300 7 700 2.6 500000 12 400 8 650 10 300 7 650 9 550 4 200 . . 3 300 9 650 1.9 1000000 18 400 13 150 14 700 9 750 12 150 4 800 . . . . 13 600 1.4 2000000 24 800 19 450 19 800 11 600 14 100 . . . . . . 19 750 1.0 5000000 31 600 31 100 26 700 13 050 14 700 . . . . . . 32 950 0.7 10000000 33 850 42 900 31 200 . . . . . . . . . . 44 000 0.4 15000000 . . . . . . . . . . . . . . . . 49 600 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% 8 600 4 200 6 100 3 000 4 200 1 400 500 1 800 8 800 Relative Standard Error (RSE) of 50% 2 800 1 400 2 000 1 000 1 400 400 100 700 2 300