# Australian Bureau of Statistics

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 6220.0 - Persons Not in the Labour Force, Australia, September 2012  Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 07/03/2013
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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 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 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 the estimated number of people in Australia who were discouraged job seekers was 106,600. Since the estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 5,100 and 6,050 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 101,400 to 111,800 and about 19 chances in 20 that the value will fall within the range 96,200 to 117,000. This example is illustrated in the following diagram.

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.*3.2) 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.**0.4), 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 paragraph 3, of the 106,600 people who were discouraged job seekers, 56,300 or 52.8% were females. The SE of 56,300 may be calculated by interpolation as 4,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,000/56,300=7.1%. The SE for 106,600 was calculated previously as 5,200 which converted to an RSE is 5,200/106,600=4.9%. Applying the above formula, the RSE of the proportion is:

8 Therefore, the SE for the proportion of discouraged job seekers who were females is 2.7 percentage points (=(52.8/100)x5.1). Therefore, there are about two chances in three that the proportion of females who were discouraged job seekers was between 50.1% and 55.5% and 19 chances in 20 that the proportion is within the range 47.4% to 58.2%.

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 NSW Vic. Qld. SA WA Tas. NT ACT SE RSE Size of Estimate (persons) no. no. no. no. no. no. no. no. no. % 100 160 170 150 150 160 110 90 90 110 110.0 200 270 270 240 220 240 160 130 160 200 100.0 300 350 340 310 280 310 200 150 200 270 90.0 500 470 460 430 360 410 250 190 270 390 78.0 700 580 560 520 420 490 290 230 320 490 70.0 1,000 710 680 640 490 580 340 270 370 620 62.0 1,500 880 830 800 590 700 400 330 430 790 52.7 2,000 1 030 960 930 670 800 440 380 470 930 46.5 2,500 1 150 1 050 1 050 750 900 500 450 500 1 050 42.0 3,000 1 250 1 150 1 150 800 950 500 450 500 1 150 38.3 3,500 1 350 1 250 1 200 850 1 000 550 500 550 1 250 35.7 4,000 1 450 1 350 1 300 900 1 050 550 550 550 1 350 33.8 5,000 1 600 1 450 1 400 1 000 1 150 600 650 650 1 550 31.0 7,000 1 850 1 700 1 650 1 100 1 350 700 850 750 1 800 25.7 10,000 2 150 1 950 1 900 1 250 1 500 850 1 150 950 2 100 21.0 15,000 2 500 2 300 2 200 1 500 1 750 1 050 1 600 1 250 2 500 16.7 20,000 2 800 2 550 2 400 1 700 2 000 1 250 2 050 1 500 2 800 14.0 30,000 3 200 2 900 2 750 2 100 2 500 1 550 2 800 1 850 3 250 10.8 40,000 3 550 3 200 3 150 2 450 3 000 1 750 3 450 2 050 3 550 8.9 50,000 3 850 3 550 3 500 2 750 3 400 2 000 4 000 2 200 3 850 7.7 100,000 5 400 5 100 5 100 3 900 5 000 2 700 6 250 2 500 5 100 5.1 150,000 6 850 6 550 6 450 4 700 6 150 3 250 7 850 2 500 6 050 4.0 200,000 8 200 7 800 7 600 5 350 7 050 3 650 . . . . 6 950 3.5 300,000 10 350 9 900 9 300 6 300 8 500 4 250 . . . . 8 450 2.8 500,000 13 350 13 300 11 800 7 550 10 500 5 050 . . . . 11 050 2.2 1,000,000 17 850 19 600 15 450 9 400 13 600 . . . . . . 16 350 1.6 2,000,000 22 250 28 350 19 200 11 200 16 950 . . . . . . 23 700 1.2 5,000,000 26 700 45 150 23 500 . . . . . . . . . . 34 200 0.7 10,000,000 28 300 63 050 . . . . . . . . . . . . 41 050 0.4 15,000,000 . . . . . . . . . . . . . . . . 44 050 0.3 . . not applicable

 T2 levels at which estimates have a relative standard errors of 25% and 50%(a) NSW Vic. Qld SA WA Tas. NT ACT Australia Percentage no. no. no. no. no. no. no. no. no. RSE of 25% 7 700 6 600 6 300 3 300 4 500 1 700 1 200 1 800 7 300 RSE of 50% 2 100 1 800 1 700 1 000 1 300 500 300 600 1 700 (a) Refers to the number of people contributing to the estimate