6220.0 - Persons Not in the Labour Force, Australia, September 2013
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 26/03/2014  Final
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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 117,200. Since the estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 6,050 and 7,250 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 110,700 to 123,700 and about 19 chances in 20 that the value will fall within the range 104,200 to 130,200. 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 117,200 people who were discouraged job seekers, 55,000 or 46.9% were females. The SE of 55,000 may be calculated by interpolation as 4,700. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,700/55,000=8.5%. The SE for 117,200 was calculated previously as 6,500 which converted to an RSE is 6,500/117,200=5.5%. 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 3.0 percentage points (=(46.9/100)x6.5). Therefore, there are about two chances in three that the proportion of females who were discouraged job seekers was between 43.9% and 49.9% and 19 chances in 20 that the proportion is within the range 40.9% to 52.9%.

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. % 100 180 150 200 170 170 110 80 120 140 140.0 200 300 230 330 250 260 160 110 210 240 120.0 300 390 290 440 310 330 200 130 270 320 106.7 500 530 400 600 400 440 250 170 370 460 92.0 700 650 480 730 470 520 290 200 430 580 82.9 1,000 800 580 900 560 620 340 240 500 730 73.0 1,500 990 710 1 120 670 760 400 290 580 940 62.7 2,000 1 150 820 1 300 760 860 440 330 630 1 120 56.0 2,500 1 300 900 1 450 850 950 450 350 650 1 250 50.0 3,000 1 400 1 000 1 600 900 1 050 500 400 700 1 400 46.7 3,500 1 500 1 050 1 700 950 1 100 550 450 750 1 500 42.9 4,000 1 600 1 150 1 800 1 000 1 150 550 500 750 1 650 41.3 5,000 1 800 1 250 2 000 1 100 1 250 600 550 850 1 800 36.0 7,000 2 100 1 450 2 300 1 250 1 450 700 750 1 000 2 150 30.7 10,000 2 400 1 650 2 650 1 400 1 600 850 1 000 1 300 2 500 25.0 15,000 2 800 1 950 3 050 1 650 1 900 1 050 1 400 1 700 3 000 20.0 20,000 3 150 2 150 3 350 1 900 2 150 1 200 1 800 2 000 3 350 16.8 30,000 3 600 2 500 3 900 2 350 2 700 1 500 2 450 2 450 3 850 12.8 40,000 4 000 2 750 4 400 2 750 3 200 1 750 3 000 2 750 4 250 10.6 50,000 4 350 3 000 4 850 3 100 3 650 1 950 3 500 2 950 4 600 9.2 100,000 6 050 4 350 7 150 4 450 5 350 2 700 5 450 3 350 6 050 6.1 150,000 7 700 5 600 9 050 5 350 6 600 3 200 6 900 3 350 7 250 4.8 200,000 9 200 6 650 10 600 6 050 7 600 3 600 . . . . 8 300 4.2 300,000 11 600 8 450 13 050 7 100 9 100 4 200 . . . . 10 100 3.4 500,000 15 000 11 350 16 500 8 550 11 300 5 000 . . . . 13 200 2.6 1,000,000 20 050 16 750 21 650 10 600 14 600 . . . . . . 19 550 2.0 2,000,000 24 950 24 200 26 850 12 650 18 250 . . . . . . 28 300 1.4 5,000,000 30 000 38 550 32 900 . . . . . . . . . . 40 800 0.8 10,000,000 31 800 53 850 . . . . . . . . . . . . 49 000 0.5 15,000,000 . . . . . . . . . . . . . . . . 52 550 0.4
. . 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% 9 400 5 000 10 900 4 100 5 100 1 600 900 2 700 10 100 RSE of 50% 2 700 1 300 3 300 1 200 1 500 500 200 1 000 2 600
(a) Refers to the number of people contributing to the estimate