6226.0.55.001 - Persons Not In the Labour Force, Underemployed Workers and Job Search Experience, Australia, February 2014
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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 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, taken from Job Search Experience, is as follows. JSE table 3 shows that 249,300 unemployed females were looking for full-time work. Since this estimate is between 200,000 and 300,000, table T2 shows that the SE for Australia will lie between 6,500 and 7,700 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 242,200 to 256,400 and about 19 chances in 20 that the value will fall within the range 235,100 to 263,500. 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. **0.2), 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%. Table T3 presents the levels at which estimates have RSEs of 25% and 50%.

MEANS AND MEDIANS

6 The RSEs of means and medians are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median (see table T2) and then multiplying the resulting number by the following factors for Australian estimates:
• For JSE
• mean duration of unemployment: 1.6
• median duration of unemployment: 2.5
• For UEW
• Mean duration of insufficient work: 1.6
• Median duration of insufficient work: 2.5
• Mean preferred number of extra hours: 0.7

7 The following is an example of the calculation of SEs where the use of a factor is required. JSE table 4 shows that the estimated median duration of unemployment for unemployed females in Australia was 10 weeks and shows that the number of unemployed females was estimated as 407,600. The SE of 407,600 can be calculated from table T2 (by interpolation) as 8,700. To convert this to an RSE express the SE as a percentage of the estimate or 8,700/407,600 = 2.1%.

8 The RSE of the estimate of median duration of unemployment for unemployed females is calculated by multiplying this number (2.1%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.1 x 2.5 = 5.3%. The SE of this estimate of median duration of unemployment for unemployed females is therefore 5.3% of 10 weeks, i.e. approximately one week. Therefore, there are two chances in three that the median duration of unemployment for females that would have been obtained if all dwellings had been included in the survey would have been within the range 9 to 11 weeks and about 19 chances in 20 that it would have been within the range 8 weeks to 12 weeks.

9 Table T3 represents the minimum size of estimates, based on the SE model described in paragraph 2, required to have RSEs of less than 25% and 50% respectively. For example, an estimate of median duration of unemployment for Australia based on less than 35,600 persons will have an RSE of at least 25%, and an estimate of median duration of unemployment for Australia based on less than 12,800 will have an RSE of at least 50%. For all other estimates, (i.e. those estimates based purely on number of persons in a specific category), an estimate of less than 8,800 for the Australian total will have an RSE of at least 25% and an estimate of less than 2,300 will have an RSE of at least 50%.

PROPORTIONS AND PERCENTAGES

10 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:

11 Considering the example from paragraph 3, of the 249,300 unemployed females who were looking for full-time work, 51,100 or 20.5% had been unemployed for one year or more. The SE of 51,100 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 4,000/51,100 = 7.8%. The SE for 249,300 was calculated previously as 7,100, which converted to an RSE is 7,100/249,300 = 2.8%. Applying the above formula, the RSE of the proportion is:

12 Therefore, the SE for the proportion of unemployed females looking for full-time work who had been unemployed for one year or more is 1.5 percentage points (=20.5/100) x 7.3). Therefore, there are about two chances in three that the proportion of unemployed females looking for full-time work who have been unemployed for one year or more is between 19.0% and 22.0% and 19 chances in 20 that the proportion is within the range 17.5% to 23.5%.

DIFFERENCES

13 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:

14 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 (PNILF) 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 80 120 140 140.0 200 300 230 330 250 260 160 110 210 240 120.0 300 390 290 440 310 330 200 140 270 320 106.7 500 530 400 600 400 440 250 170 370 460 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 1 120 670 760 400 300 580 940 62.7 2,000 1 150 820 1 300 760 860 440 340 630 1 120 56.0 2,500 1 300 900 1 450 850 950 450 400 650 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 1 250 600 600 850 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 1 450 1 700 3 000 20.0 20,000 3 150 2 150 3 350 1 900 2 150 1 200 1 850 2 000 3 350 16.8 30,000 3 600 2 500 3 900 2 350 2 700 1 500 2 500 2 450 3 850 12.8 40,000 4 000 2 750 4 400 2 750 3 200 1 750 3 100 2 750 4 250 10.6 50,000 4 350 3 000 4 850 3 100 3 650 1 950 3 600 2 950 4 600 9.2 100,000 6 050 4 350 7 150 4 450 5 350 2 700 5 650 3 350 6 050 6.1 150,000 7 700 5 600 9 050 5 350 6 600 3 200 7 100 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 STANDARD ERRORS OF ESTIMATES (UEW/JSE) NSW Vic. Qld. SA WA Tas. NT ACT SE RSE Size of Estimate (persons) 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 80 200 220 110.0 300 570 380 440 310 380 190 100 250 310 103.3 500 700 470 560 380 460 230 130 320 440 88.0 700 810 530 650 430 530 270 150 360 560 80.0 1,000 930 610 760 490 610 310 180 400 700 70.0 1,500 1 100 710 900 580 710 350 210 430 900 60.0 2,000 1 230 800 1 010 640 790 390 230 460 1 070 53.5 2,500 1 350 850 1 100 700 850 400 250 500 1 200 48.0 3,000 1 450 950 1 200 750 900 450 250 500 1 350 45.0 3,500 1 550 1 000 1 250 800 1 000 450 250 550 1 450 41.4 4,000 1 600 1 050 1 300 850 1 050 500 300 550 1 550 38.8 5,000 1 750 1 150 1 400 900 1 100 500 300 600 1 700 34.0 7,000 2 000 1 300 1 600 1 000 1 250 600 400 700 2 000 28.6 10,000 2 300 1 450 1 800 1 150 1 450 700 500 800 2 300 23.0 15,000 2 650 1 700 2 000 1 300 1 650 850 650 1 000 2 700 18.0 20,000 2 950 1 900 2 200 1 450 1 850 950 850 1 150 3 000 15.0 30,000 3 400 2 200 2 500 1 700 2 100 1 250 1 150 1 500 3 350 11.2 40,000 3 800 2 400 2 800 1 950 2 350 1 450 1 500 1 750 3 650 9.1 50,000 4 100 2 600 3 050 2 200 2 550 1 650 1 800 2 000 3 950 7.9 100,000 5 200 3 450 4 200 3 300 3 750 2 400 3 100 2 650 4 950 5.0 150,000 6 100 4 150 5 150 4 250 4 950 2 850 4 250 3 000 5 800 3.9 200,000 7 050 4 850 6 000 4 950 5 950 3 150 5 300 3 150 6 500 3.3 300,000 8 850 6 250 7 650 6 100 7 500 3 650 7 200 3 300 7 700 2.6 500,000 12 400 8 650 10 300 7 650 9 550 4 200 . . 3 300 9 650 1.9 1,000,000 18 400 13 150 14 700 9 750 12 150 4 800 . . . . 13 600 1.4 2,000,000 24 800 19 450 19 800 11 600 14 100 . . . . . . 19 750 1.0 5,000,000 31 600 31 100 26 700 13 050 14 700 . . . . . . 32 950 0.7 10,000,000 33 850 42 900 31 200 . . . . . . . . . . 44 000 0.4 15,000,000 . . . . . . . . . . . . . . . . 49 600 0.3 . . not applicable

 T3 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. Persons not in the labour force 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 1 500 500 300 1 000 2 600 Underemployed Workers 25% RSE Mean duration of insufficient work 18 300 9 800 13 000 5 800 9 400 2 500 1 200 3 000 19 200 Median duration of insufficient work 44 400 22 900 32 500 18 100 21 700 6 700 11 900 13 400 35 300 Mean preferred number of extra hours 5 300 3 100 3 800 2 000 2 900 1 000 400 1 100 5 000 All other estimates 8 600 4 200 6 100 3 000 4 200 1 400 500 1 800 8 800 Underemployed Workers 50% RSE Mean duration of insufficient work 6 100 3 200 4 700 2 000 3 200 900 300 1 200 6 100 Median duration of insufficient work 15 000 7 600 11 800 6 300 7 400 2 400 2 700 4 000 12 600 Mean preferred number of extra hours 1 700 1 000 1 200 600 1 000 300 100 400 1 100 All other estimates 2 800 1 400 2 000 1 000 1 400 400 100 700 2 300 Job Search Experience 25% RSE Mean duration of unemployment 15 300 7 500 10 100 5 000 7 400 2 200 800 3 100 18 400 Median duration of unemployment 40 600 20 300 26 700 13 900 21 200 7 900 2 600 9 100 35 600 All other estimates 8 600 4 200 6 100 3 000 4 200 1 400 500 1 800 8 800 Job Search Experience 50% RSE Mean duration of unemployment 5 100 2 500 3 600 1 700 2 500 800 200 1 200 5 800 Median duration of unemployment 13 700 6 800 9 800 4 800 7 200 2 800 900 3 000 12 800 All other estimates 2 800 1 400 2 000 1 000 1 400 400 100 700 2 300 (a) Refers to the number of persons contributing to the estimate.