6265.0 - Underemployed Workers, Australia, September 2013
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 26/02/2014  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, and 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 is as follows. Table 4 shows the estimated number of female underemployed part-time workers was 493,800. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,700 and 9,650 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 484,200 to 503,400 and about 19 chances in 20 that the value will fall within the range 474,600 to 513,000. 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.**0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of less than 25%.

MEANS AND MEDIANS

6 The RSEs of estimates of mean duration of insufficient work, median duration of insufficient work and mean preferred number of extra hours are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median ( see table T1) and then multiplying the resulting number by the following factors:

• 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. Table 4 shows that the estimated number of male underemployed part-time workers was 323,400 with a median duration of insufficient work of 30 weeks. The SE of 323,400 can be calculated from table T1 (by interpolation) as 7,700. To convert this to an RSE we express the SE as a percentage of the estimate or 7,700/323,400 = 2.4%.

8 The RSE of this estimate of median duration of insufficient work is calculated by multiplying this number (2.4%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.5 x 2.4 = 6.0%. The SE of this estimate of median duration of insufficient work is therefore 6.0% of 30, i.e. about 2 weeks (rounded to the nearest whole week). Therefore, there are two chances in three that the median duration of insufficient work for males that would have been obtained if all dwellings had been included in the survey would have been within the range 28-32 weeks, and about 19 chances in 20 that it would have been within the range 26-34 weeks.

PROPORTIONS AND PERCENTAGES

9 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.

10 Considering the example from paragraph 3, of the 493,800 female underemployed part-time workers, 199,800 or 40.5% had insufficient work for 52 weeks and over. The SE of 199,800 may be calculated by interpolation as 6,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 6,500/199,800 = 3.3%. The SE for 493,800 was calculated previously as 9,600, which converted to an RSE is 9,600/493,800 = 1.9%. Applying the above formula, the RSE of the proportion is:

11 Therefore, the SE for the proportion of females who have a current period of insufficient work of 52 weeks or more is 1.1 percentage points (=(40.5/100)x2.7). Therefore, there are about two chances in three that the proportion of females who have a current period of insufficient work of 52 weeks or more was between 39.4% and 41.6% and 19 chances in 20 that the proportion is within the range 38.3% and 42.7%.

DIFFERENCES

12 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:

13 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 AUST. NSW Vic. Qld. SA WA Tas. NT ACT SE RSE Size of Estimate (persons) no. no. no. no. no. no. no. no. no. % 100 360 250 250 190 240 110 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 1,000 930 610 760 490 610 310 170 400 700 70.0 1,500 1 100 710 900 580 710 350 200 430 900 60.0 2,000 1 230 800 1 010 640 790 390 220 460 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 1 250 600 350 700 2 000 28.6 10,000 2 300 1 450 1 800 1 150 1 450 700 450 800 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 1 850 950 800 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 1 450 1 750 3 650 9.1 50,000 4 100 2 600 3 050 2 200 2 550 1 650 1 700 2 000 3 950 7.9 100,000 5 200 3 450 4 200 3 300 3 750 2 400 3 000 2 650 4 950 5.0 150,000 6 100 4 150 5 150 4 250 4 950 2 850 4 100 3 000 5 800 3.9 200,000 7 050 4 850 6 000 4 950 5 950 3 150 5 150 3 150 6 500 3.3 300,000 8 850 6 250 7 650 6 100 7 500 3 650 7 000 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

 T2 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. 25% RSE Mean duration of insufficient work 18 300 9 800 13 000 5 800 9 400 2 500 1 100 3 000 19 200 Median duration of insufficient work 44 400 22 900 32 500 18 100 21 700 6 700 10 300 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 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 2 600 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 (a) Refers to the number of persons contributing to the estimate.