6265.0 - Underemployed Workers, Australia, Sep 2004
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 15/03/2005
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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 5 shows the estimated number of female part-time workers who want more hours was 382,600. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,250 and 8,800 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 374,700 to 390,500 and about 19 chances in 20 that the value will fall within the range 366,800 to 398,400. 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: 1.7
• median duration of insufficient work: 2.1
• mean preferred number of extra hours: 0.8.

7 The following is an example of the calculation of SEs where the use of a factor is required. Table 5 shows that the estimated number of male part-time workers who want more hours was 230,300 with a median duration of insufficient work of 26 weeks. The SE of 230,300 can be calculated from table T1 (by interpolation) as 6,600. To convert this to a RSE we express the SE as a percentage of the estimate or 6,600/230,300 =2.9%.

8 The RSE of the estimate of median duration of insufficient work is calculated by multiplying this number (2.9%) by the appropriate factor shown in paragraph 6 (in this case 2.1): 2.9 x 2.1 = 6.1%. The SE of this estimate of median duration of insufficient work is therefore 6.1% of 26, i.e. about 2 (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 24-28 weeks, and about 19 chances in 20 that it would have been within the range 22-30 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 382,600 females who usually work part time and want more hours, 143,400 or 37.5% had insufficient work for 52 weeks or more. The SE of 143,400 may be calculated by interpolation as 5,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 5,500/143,400 = 3.8%. The SE for 382,600 was calculated previously as 7,900, which converted to an RSE is 7,900/382,600 = 2.1%. 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 1.2 percentage points (=(37.5/100)x3.2). 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 36.3% and 38.7% and 19 chances in 20 that the proportion is within the range 35.1% to 39.9%.

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.

 T1 STANDARD ERRORS OF ESTIMATES AUST. NSW Vic. Qld SA WA Tas. NT ACT SE RSE Size of estimates (persons) no. no. no. no. no. no. no. no. no. % 100 90 100 180 160 160 110 110 130 80 80.0 200 160 170 260 220 220 140 150 160 140 70.0 300 220 230 310 260 260 170 180 180 190 63.3 500 330 320 390 320 340 210 220 220 270 54.0 700 420 400 460 370 390 240 250 240 350 50.0 1,000 530 500 540 420 460 280 290 270 440 44.0 1,500 690 630 650 500 550 330 340 310 580 38.7 2,000 820 750 740 570 620 370 380 350 700 35.0 2,500 950 850 800 600 700 400 400 400 800 32.0 3,000 1,050 950 900 650 750 450 450 400 900 30.0 3,500 1,150 1,000 950 700 800 450 450 450 1,000 28.6 4,000 1,250 1,100 1,000 750 850 500 500 450 1,050 26.3 5,000 1,400 1,200 1,100 850 900 550 550 500 1,200 24.0 7,000 1,650 1,400 1,300 950 1,050 600 600 550 1,450 20.7 10,000 1,950 1,700 1,500 1,100 1,200 700 700 650 1,750 17.5 15,000 2,350 2,000 1,800 1,300 1,450 800 800 750 2,150 14.3 20,000 2,700 2,250 2,050 1,450 1,600 900 900 850 2,450 12.3 30,000 3,150 2,650 2,450 1,700 1,850 1,050 1,050 1,000 2,950 9.8 40,000 3,500 2,900 2,750 1,900 2,100 1,200 1,150 1,100 3,350 8.4 50,000 3,800 3,150 3,000 2,100 2,250 1,300 1,250 1,250 3,700 7.4 100,000 4,750 4,000 4,000 2,750 2,900 1,700 1,600 1,650 4,850 4.9 150,000 5,350 4,600 4,750 3,250 3,350 1,950 1,850 2,000 5,600 3.7 200,000 5,900 5,150 5,300 3,650 3,750 2,150 2,050 2,300 6,250 3.1 300,000 6,900 6,100 6,250 4,300 4,300 2,500 . . 2,750 7,250 2.4 500,000 8,550 7,700 7,650 5,250 5,050 3,050 . . . . 8,800 1.8 1,000,000 11,950 10,800 10,050 6,850 6,350 . . . . . . 11,550 1.2 2,000,000 17,600 15,650 13,100 9,000 7,800 . . . . . . 15,250 0.8 5,000,000 31,550 26,900 18,450 . . . . . . . . . . 23,400 0.5 10,000,000 . . . . . . . . . . . . . . . . 40,950 0.4 . . 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. RSE OF 25% Mean duration of current period of insufficient work 11,800 10,800 8,300 4,600 5,600 2,000 1,300 2,100 12,000 Median duration of current period of insufficient work 18,900 14,300 12,200 6,700 8,000 3,200 2,800 2,900 16,300 Mean preferred number of extra hours 5,300 4,400 4,200 2,300 2,700 900 800 1,100 4,100 All other estimates 6,200 4,700 4,100 2,500 2,900 1,200 1,000 1,100 4,600 RSE OF 50% Mean duration of current period of insufficient work 2,800 2,800 2,400 1,400 1,700 600 400 700 2,500 Median duration of current period of insufficient work 5,000 3,900 3,500 2,100 2,400 1,000 900 1,000 3,700 Mean preferred number of extra hours 900 900 1,200 700 800 300 300 400 600 All other estimates 1,200 1,000 1,200 800 900 400 300 400 700 (a) Refers to the number of persons contributing to the estimate.