6206.0 - Labour Force Experience, Australia, Feb 2007
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 17/08/2007
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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 ERRORS

3 An example of the calculation and the use of SEs in relation to estimates of people is as follows. Table 3 shows that the estimated number of people aged 15 years and over in the labour force for part of the year was 3,490,700. Since this estimate is between 2,000,000 and 5,000,000, table T1 shows that the SE for Australia will lie between 17,150 and 29,250 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 3,467,500 to 3,513,900, and about 19 chances in 20 that the value will fall within the range 3,444,300 to 3,537,100. 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. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less.

MEANS AND MEDIANS

6 The RSEs of estimates of mean and median duration of time spent looking for work are obtained by first finding the RSE of the estimate of the total number of people contributing to the estimate (see table T1) and then multiplying the resulting number by the following factors:

• mean duration of time spent looking for work (weeks): 0.76
• median duration of time spent looking for work (weeks): 1.63

7 The following is an example of the calculation of SEs where the use of a factor is required. Table 11 shows that the estimated number of males aged 15 years and over looking for work at some time during the year was 774,700 with a median duration of time spent looking for work of 10 weeks. The SE of 774,700 can be calculated from table T1 (by interpolation) as 10,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 10,000/774,700 = 1.3%.

8 The RSE of the estimate of median duration of time spent looking for work for males aged 15 years and over is calculated by multiplying this number (1.3%) by the appropriate factor shown in the previous paragraph (in this case 1.63): 1.3 x 1.63 = 2.1%. The approximate SE of this estimate of median duration of time spent looking for work for males aged 15 years and over is therefore 2.1% of 10 weeks, i.e. about 0.2 weeks. Therefore, there are two chances in three that the median duration of time spent looking for work for males aged 15 years and over that would have been obtained if all dwellings had been included in the survey would have been within the range 9.8 weeks to 10.2 weeks, and about 19 chances in 20 that it would have been within the range 9.6 weeks to 10.4 weeks.

9 Estimates of means and medians produced from population estimates smaller than the values provided in table T2 have RSEs larger than 25% and should be used with caution. Table T2 also indicates the size of population estimates that would produce means and medians with RSEs greater than 50%, which are considered too unreliable for general use.

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 the previous page, of the 3,490,700 people aged 15 years and over in the labour force for part of the year, 515,000, or 14.8%, looked for work at some time during the year. The SE of 515,000 may be calculated by interpolation as 8,200. To convert this to an RSE we express the SE as a percentage of the estimate, or 8,200/515,000 = 1.6%. The SE for 3,490,700 was calculated previously as 23,200, which converted to an RSE is 23,200/3,490,700 = 0.7%. Applying the above formula, the RSE of the proportion is:

12 Therefore, the SE for the proportion of people aged 15 years and over who looked for work at some time during the year is 0.2 percentage points (=(14.8/100)x1.4). Therefore, there are about two chances in three that the proportion of people aged 15 years and over who looked for work at some time during the year is between 14.6% and 15%, and 19 chances in 20 that the proportion is within the range 14.4% to 15.2%.

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 AUST. NSW Vic. Qld SA WA Tas. NT ACT SE RSE Size of estimate (persons) no. no. no. no. no. no. no. no. no. % 100 290 250 250 150 160 100 90 140 100 100.0 200 380 330 330 210 220 140 140 180 180 90.0 300 440 390 390 250 260 180 170 200 240 80.0 500 540 470 470 300 330 220 230 230 350 70.0 700 620 540 540 350 380 260 270 260 430 61.4 1000 710 620 610 400 440 300 320 280 540 54.0 1500 830 730 710 470 520 340 380 320 690 46.0 2000 920 810 790 530 590 370 420 340 820 41.0 2500 1 000 900 850 550 650 400 450 350 900 36.0 3000 1 100 950 900 600 700 400 500 400 1 000 33.3 3500 1 150 1 000 950 650 750 450 500 400 1 100 31.4 4000 1 200 1 050 1 000 700 750 450 500 400 1 200 30.0 5000 1 300 1 150 1 100 750 850 500 550 450 1 300 26.0 7000 1 500 1 300 1 250 850 950 550 700 500 1 550 22.1 10000 1 700 1 500 1 400 950 1 100 650 850 600 1 800 18.0 15000 2 000 1 750 1 600 1 100 1 250 800 1 150 750 2 100 14.0 20000 2 200 1 950 1 800 1 200 1 400 950 1 450 850 2 300 11.5 30000 2 600 2 300 2 050 1 450 1 600 1 250 1 950 1 100 2 650 8.8 40000 2 850 2 550 2 250 1 700 1 750 1 500 2 500 1 350 2 900 7.3 50000 3 100 2 800 2 450 1 900 1 950 1 750 2 950 1 500 3 100 6.2 100000 4 050 3 600 3 400 2 900 3 050 2 600 5 300 2 050 4 000 4.0 150000 4 800 4 350 4 250 3 700 4 100 3 200 7 500 2 350 4 700 3.1 200000 5 550 5 200 5 100 4 400 4 950 3 650 9 700 2 450 5 300 2.7 300000 7 100 6 800 6 800 5 450 6 250 4 300 14 050 2 550 6 350 2.1 500000 9 950 9 300 9 550 6 900 7 950 5 150 . . . . 8 100 1.6 1000000 14 950 13 700 13 500 9 000 10 050 6 250 . . . . 11 600 1.2 2000000 21 350 19 350 16 550 11 000 11 400 . . . . . . 17 150 0.9 5000000 31 500 28 550 17 350 13 000 11 500 . . . . . . 29 250 0.6 10000000 39 750 36 450 15 250 . . . . . . . . . . 39 200 0.4 15000000 . . . . . . . . . . . . . . . . 44 050 0.3 20000000 . . . . . . . . . . . . . . . . 46 700 0.2 . . 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 time spent looking for work 3 500 2 800 2 700 1 400 1 700 800 900 800 3 200 Median duration of time spent looking for work 11 900 9 800 8 700 4 700 5 800 2 700 3 100 2 400 12 800 All other estimates 5 400 4 400 4 100 2 200 2 600 1 300 1 500 1 200 5 500 50% RSE Mean duration of time spent looking for work 1 100 900 900 400 500 200 200 300 600 Median duration of time spent looking for work 3 900 3 200 3 000 1 600 1 900 900 1 100 900 3 700 All other estimates 1 800 1 400 1 400 700 800 400 400 400 1 200 (a) Refers to the number of people contributing to the estimate.