6222.0 - Job Search Experience, Australia, Jul 2007
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 07/12/2007
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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 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 unemployed women in Australia who were looking for full-time work was 131,400. Since this estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 4,000 and 4,700 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 127,000 to 135,800 and about 19 chances in 20 that the value will fall within the range 122,600 to 140,200. 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 less than 25%.

MEANS AND MEDIANS

6 The RSEs of estimates of mean duration of unemployment and median duration of unemployment 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 unemployment: 1.6
• median duration of unemployment: 2.5

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 median duration of unemployment for unemployed women in Australia was 12 weeks and shows that the number of unemployed women was estimated as 210,100. The SE of 210,100 can be calculated from table T1 (by interpolation) as 5,400. To convert this to an RSE we express the SE as a percentage of the estimate or 5,400/210,100 =2.6%.

8 The RSE of the estimate of median duration of unemployment for unemployed women is calculated by multiplying this number (2.6%) by the appropriate factor shown in the previous paragraph (in this case 2.5): 2.6 x 2.5 = 6.5%. The SE of this estimate of median duration of unemployment for unemployed women is therefore 6.5% of 12, i.e. almost one week. Therefore, there are two chances in three that the median duration of unemployment for women that would have been obtained if all dwellings had been included in the survey would have been within the range 11 weeks to 13 weeks, and about 19 chances in 20 that it would have been within the range 10 weeks to 14 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 the previous page, of the 131,400 unemployed women who were looking for full-time work, 24,900 or 18.9% had been unemployed for one year or more. The SE of 24,900 may be calculated by interpolation as 2,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 2,500/24,900 = 10.0%. The SE for 131,400 was calculated previously as 4,400, which converted to an RSE is 4,400/131,400 = 3.3%. Applying the above formula, the RSE of the proportion is:

11 Therefore, the SE for the proportion of unemployed women looking for full-time work who had been unemployed for one year or more is 1.8 percentage points (=(18.9/100)x9.4). Therefore, there are about two chances in three that the proportion of unemployed women looking for full-time work who have been unemployed for one year or more is between 17.1% and 20.7% and 19 chances in 20 that the proportion is within the range 15.3% to 22.5%.

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 NSW Vic. Qld SA WA Tas. NT ACT Aust. Size of estimate (persons) no. no. no. no. no. no. no. no. no. % 100 290 250 250 150 160 100 90 140 100 100.0 200 380 330 330 210 220 140 150 180 180 90.0 300 440 390 390 250 260 180 190 200 240 80.0 500 540 470 470 300 330 220 250 230 350 70.0 700 620 540 540 350 380 260 300 260 430 61.4 1,000 710 620 610 400 440 300 350 280 540 54.0 1,500 830 730 710 470 520 340 410 320 690 46.0 2,000 920 810 790 530 590 370 460 340 820 41.0 2,500 1 000 900 850 550 650 400 500 350 900 36.0 3,000 1 100 950 900 600 700 400 500 400 1 000 33.3 3,500 1 150 1 000 950 650 750 450 550 400 1 100 31.4 4,000 1 200 1 050 1 000 700 750 450 600 400 1 200 30.0 5,000 1 300 1 150 1 100 750 850 500 650 450 1 300 26.0 7,000 1 500 1 300 1 250 850 950 550 750 500 1 550 22.1 10,000 1 700 1 500 1 400 950 1 100 650 950 600 1 800 18.0 15,000 2 000 1 750 1 600 1 100 1 250 800 1 300 750 2 100 14.0 20,000 2 200 1 950 1 800 1 200 1 400 950 1 600 850 2 300 11.5 30,000 2 600 2 300 2 050 1 450 1 600 1 250 2 150 1 100 2 650 8.8 40,000 2 850 2 550 2 250 1 700 1 750 1 500 2 750 1 350 2 900 7.3 50,000 3 100 2 800 2 450 1 900 1 950 1 750 3 250 1 500 3 100 6.2 100,000 4 050 3 600 3 400 2 900 3 050 2 600 5 850 2 050 4 000 4.0 150,000 4 800 4 350 4 250 3 700 4 100 3 200 8 300 2 350 4 700 3.1 200,000 5 550 5 200 5 100 4 400 4 950 3 650 10 700 2 450 5 300 2.7 300,000 7 100 6 800 6 800 5 450 6 250 4 300 15 450 2 550 6 350 2.1 500,000 9 950 9 300 9 550 6 900 7 950 5 150 . . 2 550 8 100 1.6 1,000,000 14 950 13 700 13 500 9 000 10 050 6 250 . . . . 11 600 1.2 2,000,000 21 350 19 350 16 550 11 000 11 400 . . . . . . 17 150 0.9 5,000,000 31 500 28 550 17 350 13 000 11 500 . . . . . . 29 250 0.6 10,000,000 39 750 36 450 15 250 . . . . . . . . . . 39 200 0.4 15,000,000 . . . . . . . . . . . . . . . . 44 050 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 unemployment 9 600 8 000 7 000 3 800 4 400 2 000 1 700 1 900 12 100 Median duration of unemployment 25 200 21 900 18 900 11 400 13 400 6 900 5 800 4 200 24 400 All other estimates 5 400 4 400 4 100 2 200 2 600 1 300 1 800 1 200 5 500 50% RSE Mean duration of unemployment 3 100 2 600 2 400 1 300 1 400 700 500 700 3 400 Median duration of unemployment 8 300 7 100 6 600 4 000 4 500 2 500 1 900 1 600 8 000 All other estimates 1 800 1 400 1 400 700 800 400 500 400 1 200 (a) Refers to the number of people contributing to the estimate.