# Australian Bureau of StatisticsCelebrating the International Year of Statistics 2013

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 6222.0 - Job Search Experience, Australia, July 2012  Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 16/01/2013
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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 is as follows. Table 4 shows that 166,000 unemployed females were looking for full-time work. Since this estimate is between 150,000 and 200,000, table T1 shows that the SE for Australia will lie between 5,000 and 5,600 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 160,800 to 171,200 and about 19 chances in 20 that the value will fall within the range 155,600 to 176,400. 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 T2 presents the levels at which estimates have RSEs of 25% and 50%.

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 for Australian estimates:
• 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 females in Australia was 13 weeks and shows that the number of unemployed females was estimated as 271,700. The SE of 271,700 can be calculated from table T1 (by interpolation) as 6,400. To convert this to an RSE we express the SE as a percentage of the estimate or 6,400/271,700 =2.4%.

8 The RSE of the estimate of median duration of unemployment for unemployed females is calculated by multiplying this number (2.4%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.4 x 2.5 = 6%. The SE of this estimate of median duration of unemployment for unemployed females is therefore 6% of 13 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 12 to 14 weeks and about 19 chances in 20 that it would have been within the range 11 weeks to 15 weeks.

9 Table T2 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 29,000 persons will have an RSE of at least 25%, and an estimate of median duration of unemployment for Australia based on less than 10,000 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 6,800 for the Australian total will have an RSE of at least 25% and an estimate of less than 1,600 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 the previous page, of the 166,000 unemployed females who were looking for full-time work, 31,700 or 19.1% had been unemployed for one year or more. The SE of 31,700 may be calculated by interpolation as 2,900. To convert this to an RSE we express the SE as a percentage of the estimate, or 2,900/31,700 = 9.1%. The SE for 166,000 was calculated previously as 5,200, which converted to an RSE is 5,200/166,000 = 3.1%. 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 1.6 percentage points (=19.1/100)x8.6). 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 17.4% and 20.6% and 19 chances in 20 that the proportion is within the range 15.8% to 22.2%.

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 NSW Vic. Qld. SA WA Tas. NT ACT Aust. Size of estimate (persons) No. No. No. No. No. No. No. No. No. % 100 290 290 220 180 220 110 80 100 110 110.0 200 400 380 320 240 290 160 120 170 190 95.0 300 470 440 390 280 340 190 150 210 260 86.7 500 580 540 500 340 420 240 190 270 380 76.0 700 660 620 580 390 480 270 230 300 480 68.6 1,000 760 710 680 450 550 310 270 330 610 61.0 1,500 900 830 810 530 640 360 310 360 780 52.0 2,000 1 010 930 910 590 710 390 340 390 920 46.0 2,500 1 100 1 000 1 000 650 800 400 350 400 1 050 42.0 3,000 1 200 1 100 1 050 700 850 450 400 450 1 150 38.3 3,500 1 250 1 150 1 100 700 900 450 400 450 1 250 35.7 4,000 1 300 1 200 1 200 750 900 500 450 450 1 350 33.8 5,000 1 450 1 300 1 250 800 1 000 500 500 500 1 500 30.0 7,000 1 650 1 500 1 450 900 1 150 600 550 600 1 700 24.3 10,000 1 850 1 700 1 600 1 050 1 300 700 700 700 2 000 20.0 15,000 2 150 1 950 1 800 1 200 1 500 850 1 000 850 2 350 15.7 20,000 2 400 2 200 1 950 1 350 1 650 1 000 1 250 1 000 2 550 12.8 30,000 2 800 2 550 2 250 1 550 1 900 1 250 1 800 1 250 2 900 9.7 40,000 3 100 2 800 2 500 1 800 2 100 1 500 2 250 1 500 3 150 7.9 50,000 3 350 3 050 2 750 2 000 2 300 1 700 2 700 1 650 3 400 6.8 100,000 4 250 4 000 3 750 3 000 3 400 2 400 4 650 2 250 4 300 4.3 150,000 5 000 4 850 4 600 3 850 4 450 2 850 6 400 2 500 5 000 3.3 200,000 5 750 5 650 5 400 4 550 5 350 3 200 8 000 2 650 5 600 2.8 300,000 7 250 7 250 6 850 5 550 6 750 3 700 10 900 2 800 6 650 2.2 500,000 10 150 10 050 9 250 7 000 8 600 4 250 . . 2 800 8 350 1.7 1,000,000 15 100 15 250 13 200 8 900 10 950 4 850 . . . . 11 750 1.2 2,000,000 20 350 22 550 17 700 10 600 12 700 . . . . . . 17 050 0.9 . . 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 11 200 9 500 8 600 4 400 6 200 2 300 1 600 2 400 14 700 Median duration of unemployment 29 800 25 700 22 600 12 100 18 100 8 100 5 000 6 700 29 000 All other estimates 6 300 5 400 5 100 2 600 3 500 1 400 1 100 1 400 6 800 50% RSE Mean duration of unemployment 3 700 3 100 3 000 1 500 2 100 800 500 1 000 4 400 Median duration of unemployment 9 900 8 600 8 400 4 100 6 200 2 800 1 700 2 400 10 000 All other estimates 2 000 1 800 1 700 800 1 200 500 300 600 1 600 (a) Refers to the number of persons contributing to the estimate.