6209.0 - Labour Mobility, Australia, February 2013
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 21/08/2013  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 11 shows that 366,600 people involuntarily ceased their last job during the year and their duration in that job was less than 12 months. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,150 and 9,000 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 358,800 to 374,400 and about 19 chances in 20 that the value will fall within the range 351,000 to 382,200. 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%.

PROPORTIONS AND PERCENTAGES

6 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.

7 Considering the previous example from Table 11, of the 366,600 people who ceased their last job involuntarily during the year ending February 2013, and their duration of last job was less than 12 months, 210,900 or 57.5% gave their reason as 'Job was temporary or seasonal'. The SE of 210,900 may be calculated by interpolation as 6,200. To convert this to an RSE we express the SE as a percentage of the estimate, or 6,200/210,900 = 2.9%. The SE for 366,600 was calculated previously as 7,800, which converted to an RSE 7,800/366,600=2.1%. Applying the above formula, the RSE of the proportion is:

8 Therefore, the SE for the proportion of people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months is 1.2 percentage points (=(57.5/100)x2.0). Therefore, there are about two chances in three that the proportion of people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months or more was between 56.3% and 58.7% and 19 chances in 20 that the proportion is within the range 55.1% to 59.9%.

DIFFERENCES

9 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:

10 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, 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 SE RSE Size of Estimate (persons) no. no. no. no. no. no. no. no. no. % 100 320 310 240 190 230 120 90 110 120 120.0 200 430 410 340 260 310 170 130 180 210 105.0 300 510 480 420 300 370 210 160 230 290 96.7 500 620 580 540 370 450 260 210 290 410 82.0 700 720 670 630 420 510 290 250 330 520 74.3 1,000 830 770 740 490 590 340 290 360 660 66.0 1,500 970 900 870 570 690 390 340 390 840 56.0 2,000 1 090 1 000 980 630 770 430 380 420 990 49.5 2,500 1 200 1 100 1 050 700 850 450 400 450 1 100 44.0 3,000 1 250 1 150 1 150 750 900 500 450 450 1 250 41.7 3,500 1 350 1 250 1 200 800 950 500 450 500 1 350 38.6 4,000 1 400 1 300 1 250 800 1 000 550 450 500 1 450 36.3 5,000 1 550 1 400 1 400 900 1 100 550 500 550 1 600 32.0 7,000 1 750 1 600 1 550 1 000 1 250 650 600 650 1 850 26.4 10,000 2 000 1 850 1 750 1 150 1 400 750 800 750 2 150 21.5 15,000 2 350 2 150 1 950 1 300 1 600 900 1 100 900 2 500 16.7 20,000 2 600 2 350 2 100 1 450 1 800 1 050 1 400 1 050 2 750 13.8 30,000 3 000 2 750 2 450 1 700 2 050 1 350 1 950 1 350 3 150 10.5 40,000 3 350 3 050 2 700 1 950 2 250 1 600 2 450 1 600 3 400 8.5 50,000 3 600 3 300 2 950 2 150 2 500 1 800 2 950 1 800 3 650 7.3 100,000 4 600 4 300 4 050 3 250 3 650 2 600 5 100 2 400 4 650 4.7 150,000 5 400 5 200 4 950 4 150 4 800 3 100 7 000 2 700 5 400 3.6 200,000 6 250 6 100 5 800 4 900 5 800 3 450 8 750 2 850 6 050 3.0 300,000 7 850 7 800 7 400 6 000 7 300 4 000 11 950 3 000 7 150 2.4 500,000 11 000 10 850 9 950 7 550 9 300 4 600 . . 3 000 9 000 1.8 1,000,000 16 300 16 500 14 250 9 600 11 850 5 250 . . . . 12 700 1.3 2,000,000 21 950 24 350 19 150 11 450 13 700 . . . . . . 18 400 0.9 5,000,000 28 000 39 000 25 850 12 900 14 300 . . . . . . 30 700 0.6 10,000,000 30 000 53 750 30 200 . . . . . . . . . . 41 000 0.4 15,000,000 . . . . . . . . . . . . . . . . 46 250 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. Relative Standard Error of 25% 7 100 6 100 5 800 2 900 4 000 1 600 1 300 1 600 7 800 Relative Standard Error of 50% 2 300 2 000 1 900 1 000 1 300 500 400 600 2 000 (a) Refers to the number of people contributing to the estimate