6220.0 - Persons Not in the Labour Force, Australia, Sep 2005
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 17/03/2006
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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 4 shows that the estimated number of people in Australia who were discouraged job seekers was 63,100. Since this estimate is between 50,000 and 100,000, table T1 shows the SE for Australia will be between 3,750 and 4,800, 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 in the range 59,100 to 67,100, and about 19 chances in 20 that the value will fall within the range 55,100 to 71,100. 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.

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 example above, of the 63,100 people who were discouraged job seekers, 25,000 or 39.6% were males. The SE of 25,000 may be calculated by interpolation as 2,800. To convert this to an RSE we express the SE as a percentage of the estimate, or 2,800/25,000 = 11.2%. The SE for 63,000 was calculated previously as 4,000, which converted to an RSE is 4,000/63,100 = 6.3%. Applying the above formula, the RSE of the proportion is

8 Therefore, the SE for the proportion of males who were discouraged job seekers is 3.7 percentage points (=(39.6/100)x9.3). Therefore, there are about two chances in three that the proportion of males who were discouraged job seekers is between 35.9% and 43.3% and 19 chances in 20 that the proportion is within the range 32.2% to 47.0%.

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 subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.

11 SEs contained in table T1 are applicable to all estimates from this survey.

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. % 100 120 170 160 100 120 100 140 90 120 120.0 200 210 260 240 170 190 150 180 140 200 100.0 300 280 330 300 220 240 190 220 180 260 86.7 500 400 430 400 300 330 240 280 230 370 74.0 700 500 520 480 360 400 280 330 270 450 64.3 1000 630 620 580 361 480 320 400 320 560 56.0 1500 800 750 710 530 590 380 490 370 710 47.3 2000 930 870 820 600 670 420 570 410 830 41.5 2500 1 050 950 900 650 750 450 650 450 950 38.0 3000 1 150 1 050 1 000 700 800 450 700 450 1 050 35.0 3500 1 250 1 100 1 050 750 850 500 750 500 1 150 32.9 4000 1 350 1 200 1 150 800 900 500 850 500 1 200 30.0 5000 1 500 1 300 1 250 850 1 000 550 950 550 1 350 27.0 7000 1 700 1 500 1 450 950 1 100 650 1 200 650 1 600 22.9 10000 2 000 1 750 1 650 1 150 1 250 850 1 650 800 1 900 19.0 15000 2 350 2 050 1 950 1 350 1 450 1 050 2 300 1 050 2 300 15.3 20000 2 600 2 250 2 150 1 550 1 650 1 300 2 950 1 250 2 600 13.0 30000 3 000 2 650 2 500 1 850 2 100 1 600 4 050 1 550 3 050 10.2 40000 3 350 2 900 2 800 2 150 2 550 1 850 5 000 1 750 3 450 8.6 50000 3 700 3 200 3 100 2 450 2 900 2 100 5 900 1 900 3 750 7.5 100000 5 150 4 650 4 700 3 550 4 300 2 950 9 500 2 350 4 800 4.8 150000 6 400 5 950 6 150 4 400 5 350 3 500 12 350 2 500 5 600 3.7 200000 7 550 7 050 7 300 5 050 6 150 3 900 . . . . 6 350 3.2 300000 9 700 8 800 9 050 6 000 7 450 4 550 . . . . 7 800 2.6 500000 13 250 11 500 11 300 7 150 9 300 5 350 . . . . 10 550 2.1 1000000 18 800 16 000 14 000 8 450 12 150 . . . . . . 16 600 1.7 2000000 24 450 21 600 15 650 9 300 15 250 . . . . . . 24 250 1.2 5000000 30 400 30 450 15 550 . . . . . . . . . . 35 250 0.7 10000000 32 450 37 950 . . . . . . . . . . . . 42 450 0.4 15000000 . . . . . . . . . . . . . . . . 45 550 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. RSE of 25% 6 800 5 400 5 000 2 700 3 400 1 500 2 600 1 500 5 900 RSE of 50% 1 700 1 500 1 400 700 900 500 600 400 1 300 (a) Refers to the number of people contributing to the estimate.