6310.0 - Employee Earnings, Benefits and Trade Union Membership, Australia, August 2011
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 27/04/2012
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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 5 shows the estimated number of part-time employees in main job was 3,046,100. Since the estimate is between 2,000,000 and 5,000,000, table T1 shows that the SE for Australia will lie between 17,050 and 28,450 and can be approximated by interpolation using the following general formula:

4 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 3,025,100 to 3,067,100 and about 19 chances in 20 that the value will fall within the range 3,004,100 to 3,088,100. 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 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 and median weekly earnings (see paragraph 20 of the Explanatory Notes) 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 weekly earnings: 0.9
• median weekly earnings: 1.0

7 The following is an example of the calculation of SEs where the use of a factor is required. Table 5 shows an estimate of 3,046,100 part-time employees in main job and table 4 shows mean weekly earnings for the same group as \$485. The SE of 3,046,100 was calculated previously as 21,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 21,000/3,046,100 = 0.7%.

8 The RSE of the estimate of mean weekly earnings is calculated by multiplying this number, 0.7%, by the appropriate factor shown in paragraph 6 (in this case 0.9): 0.7 x 0.9 = 0.63%. The approximate SE of this estimate of mean weekly earnings of part-time employees in main job is therefore 0.63% of \$485, that is \$3 (to the nearest dollar). Therefore, there are two chances in three that the mean weekly earnings for female part-time employees that would have been obtained if all dwellings had been included in the survey would have been within the range \$482 to \$488, and about 19 chances in 20 that it would have been within the range \$479 to \$491.

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

ALL OTHER ESTIMATES

10 All other estimates produced from population estimates smaller than the values in T2 have RSEs larger than 25% and should be used with caution. T2 also indicates the size of the population estimates with RSEs greater than 50% which are considered too unreliable for general use.

PROPORTIONS AND PERCENTAGES

11 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.

12 Considering the example from the previous page, of the 3,046,100 part-time employees in their main job, 835,800 or 27.4% were males. The SE and RSE of 3,046,100 were calculated previously as 21,000 and 0.7% respectively. The SE for 835,800 calculated by interpolation is 10,600 which converted to a RSE is 10,600/835,800 = 1.3%. Applying the above formula, the RSE of the proportion is:

13 The SE for the proportion, 27.4%, of male part-time employees, is 0.3 percentage points, calculated as (27.4/100)x1.1. There are about two chances in three that the proportion of male part-time employees, was between 27.1% and 27.7%, and 19 chances in 20 that the proportion is within the range 26.8% to 27.4%.

DIFFERENCES

14 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:

15 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. SE RSE 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 1000 760 710 680 450 550 310 260 330 610 61.0 1500 900 830 810 530 640 360 310 360 780 52.0 2000 1 010 930 910 590 710 390 340 390 920 46.0 2500 1 100 1 000 1 000 650 800 400 350 400 1 050 42.0 3000 1 200 1 100 1 050 700 850 450 400 450 1 150 38.3 3500 1 250 1 150 1 100 700 900 450 400 450 1 250 35.7 4000 1 300 1 200 1 200 750 900 500 450 450 1 350 33.8 5000 1 450 1 300 1 250 800 1 000 500 450 500 1 500 30.0 7000 1 650 1 500 1 450 900 1 150 600 550 600 1 700 24.3 10000 1 850 1 700 1 600 1 050 1 300 700 700 700 2 000 20.0 15000 2 150 1 950 1 800 1 200 1 500 850 1 000 850 2 350 15.7 20000 2 400 2 200 1 950 1 350 1 650 1 000 1 250 1 000 2 550 12.8 30000 2 800 2 550 2 250 1 550 1 900 1 250 1 750 1 250 2 900 9.7 40000 3 100 2 800 2 500 1 800 2 100 1 500 2 250 1 500 3 150 7.9 50000 3 350 3 050 2 750 2 000 2 300 1 700 2 650 1 650 3 400 6.8 100000 4 250 4 000 3 750 3 000 3 400 2 400 4 650 2 250 4 300 4.3 150000 5 000 4 850 4 600 3 850 4 450 2 850 6 350 2 500 5 000 3.3 200000 5 750 5 650 5 400 4 550 5 350 3 200 7 950 2 650 5 600 2.8 300000 7 250 7 250 6 850 5 550 6 750 3 700 10 850 2 800 6 650 2.2 500000 10 150 10 050 9 250 7 000 8 600 4 250 . . 2 800 8 350 1.7 1000000 15 100 15 250 13 200 8 900 10 950 4 850 . . . . 11 750 1.2 2000000 20 350 22 550 17 700 10 600 12 700 . . . . . . 17 050 0.9 5000000 25 900 36 100 23 900 11 900 13 250 . . . . . . 28 450 0.6 10000000 27 750 49 750 27 950 . . . . . . . . . . 37 950 0.4 . . not applicable

 T2 POPULATION LEVELS AT WHICH ESTIMATES HAVE RSES OF 25% AND 50% NSW Vic. Qld SA WA Tas. NT ACT Aust. no. no. no. no. no. no. no. no. no. 25% RSE Mean weekly earnings 5 600 5 000 4 000 1 900 3 000 1 100 500 1 300 5 900 Median weekly earnings 6 300 5 500 5 100 2 500 3 800 1 400 700 1 500 7 200 Relative standard error of all other estimates 6 300 5 400 5 100 2 600 3 500 1 400 1 100 1 400 6 800 50% RSE Mean weekly earnings 1 800 1 600 1 300 600 1 000 300 100 500 1 400 Median weekly earnings 2 000 1 800 1 700 800 1 200 400 200 600 1 800 Relative standard error of all other estimates 2 000 1 800 1 700 800 1 200 500 300 600 1 600