6310.0 - Employee Earnings, Benefits and Trade Union Membership, Australia, Aug 2005
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 28/03/2006
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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 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 female part-time employees in main job was 1,868,900. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows that the SE for Australia will lie between 11,600 and 17,150 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 1,852,500 to 1,885,300 and about 19 chances in 20 that the value will fall within the range 1,836,100 to 1,901,700. 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 and median weekly earnings (see paragraphs 18 and 19 of the Explanatory Notes) are obtained by first finding the RSE of the estimate of the total number of persons contributing to the estimate (see table T1) and then multiplying the resulting number by the following factors:

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 1,868,900 female part-time employees in main job and table 4 shows mean weekly earnings for the same group as \$374. The SE of 1,868,900 was calculated previously as 16,400. To convert this to an RSE we express the SE as a percentage of the estimate, or 16,400/1,868,700 = 0.9%.

8 The RSE of the estimate of mean weekly earnings is calculated by multiplying this number (0.9%) by the appropriate factor shown in paragraph 6 (in this case 0.9): 0.9 x 0.9 =0.8%. The approximate SE of this estimate of mean weekly earnings of female part-time employees in main job is therefore 0.8% of \$374, that is about \$2.99. 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 \$371.01 to \$376.99, and about 19 chances in 20 that it would have been within the range \$368.02 to \$379.98.

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, the 1,868,900 females who were part-time employees in their main job represent 47% of the 3,979,400 female employees. The SE and RSE of 1,868,900 were calculated previously as 16,400 and 0.9% respectively. The SE for 3,979,400 calculated by interpolation is 25,100, which converted to a RSE is 25,100/3,979,400 =0.6%. Applying the above formula, the RSE of the proportion is:

11 Therefore, the SE for the proportion (47%) is 0.2 percentage points (=(47/100)x 0.5). Therefore, there are about two chances in three that the proportion of female part-time employees was between 46.8% and 47.2%, and 19 chances in 20 that the proportion is within the range 46.6% to 47.4%.

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 AUST. NSW Vic. Qld SA WA Tas. NT ACT SE RSE Size of estimate (persons) no. no. no. no. no. no. no. no. no. % 100 290 250 250 150 160 100 100 140 100 100 200 380 330 330 210 220 140 150 180 180 90 300 440 390 390 250 260 180 200 200 240 80 500 540 470 470 300 330 220 260 230 350 70 700 620 540 540 350 380 260 310 260 430 61 1,000 710 620 610 400 440 300 360 280 540 54 1,500 830 730 710 470 520 340 430 320 690 46 2,000 920 810 790 530 590 370 480 340 820 41 2,500 1 000 900 850 550 650 400 500 350 900 36 3,000 1 100 950 900 600 700 400 550 400 1 000 33 3,500 1 150 1 000 950 650 750 450 550 400 1 100 31 4,000 1 200 1 050 1 000 700 750 450 600 400 1 200 30 5,000 1 300 1 150 1 100 750 850 500 650 450 1 300 26 7,000 1 500 1 300 1 250 850 950 550 800 500 1 550 22 10,000 1 700 1 500 1 400 950 1 100 650 1 000 600 1 800 18 15,000 2 000 1 750 1 600 1 100 1 250 800 1 350 750 2 100 14 20,000 2 200 1 950 1 800 1 200 1 400 950 1 650 850 2 300 12 30,000 2 600 2 300 2 050 1 450 1 600 1 250 2 250 1 100 2 650 9 40,000 2 850 2 550 2 250 1 700 1 750 1 500 2 850 1 350 2 900 7 50,000 3 100 2 800 2 450 1 900 1 950 1 750 3 400 1 500 3 100 6 100,000 4 050 3 600 3 400 2 900 3 050 2 600 6 050 2 050 4 000 4 150,000 4 800 4 350 4 250 3 700 4 100 3 200 8 600 2 350 4 700 3 200,000 5 550 5 200 5 100 4 400 4 950 3 650 11 100 2 450 5 300 3 300,000 7 100 6 800 6 800 5 450 6 250 4 300 16 050 2 550 6 350 2 500,000 9 950 9 300 9 550 6 900 7 950 5 150 . . 2 550 8 100 2 1,000,000 14 950 13 700 13 500 9 000 10 050 6 250 . . . . 11 600 1 2,000,000 21 350 19 350 16 550 11 000 11 400 . . . . . . 17 150 1 5,000,000 31 500 28 550 17 350 13 000 11 500 . . . . . . 29 250 1 10,000,000 39 750 36 450 15 250 . . . . . . . . . . 39 200 - 15,000,000 . . . . . . . . . . . . . . . . 44 050 - . . not applicable - nil or rounded to zero (including null cells)

 T2 LEVELS AT WHICH ESTIMATES HAVE RSE'S 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 weekly earnings 4 900 4 100 3 200 1 600 2 200 1 000 800 1 000 4 800 Median weekly earnings 5 500 4 500 4 100 2 100 2 800 1 300 1 200 1 200 5 900 All other estimates 5 400 4 400 4 100 2 200 2 600 1 300 1 900 1 200 5 500 50% RSE Mean weekly earnings 1 600 1 300 1 100 500 700 300 200 400 1 000 Median weekly earnings 1 800 1 500 1 400 700 900 400 300 500 1 400 All other estimates 1 800 1 400 1 400 700 800 400 500 400 1 200 (a) Refers to the number of persons contributing to the estimate.