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6310.0 - Employee Earnings, Benefits and Trade Union Membership, Australia, August 2011 Quality Declaration 
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:

Equation: Calculation of standard errors

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:

Diagram: CALCULATION OF STANDARD ERROR

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.

Equation: Calculation of relative standard errors of proportions and percentages

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:

Equation: Example calculation of relative standard errors of proportions

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:

Equation: Calculation of differences between estimates

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




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