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6359.0 - Forms of Employment, Australia, November 2012 Quality Declaration 
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 19/04/2013   
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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; 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 2 shows that the estimated number of persons in Australia who were other business operators was 1,036,900. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows the SE for Australia will be between 11,750 and 17,050 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 in the range 1,025,000 to 1,048,800, and about 19 chances in 20 that the value will fall within the range 1,013,100 to 1,060,700. This example is illustrated in the diagram below:

Diagram: CALCULATION OF STANDARD ERRORS

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 that 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:

Equation: Calculation of relative standard errors of proportions and percentages

7 Considering the example above, of the 1,036,900 persons who were other business operators, 407,800 or 39.3% were female. The SE of 407,800, may be calculated by interpolation as 7,500. To convert this to an RSE we express the SE as a percentage of the estimate, or 7,500/407,800 = 1.8%. The SE for 1,036,900 was calculated previously as 11,900, which converted to an RSE is 11,900/1,036,900 = 1.1%. Applying the above formulae, the RSE of the proportion is:

Equation: Example calculation of relative standard errors of proportions

8 The SE for the proportion of females who were other business operators, is 0.6 percentage points, calculated as (39.3/100)x1.4. There are about two chances in three that the proportion of female business operators is between 38.7% and 39.9% and 19 chances in 20 that the proportion is within the range 38.1% to 40.4%.

9 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 that would produce all other estimates with RSEs greater than 50% are considered too unreliable for general use.


DIFFERENCES

10 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 appropriate SE of the difference between two estimates (x-y) may be calculated by the following formulae:

Equation: Calculation of differences between estimates

11 While this formulae 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
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
15000000
. .
. .
. .
. .
. .
. .
. .
. .
42 850
0.3

. . 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.

Relative Standard Error (RSE) of 25%
6 300
5 400
5 100
2 600
3 500
1 400
1 100
1 400
6 800
Relative Standard Error (RSE) of 50%
2 000
1 800
1 700
800
1 200
500
300
600
1 600




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