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6359.0 - Forms of Employment, Australia, November 2013 Quality Declaration 
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 07/05/2014  Final
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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 1,013,500. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows the SE for Australia will be between 13,600 and 19.750 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 999,800 to 1,013,500, and about 19 chances in 20 that the value will fall within the range 986,100 to 1,040,900. 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 1,013,500 persons who were other business operators, 404,000 or 39.9% were female. The SE of 404,000, may be calculated by interpolation as 8,700. To convert this to an RSE we express the SE as a percentage of the estimate, or 8,700/404,000 = 2.2%. The SE for 1,013,500 was calculated previously as 13,700, which converted to an RSE is 13,700/1,013,500 = 1.4%. 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 (39.9/100)x1.7. There are about two chances in three that the proportion of female business operators is between 39.2% and 40.6% and 19 chances in 20 that the proportion is within the range 38.5% to 41.3%.

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
Size of estimate
no.
no.
no.
no.
no.
no.
no.
no.
no.
%

100
360
250
250
190
240
110
50
120
130
130.0
200
480
320
360
260
320
150
80
200
220
110.0
300
570
380
440
310
380
190
100
250
310
103.3
500
700
470
560
380
460
230
120
320
440
88.0
700
810
530
650
430
530
270
140
360
560
80.0
1000
930
610
760
490
610
310
170
400
700
70.0
1500
1 100
710
900
580
710
350
200
430
900
60.0
2000
1 230
800
1 010
640
790
390
220
460
1 070
53.5
2500
1 350
850
1 100
700
850
400
250
500
1 200
48.0
3000
1 450
950
1 200
750
900
450
250
500
1 350
45.0
3500
1 550
1 000
1 250
800
1 000
450
250
550
1 450
41.4
4000
1 600
1 050
1 300
850
1 050
500
250
550
1 550
38.8
5000
1 750
1 150
1 400
900
1 100
500
300
600
1 700
34.0
7000
2 000
1 300
1 600
1 000
1 250
600
350
700
2 000
28.6
10000
2 300
1 450
1 800
1 150
1 450
700
450
800
2 300
23.0
15000
2 650
1 700
2 000
1 300
1 650
850
650
1 000
2 700
18.0
20000
2 950
1 900
2 200
1 450
1 850
950
800
1 150
3 000
15.0
30000
3 400
2 200
2 500
1 700
2 100
1 250
1 150
1 500
3 350
11.2
40000
3 800
2 400
2 800
1 950
2 350
1 450
1 450
1 750
3 650
9.1
50000
4 100
2 600
3 050
2 200
2 550
1 650
1 700
2 000
3 950
7.9
100000
5 200
3 450
4 200
3 300
3 750
2 400
2 950
2 650
4 950
5.0
150000
6 100
4 150
5 150
4 250
4 950
2 850
4 050
3 000
5 800
3.9
200000
7 050
4 850
6 000
4 950
5 950
3 150
5 100
3 150
6 500
3.3
300000
8 850
6 250
7 650
6 100
7 500
3 650
6 950
3 300
7 700
2.6
500000
12 400
8 650
10 300
7 650
9 550
4 200
. .
3 300
9 650
1.9
1000000
18 400
13 150
14 700
9 750
12 150
4 800
. .
. .
13 600
1.4
2000000
24 800
19 450
19 800
11 600
14 100
. .
. .
. .
19 750
1.0
5000000
31 600
31 100
26 700
13 050
14 700
. .
. .
. .
32 950
0.7
10000000
33 850
42 900
31 200
. .
. .
. .
. .
. .
44 000
0.4
15000000
. .
. .
. .
. .
. .
. .
. .
. .
49 600
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%
8 600
4 200
6 100
3 000
4 200
1 400
500
1 800
8 800
Relative Standard Error (RSE) of 50%
2 800
1 400
2 000
1 000
1 400
400
100
700
2 300




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