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6265.0 - Underemployed Workers, Australia, Sep 2010 Quality Declaration 
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 08/03/2011   
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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, and 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 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 4 shows the estimated number of female underemployed part-time workers was 445,900. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,300 and 9,200 and can be approximated by interpolation using the following general formula:

Equation: Calcation of standard errors

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 437,200 to 454,600 and about 19 chances in 20 that the value will fall within the range 428,500 to 463,300. This example is illustrated in the following diagram.

Diagram: Confidence intervals of estimates

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.*3.2) 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 duration of insufficient work, median duration of insufficient work and mean preferred number of extra hours 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:
  • mean duration of insufficient work: 1.6
  • median duration of insufficient work: 2.5
  • mean preferred number of extra hours: 0.7

7 The following is an example of the calculation of SEs where the use of a factor is required. Table 4 shows that the estimated number of male underemployed part-time workers was 288,000 with a median duration of insufficient work of 26 weeks. The SE of 288,000 can be calculated from table T1 (by interpolation) as 7,200. To convert this to an RSE we express the SE as a percentage of the estimate or 7,200/288,800 = 2.5%.

8 The RSE of the estimate of median duration of insufficient work is calculated by multiplying this number (2.5%) by the appropriate factor shown in paragraph 7 (in this case 2.5): 2.5 x 2.5 = 6.3%. The SE of this estimate of median duration of insufficient work is therefore 6.3% of 26, i.e. about 2 (rounded to the nearest whole week). Therefore, there are two chances in three that the median duration of insufficient work for males that would have been obtained if all dwellings had been included in the survey would have been within the range 24-28 weeks, and about 19 chances in 20 that it would have been within the range 22-30 weeks.


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.

Equation: Calculation of relative standard errors of proportions and percentages

10 Considering the example from paragraph 3, of the 445,900 female underemployed part-time workers, 179,300 or 40.0% had insufficient work for 52 weeks and over. The SE of 179,300 may be calculated by interpolation as 5,900. To convert this to an RSE we express the SE as a percentage of the estimate, or 5,900/179,300 = 3.3%. The SE for 445,900 was calculated previously as 8,700, which converted to an RSE is 8,700/445,900 = 2.0%. Applying the above formula, the RSE of the proportion is:

Equation: Example calculation of relative standard errors of proportions

11 Therefore, the SE for the proportion of females who have a current period of insufficient work of 52 weeks or more is 1.0 percentage points (=(40.0/100)x2.6). Therefore, there are about two chances in three that the proportion of females who have a current period of insufficient work of 52 weeks or more was between 39.0% and 41.0% and 19 chances in 20 that the proportion is within the range 38.0% to 42.0%.


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:

Equation: Calculation of differences between estimates

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

STANDARD ERRORS OF ESTIMATES

NSW
Vic.
Qld
SA
WA
Tas.
NT
ACT
SE
RSE
Size of Estimate (persons)
no.
no.
no.
no.
no.
no.
no.
no.
no.
%

100
320
310
240
190
240
120
90
110
120
120.0
200
440
420
350
260
320
170
130
180
210
105.0
300
520
490
430
310
380
210
160
230
290
96.7
500
640
600
550
380
460
260
210
300
420
84.0
700
730
680
640
430
530
300
250
330
530
75.7
1,000
840
780
750
500
600
340
290
370
670
67.0
1,500
990
910
890
580
710
400
340
400
860
57.3
2,000
1 110
1 020
1 000
650
790
440
380
430
1 010
50.5
2,500
1 200
1 100
1 100
700
850
450
400
450
1 150
46.0
3,000
1 300
1 200
1 150
750
900
500
450
500
1 250
41.7
3,500
1 400
1 250
1 250
800
950
500
450
500
1 350
38.6
4,000
1 450
1 350
1 300
850
1 000
550
450
500
1 450
36.3
5,000
1 600
1 450
1 400
900
1 100
600
500
550
1 650
33.0
7,000
1 800
1 650
1 600
1 000
1 250
650
600
650
1 900
27.1
10,000
2 050
1 850
1 750
1 150
1 400
750
800
750
2 200
22.0
15,000
2 400
2 150
2 000
1 300
1 650
950
1 100
950
2 550
17.0
20,000
2 650
2 400
2 150
1 450
1 800
1 100
1 400
1 100
2 850
14.3
30,000
3 100
2 800
2 500
1 750
2 100
1 350
1 950
1 350
3 200
10.7
40,000
3 400
3 100
2 750
2 000
2 300
1 650
2 450
1 650
3 500
8.8
50,000
3 700
3 350
3 050
2 200
2 550
1 850
2 950
1 850
3 750
7.5
100,000
4 700
4 400
4 150
3 300
3 750
2 650
5 100
2 450
4 750
4.8
150,000
5 550
5 350
5 100
4 250
4 950
3 150
7 000
2 750
5 500
3.7
200,000
6 350
6 250
5 950
5 000
5 950
3 550
8 750
2 950
6 150
3.1
300,000
8 000
7 950
7 550
6 150
7 450
4 050
11 950
3 100
7 300
2.4
500,000
11 200
11 050
10 200
7 700
9 500
4 700
. .
3 100
9 200
1.8
1,000,000
16 650
16 850
14 550
9 800
12 100
5 350
. .
. .
12 950
1.3
2,000,000
22 450
24 900
19 600
11 650
14 000
. .
. .
. .
18 800
0.9
5,000,000
28 600
39 800
26 400
13 150
14 600
. .
. .
. .
31 400
0.6
10,000,000
30 650
54 900
30 900
. .
. .
. .
. .
. .
41 900
0.4
15,000,000
. .
. .
. .
. .
. .
. .
. .
. .
47 250
0.3

. . not applicable



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