6239.0 - Barriers and Incentives to Labour Force Participation, Australia, July 2012 to June 2013 Quality Declaration 
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 28/11/2013   
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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 (or occupants) 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.

2 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.

    RSE% = (SE/estimate ) x 100
3 RSEs for Barriers and Incentives estimates have been calculated using the Jackknife method of variance estimation. This process involves the calculation of 30 'replicate' estimates based on 30 different sub-samples of the original sample. The variability of estimates obtained from these sub-samples is used to estimate the sample variability surrounding the main estimate.

4 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication. However, RSEs for all these estimates are available free-of-charge on the ABS web site
<www.abs.gov.au>, released in spreadsheet format from the Downloads tab for this publication. As a guide, the population estimates and RSEs for selected data from table 2 are presented at a table in this Technical Note.

5 In the tables in this publication, only estimates (numbers, percentages, means and medians) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *13.5) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g.**2.1) to indicate that they are considered too unreliable for general use.

CALCULATION OF STANDARD ERROR AND RELATIVE STANDARD ERROR

6 RSEs are routinely presented as the measure of sampling error in this publication and related products. SEs can be calculated using the estimates (counts or means) and the corresponding RSEs.

7 An example of the calculation of the SE from an RSE follows. The table shows that the estimated number of males aged 18–24 years who did not prefer to work more hours is 226,900, and the RSE for this estimate was 9.5%. The SE is:
    SE of estimate
    = (RSE / 100) x estimate
    = 0.095 x 226,900
    = 21,600 (rounded to the nearest 100)
8 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 would fall within the range 205,300 to 248,500 and about 19 chances in 20 that the value would fall within the range 183,700 to 270,100. This example is illustrated in the following diagram.

Published estimate between 183.7 to 270.1

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 RSEs of proportions not provided in the spreadsheets is given below. This formula is only valid when x is a subset of y.

RSE (x/y) = square root of (RSE(x)2) - (RSE(y)2)2

10 Considering the table, of the 1,021,300 males who worked 0–34 hours each week, 692,400 or 67.8% did not prefer to work more hours. The RSE of 692,400 is 4.6% and the RSE for 1,021,300 is 3.6%. Applying the above formula, the RSE for the proportion of males who did not prefer to work more hours is:

RSE = square root of (4.6)2 - (3.6)2 = 2.9%

11 Therefore, the SE for the proportion of males who worked 0–34 hours per week who did not prefer more hours was 2.0 percentage points (= (67.8/100) x 2.9). Therefore, there are about two chances in three that the proportion of males who worked 0–34 hours per week who did not prefer more hours is between 65.8% and 69.8%, and 19 chances in 20 that the proportion was within the range 63.8% to 71.8%.

Sums or Differences between estimates

12 Published estimates may also be used to calculate the sum of, or difference between, two survey estimates (of numbers, means or percentages) where these are not provided in the spreadsheets. Such estimates are also subject to sampling error.

13 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:

SE(x-y) = square root of (SE(x))2 + (SE(y))2

14 The sampling error of the sum of two estimates is calculated in a similar way. An approximate SE of the sum of two estimates (x+y) may be calculated by the following formula:

SE(x+y) = square root of (SE(x))2 + (SE(y))2

15 An example follows. From paragraph 7 the estimated number of males aged 18–24 years who did not prefer to work more hours was 226,900 and the SE was 21,600. From the table, the estimate of males aged 25–34 years who did not prefer to work more hours was 78,600, and the SE was 11,554. The estimate of males aged 18–34 years who preferred not to work more hours is:
    226,900 + 78,600 = 305,500
16 The SE of the estimate of males aged 18–34 years who did not prefer to work more hours is:

SE= square root of (21600)2 + (11554)2 = 24500 (rounded)

17 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 would fall within the range 281,000 to 330,000 and about 19 chances in 20 that the value would fall within the range 256,500 to 354,500.

18 While these formulae will only be exact for sums of, or differences between, separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all sums or differences likely to be of interest in this publication.



SELECTED ESTIMATES AND RSES


PERSONS AGED 18 YEARS AND OVER, USUALLY WORKED 0–34 HOURS PER WEEK OR NOT EMPLOYED, Whether wanted a job or more hours—By age


PERSONS WHO USUALLY WORKED 0–34 HOURS PER WEEK
PERSONS NOT IN THE LABOUR FORCE
Preferred to work more hours
Did not prefer to work more hours (a)
Total
Unemployed
Wanted a job (b)
Did not want a job (a)
Total
ESTIMATES ('000)

Males
18–24
111.8
226.9
338.6
95.8
88.3
76.3
164.6
25–34
57.4
78.6
136.0
57.3
66.4
55.1
121.5
35–44
41.5
64.6
106.2
50.2
55.1
44.4
99.5
45–54
62.5
76.1
138.6
44.6
42.5
106.3
148.9
55–64
47.6
141.5
189.1
37.1
82.2
223.5
305.8
65 and over
**8.2
104.6
112.8
**5.5
107.7
1 098.6
1 206.3
Total
328.9
692.4
1 021.3
290.4
442.3
1 604.3
2 046.6
Females
18–24
146.6
282.0
428.6
57.6
134.6
119.8
254.4
25–34
109.2
281.4
390.7
52.3
152.2
267.6
419.8
35–44
118.0
475.0
593.0
48.2
130.6
216.4
347.0
45–54
111.0
395.1
506.1
54.8
132.3
200.3
332.6
55–64
80.0
280.1
360.1
25.1
117.8
447.3
565.0
65 and over
*7.2
87.4
94.6
**2.0
103.1
1 391.0
1 494.1
Total
571.9
1 801.1
2 373.0
239.9
770.5
2 642.4
3 412.9
Persons
18–24
258.4
508.9
767.2
153.3
222.8
196.2
419.0
25–34
166.6
360.0
526.6
109.6
218.6
322.7
541.3
35–44
159.5
539.7
699.2
98.4
185.7
260.8
446.5
45–54
173.5
471.2
644.7
99.4
174.8
306.7
481.5
55–64
127.5
421.6
549.2
62.1
200.0
670.8
870.8
65 and over
*15.4
192.0
207.4
**7.5
210.9
2 489.6
2 700.5
Total
900.8
2 493.5
3 394.3
530.3
1 212.8
4 246.8
5 459.6
RSES OF ESTIMATES (%)

Males
18–24
12.1
9.5
6.2
14.8
16.2
16.1
11.5
25–34
16.6
14.7
11.2
17.0
19.6
20.4
12.0
35–44
16.8
14.5
11.3
17.3
15.1
20.9
12.6
45–54
15.9
14.1
10.0
19.4
19.4
12.2
9.1
55–64
22.5
7.5
5.9
24.6
16.2
8.8
6.5
65 and over
50.5
10.4
10.8
59.9
10.6
2.0
1.5
Total
9.0
4.6
3.6
9.0
8.3
2.6
2.5
Females
18–24
14.4
8.9
7.2
19.6
12.6
13.6
8.8
25–34
11.0
6.1
6.3
17.6
11.7
8.7
5.4
35–44
9.6
4.7
3.9
11.5
10.1
8.5
6.5
45–54
10.7
5.3
3.8
14.5
8.0
9.0
6.2
55–64
14.6
6.9
6.0
19.7
13.4
4.9
4.6
65 and over
31.5
12.2
11.1
73.7
11.3
1.0
0.7
Total
5.2
2.3
2.3
8.0
4.9
1.8
1.4
Persons
18–24
9.6
6.7
4.7
12.2
9.7
9.5
6.7
25–34
10.3
6.2
6.1
12.7
10.1
7.4
4.9
35–44
8.5
3.9
3.4
10.0
8.6
7.6
5.9
45–54
8.9
4.8
3.8
12.5
7.3
7.9
4.8
55–64
14.1
6.1
4.9
16.2
12.0
4.5
3.7
65 and over
29.9
8.2
7.8
51.5
8.6
1.1
0.8
Total
4.9
2.3
2.1
5.7
5.1
1.5
1.3

* estimate has a relative standard error of 25% to 50% and should be used with caution
** estimate has a relative standard error greater than 50% and is considered too unreliable for general use
(a) Includes people who reported 'Did not know'.
(b) Includes people who reported 'Maybe/it depends'.