TECHNICAL NOTE DATA QUALITY


INTRODUCTION

1 Since the estimates published 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 subsamples of the original sample. The variability of estimates obtained from these subsamples 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 as an attachment to this publication, Barriers and Incentives to Labour Force Participation, Australia (cat. no. 6239.0). As a guide, the population estimates and RSEs for selected data from table 1 and 2 are presented at table T1 and table T2 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. Table T2 shows that the estimated number of females aged 18-24 years who did not prefer to work more hours is 99,200, and the RSE for this estimate is 16.6%. The SE is:

SE of estimate
= (RSE / 100) x estimate
= 0.166 x 99,200
= 16,500 (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 will fall within the range 82,700 to 115,700 and about 19 chances in 20 that the value will fall within the range 66,200 to 132,200. This example is illustrated in the following diagram.

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 speadsheets is given below. This formula is only valid when x is a subset of y.



10 Considering table T2, of the 668,300 females who worked 0-15 hours each week, 486,000 or 72.7% did not prefer to work more hours. The RSE of 486,000 is 7.9% and the RSE for 668,300 is 7.2%. Applying the above formula, the RSE for the proportion of females who did not prefer to work more hours is:



11 Therefore, the SE for the proportion of females working 0-15 hours per week who did not prefer more hours is 2.4 percentage points (= (72.7/100) x 3.3). Therefore, there are about two chances in three that the proportion of females working 0-15 hours per week who did not prefer more hours is between 70.3% and 75.1%, and 19 chances in 20 that the proportion is within the range 67.9% to 77.5%.


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:



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:



15 An example follows. From paragraph 7 the estimated number of females aged 18-24 years who did not prefer to work more hours is 99,200 and the SE is 16,500. From table T2, the estimate of females aged 25-34 years who did not prefer to work more hours is 70,000, and the SE is 13,090. The estimate of females aged 18-34 years who preferred not to work more hours is:

99,200 + 70,000 = 169,200

16 The SE of the estimate of females aged 18-34 years who did not prefer to work more hours is:



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 will fall within the range 148,100 to 190,300 and about 19 chances in 20 that the value will fall within the range 127,000 to 211,400.

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

T1: PERSONS AGED 18 YEARS AND OVER , Labour force status-By sex
						Males	Females	Persons
ESTIMATES ('000)
Persons in the labour force						6 063.0	5 015.4	11 078.4
	Employed					5 870.1	4 795.7	10 665.7
		Persons who usually worked 16 hours or more per week				5 629.0	4 127.4	9 756.4
		Persons who usually worked 0-15 hours per week				241.1	668.3	909.3
			Preferred to work more hours			63.5	182.3	245.8
				Available to start work with more hours(a)		58.0	160.7	218.7
					Looked for more hours	*35.2	77.7	112.8
					Did not look for more hours	22.8	83.1	105.9
				Not available to start work with more hours		**5.5	*21.6	*27.0
			Did not prefer to work more hours(b)			177.6	486.0	663.6
Unemployed						192.9	219.7	412.7
Persons not in the labour force						1 844.8	3 162.0	5 006.8
	Wanted a paid job(c)					376.1	683.7	1 059.8
		Available to start work(a)				262.3	466.3	728.7
			Actively looked for work(d)			*16.1	*24.9	41.1
			Did not actively look for work(e)			246.2	441.4	687.6
		Not available or did not know if available to start work				113.8	217.3	331.1
	Did not want a paid job					1 468.7	2 478.4	3 947.0
Total						7 907.8	8 177.4	16 085.2
RSES OF ESTIMATES (%)
Persons in the labour force						0.7	1.2	0.7
	Employed					0.6	1.2	0.7
		Persons who usually worked 16 hours or more per week				0.7	1.7	0.8
		Persons who usually worked 0-15 hours per week				9.5	7.2	6.3
			Preferred to work more hours			18.4	12.3	8.1
				Available to start work with more hours(a)		21.0	11.8	7.6
					Looked for more hours	32.4	18.5	12.4
					Did not look for more hours	24.7	17.5	13.0
				Not available to start work with more hours		64.5	34.6	34.3
			Did not prefer to work more hours(b)			11.5	7.9	7.2
Unemployed						12.7	10.3	7.5
Persons not in the labour force						2.1	1.9	1.6
	Wanted a paid job(c)					6.7	4.0	3.4
		Available to start work(a)				8.2	5.6	4.5
			Actively looked for work(d)			29.1	26.9	21.6
			Did not actively look for work(e)			8.2	5.4	4.2
		Not available or did not know if available to start work				14.0	8.7	6.3
	Did not want a paid job					2.4	2.4	1.9
Total						-	-	-
* 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
- nil or rounded to zero (including null cells)
(a) Availability refers to in the reference week or within four weeks.
(b) Includes people who reported 'Did not know'.
(c) Includes people who reported 'Maybe/depends'.
(d) These people were not available to start work in the reference week so are defined as not in the labour force rather than unemployed.
(e) Includes 26,200 people (12,100 men and 14,100 women) who wanted a paid job and reported 'Looked, not actively'.

T2 ESTIMATES: PERSONS AGED 18 YEARS AND OVER, USUALLY WORKED 0-15 HOURS PER WEEK OR WERE NOT EMPLOYED, Whether wanted a job or more hours-By age
		PERSONS WHO USUALLY WORKED 0-15 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 paid job(b)	Did not want a paid job(a)	Total
ESTIMATES ('000)
Males
	18-24	*31.6	71.0	102.7	72.1	68.8	80.7	149.5
	25-34	**1.9	**14.1	**16.0	53.4	48.1	*40.1	88.2
	35-44	*5.6	**5.2	*10.7	36.5	44.6	50.5	95.1
	45-54	*5.2	*11.5	*16.7	*16.3	53.8	88.9	142.7
	55-64	*15.3	34.9	50.2	*13.5	83.2	265.5	348.7
	65 and over	*3.8	41.0	44.8	**1.2	77.6	943.0	1 020.6
	Total	63.5	177.6	241.1	192.9	376.1	1 468.7	1 844.8
Females
	18-24	*34.0	99.2	133.2	65.5	115.9	123.3	239.2
	25-34	33.5	70.0	103.6	55.6	129.7	235.2	364.9
	35-44	50.0	111.8	161.8	47.5	148.9	222.5	371.4
	45-54	*43.3	88.2	131.5	36.5	115.7	168.9	284.6
	55-64	20.8	82.7	103.4	*13.8	100.0	484.8	584.8
	65 and over	**0.7	34.0	34.7	**0.8	73.5	1 243.6	1 317.1
	Total	182.3	486.0	668.3	219.7	683.7	2 478.4	3 162.0
Persons
	18-24	65.6	170.2	235.8	137.5	184.7	204.0	388.7
	25-34	35.5	84.1	119.6	108.9	177.8	275.3	453.1
	35-44	55.6	117.0	172.6	84.1	193.5	273.0	466.4
	45-54	*48.5	99.7	148.2	52.7	169.5	257.8	427.3
	55-64	36.1	117.6	153.7	27.4	183.2	750.3	933.5
	65 and over	*4.5	75.0	79.5	**2.0	151.1	2 186.6	2 337.7
	Total	245.8	663.6	909.3	412.7	1 059.8	3 947.0	5 006.8
RSES OF ESTIMATES (%)
Males
	18-24	29.3	23.0	17.4	22.5	24.4	16.2	16.7
	25-34	90.3	62.6	55.8	24.5	23.9	26.3	17.7
	35-44	37.0	59.5	31.6	19.5	19.0	14.7	11.9
	45-54	47.1	48.4	33.8	31.6	15.6	15.9	12.7
	55-64	29.8	22.0	17.8	30.5	12.8	6.4	5.4
	65 and over	49.0	16.8	15.7	101.8	13.6	2.5	1.8
	Total	18.4	11.5	9.5	12.7	6.7	2.4	2.1
Females
	18-24	29.3	16.6	11.3	21.2	15.4	15.3	9.5
	25-34	22.7	18.7	14.9	14.7	11.4	7.6	6.6
	35-44	23.9	11.5	11.9	21.4	9.3	8.0	6.6
	45-54	32.8	11.8	13.4	22.1	13.5	14.6	9.3
	55-64	23.4	14.3	13.0	40.8	12.6	5.5	4.0
	65 and over	102.7	20.5	19.9	101.2	13.7	1.1	0.9
	Total	12.3	7.9	7.2	10.3	4.0	2.4	1.9
Persons
	18-24	16.3	14.2	9.4	14.6	12.4	11.4	8.7
	25-34	21.2	17.2	13.1	12.6	9.9	7.5	6.2
	35-44	23.1	10.9	11.2	14.4	8.5	7.7	5.9
	45-54	28.9	11.8	13.2	16.5	10.1	9.5	6.8
	55-64	17.5	12.4	12.0	23.6	9.5	4.1	3.4
	65 and over	43.8	14.4	13.6	71.1	9.9	1.4	1.1
	Total	8.1	7.2	6.3	7.5	3.4	1.9	1.6
* 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'.