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 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, taken from Job Search Experience, is as follows. JSE table 3 shows that 249,300 unemployed females were looking for full-time work. Since this estimate is between 200,000 and 300,000, table T2 shows that the SE for Australia will lie between 6,500 and 7,700 and can be approximated by interpolation using the following general formula:



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 242,200 to 256,400 and about 19 chances in 20 that the value will fall within the range 235,100 to 263,500. This example is illustrated in the diagram below.

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 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. **0.2), 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%. Table T3 presents the levels at which estimates have RSEs of 25% and 50%.


MEANS AND MEDIANS

6 The RSEs of means and medians are obtained by first finding the RSE of the estimate of the total number of persons contributing to the mean or median (see table T2) and then multiplying the resulting number by the following factors for Australian estimates:

• For JSE
  • mean duration of unemployment: 1.6
  • median duration of unemployment: 2.5
• For UEW
  • 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. JSE table 4 shows that the estimated median duration of unemployment for unemployed females in Australia was 10 weeks and shows that the number of unemployed females was estimated as 407,600. The SE of 407,600 can be calculated from table T2 (by interpolation) as 8,700. To convert this to an RSE express the SE as a percentage of the estimate or 8,700/407,600 = 2.1%.

8 The RSE of the estimate of median duration of unemployment for unemployed females is calculated by multiplying this number (2.1%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.1 x 2.5 = 5.3%. The SE of this estimate of median duration of unemployment for unemployed females is therefore 5.3% of 10 weeks, i.e. approximately one week. Therefore, there are two chances in three that the median duration of unemployment for females that would have been obtained if all dwellings had been included in the survey would have been within the range 9 to 11 weeks and about 19 chances in 20 that it would have been within the range 8 weeks to 12 weeks.

9 Table T3 represents the minimum size of estimates, based on the SE model described in paragraph 2, required to have RSEs of less than 25% and 50% respectively. For example, an estimate of median duration of unemployment for Australia based on less than 35,600 persons will have an RSE of at least 25%, and an estimate of median duration of unemployment for Australia based on less than 12,800 will have an RSE of at least 50%. For all other estimates, (i.e. those estimates based purely on number of persons in a specific category), an estimate of less than 8,800 for the Australian total will have an RSE of at least 25% and an estimate of less than 2,300 will have an RSE of at least 50%.


PROPORTIONS AND PERCENTAGES

10 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:



11 Considering the example from paragraph 3, of the 249,300 unemployed females who were looking for full-time work, 51,100 or 20.5% had been unemployed for one year or more. The SE of 51,100 may be calculated by interpolation as 4,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,000/51,100 = 7.8%. The SE for 249,300 was calculated previously as 7,100, which converted to an RSE is 7,100/249,300 = 2.8%. Applying the above formula, the RSE of the proportion is:



12 Therefore, the SE for the proportion of unemployed females looking for full-time work who had been unemployed for one year or more is 1.5 percentage points (=20.5/100) x 7.3). Therefore, there are about two chances in three that the proportion of unemployed females looking for full-time work who have been unemployed for one year or more is between 19.0% and 22.0% and 19 chances in 20 that the proportion is within the range 17.5% to 23.5%.


DIFFERENCES

13 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:



14 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

T1 STANDARD ERRORS OF ESTIMATES (PNILF)
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	SE	RSE
Size of Estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	180	150	200	170	170	110	80	120	140	140.0
200	300	230	330	250	260	160	110	210	240	120.0
300	390	290	440	310	330	200	140	270	320	106.7
500	530	400	600	400	440	250	170	370	460	92.0
700	650	480	730	470	520	290	200	430	580	82.9
1,000	800	580	900	560	620	340	240	500	730	73.0
1,500	990	710	1 120	670	760	400	300	580	940	62.7
2,000	1 150	820	1 300	760	860	440	340	630	1 120	56.0
2,500	1 300	900	1 450	850	950	450	400	650	1 250	50.0
3,000	1 400	1 000	1 600	900	1 050	500	400	700	1 400	46.7
3,500	1 500	1 050	1 700	950	1 100	550	450	750	1 500	42.9
4,000	1 600	1 150	1 800	1 000	1 150	550	500	750	1 650	41.3
5,000	1 800	1 250	2 000	1 100	1 250	600	600	850	1 800	36.0
7,000	2 100	1 450	2 300	1 250	1 450	700	750	1 000	2 150	30.7
10,000	2 400	1 650	2 650	1 400	1 600	850	1 000	1 300	2 500	25.0
15,000	2 800	1 950	3 050	1 650	1 900	1 050	1 450	1 700	3 000	20.0
20,000	3 150	2 150	3 350	1 900	2 150	1 200	1 850	2 000	3 350	16.8
30,000	3 600	2 500	3 900	2 350	2 700	1 500	2 500	2 450	3 850	12.8
40,000	4 000	2 750	4 400	2 750	3 200	1 750	3 100	2 750	4 250	10.6
50,000	4 350	3 000	4 850	3 100	3 650	1 950	3 600	2 950	4 600	9.2
100,000	6 050	4 350	7 150	4 450	5 350	2 700	5 650	3 350	6 050	6.1
150,000	7 700	5 600	9 050	5 350	6 600	3 200	7 100	3 350	7 250	4.8
200,000	9 200	6 650	10 600	6 050	7 600	3 600	. .	. .	8 300	4.2
300,000	11 600	8 450	13 050	7 100	9 100	4 200	. .	. .	10 100	3.4
500,000	15 000	11 350	16 500	8 550	11 300	5 000	. .	. .	13 200	2.6
1,000,000	20 050	16 750	21 650	10 600	14 600	. .	. .	. .	19 550	2.0
2,000,000	24 950	24 200	26 850	12 650	18 250	. .	. .	. .	28 300	1.4
5,000,000	30 000	38 550	32 900	. .	. .	. .	. .	. .	40 800	0.8
10,000,000	31 800	53 850	. .	. .	. .	. .	. .	. .	49 000	0.5
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	52 550	0.4
. . not applicable

T2 STANDARD ERRORS OF ESTIMATES (UEW/JSE)
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	SE	RSE
Size of Estimate (persons)	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	130	320	440	88.0
700	810	530	650	430	530	270	150	360	560	80.0
1,000	930	610	760	490	610	310	180	400	700	70.0
1,500	1 100	710	900	580	710	350	210	430	900	60.0
2,000	1 230	800	1 010	640	790	390	230	460	1 070	53.5
2,500	1 350	850	1 100	700	850	400	250	500	1 200	48.0
3,000	1 450	950	1 200	750	900	450	250	500	1 350	45.0
3,500	1 550	1 000	1 250	800	1 000	450	250	550	1 450	41.4
4,000	1 600	1 050	1 300	850	1 050	500	300	550	1 550	38.8
5,000	1 750	1 150	1 400	900	1 100	500	300	600	1 700	34.0
7,000	2 000	1 300	1 600	1 000	1 250	600	400	700	2 000	28.6
10,000	2 300	1 450	1 800	1 150	1 450	700	500	800	2 300	23.0
15,000	2 650	1 700	2 000	1 300	1 650	850	650	1 000	2 700	18.0
20,000	2 950	1 900	2 200	1 450	1 850	950	850	1 150	3 000	15.0
30,000	3 400	2 200	2 500	1 700	2 100	1 250	1 150	1 500	3 350	11.2
40,000	3 800	2 400	2 800	1 950	2 350	1 450	1 500	1 750	3 650	9.1
50,000	4 100	2 600	3 050	2 200	2 550	1 650	1 800	2 000	3 950	7.9
100,000	5 200	3 450	4 200	3 300	3 750	2 400	3 100	2 650	4 950	5.0
150,000	6 100	4 150	5 150	4 250	4 950	2 850	4 250	3 000	5 800	3.9
200,000	7 050	4 850	6 000	4 950	5 950	3 150	5 300	3 150	6 500	3.3
300,000	8 850	6 250	7 650	6 100	7 500	3 650	7 200	3 300	7 700	2.6
500,000	12 400	8 650	10 300	7 650	9 550	4 200	. .	3 300	9 650	1.9
1,000,000	18 400	13 150	14 700	9 750	12 150	4 800	. .	. .	13 600	1.4
2,000,000	24 800	19 450	19 800	11 600	14 100	. .	. .	. .	19 750	1.0
5,000,000	31 600	31 100	26 700	13 050	14 700	. .	. .	. .	32 950	0.7
10,000,000	33 850	42 900	31 200	. .	. .	. .	. .	. .	44 000	0.4
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	49 600	0.3
. . not applicable

T3 Levels at which estimates have relative standard errors of 25% and 50%(a)
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Aust.
	no.	no.	no.	no.	no.	no.	no.	no.	no.
Persons not in the labour force
RSE of 25%	9 400	5 000	10 900	4 100	5 100	1 600	900	2 700	10 100
RSE of 50%	2 700	1 300	3 300	1 200	1 500	500	300	1 000	2 600
Underemployed Workers 25% RSE
Mean duration of insufficient work	18 300	9 800	13 000	5 800	9 400	2 500	1 200	3 000	19 200
Median duration of insufficient work	44 400	22 900	32 500	18 100	21 700	6 700	11 900	13 400	35 300
Mean preferred number of extra hours	5 300	3 100	3 800	2 000	2 900	1 000	400	1 100	5 000
All other estimates	8 600	4 200	6 100	3 000	4 200	1 400	500	1 800	8 800
Underemployed Workers 50% RSE
Mean duration of insufficient work	6 100	3 200	4 700	2 000	3 200	900	300	1 200	6 100
Median duration of insufficient work	15 000	7 600	11 800	6 300	7 400	2 400	2 700	4 000	12 600
Mean preferred number of extra hours	1 700	1 000	1 200	600	1 000	300	100	400	1 100
All other estimates	2 800	1 400	2 000	1 000	1 400	400	100	700	2 300
Job Search Experience 25% RSE
Mean duration of unemployment	15 300	7 500	10 100	5 000	7 400	2 200	800	3 100	18 400
Median duration of unemployment	40 600	20 300	26 700	13 900	21 200	7 900	2 600	9 100	35 600
All other estimates	8 600	4 200	6 100	3 000	4 200	1 400	500	1 800	8 800
Job Search Experience 50% RSE
Mean duration of unemployment	5 100	2 500	3 600	1 700	2 500	800	200	1 200	5 800
Median duration of unemployment	13 700	6 800	9 800	4 800	7 200	2 800	900	3 000	12 800
All other estimates	2 800	1 400	2 000	1 000	1 400	400	100	700	2 300
(a) Refers to the number of persons contributing to the estimate.