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 is as follows. Table 4 shows that 166,000 unemployed females were looking for full-time work. Since this estimate is between 150,000 and 200,000, table T1 shows that the SE for Australia will lie between 5,000 and 5,600 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 160,800 to 171,200 and about 19 chances in 20 that the value will fall within the range 155,600 to 176,400. 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 T2 presents the levels at which estimates have RSEs of 25% and 50%.


MEANS AND MEDIANS

6 The RSEs of estimates of mean duration of unemployment and median duration of unemployment 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 for Australian estimates:

• mean duration of unemployment: 1.6
• median duration of unemployment: 2.5

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 median duration of unemployment for unemployed females in Australia was 13 weeks and shows that the number of unemployed females was estimated as 271,700. The SE of 271,700 can be calculated from table T1 (by interpolation) as 6,400. To convert this to an RSE we express the SE as a percentage of the estimate or 6,400/271,700 =2.4%.

8 The RSE of the estimate of median duration of unemployment for unemployed females is calculated by multiplying this number (2.4%) by the appropriate factor shown in paragraph 6 (in this case 2.5): 2.4 x 2.5 = 6%. The SE of this estimate of median duration of unemployment for unemployed females is therefore 6% of 13 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 12 to 14 weeks and about 19 chances in 20 that it would have been within the range 11 weeks to 15 weeks.

9 Table T2 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 29,000 persons will have an RSE of at least 25%, and an estimate of median duration of unemployment for Australia based on less than 10,000 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 6,800 for the Australian total will have an RSE of at least 25% and an estimate of less than 1,600 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 the previous page, of the 166,000 unemployed females who were looking for full-time work, 31,700 or 19.1% had been unemployed for one year or more. The SE of 31,700 may be calculated by interpolation as 2,900. To convert this to an RSE we express the SE as a percentage of the estimate, or 2,900/31,700 = 9.1%. The SE for 166,000 was calculated previously as 5,200, which converted to an RSE is 5,200/166,000 = 3.1%. 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 1.6 percentage points (=19.1/100)x8.6). 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 17.4% and 20.6% and 19 chances in 20 that the proportion is within the range 15.8% to 22.2%.


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
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	Aust.
Size of estimate (persons)	No.	No.	No.	No.	No.	No.	No.	No.	No.	%
100	290	290	220	180	220	110	80	100	110	110.0
200	400	380	320	240	290	160	120	170	190	95.0
300	470	440	390	280	340	190	150	210	260	86.7
500	580	540	500	340	420	240	190	270	380	76.0
700	660	620	580	390	480	270	230	300	480	68.6
1,000	760	710	680	450	550	310	270	330	610	61.0
1,500	900	830	810	530	640	360	310	360	780	52.0
2,000	1 010	930	910	590	710	390	340	390	920	46.0
2,500	1 100	1 000	1 000	650	800	400	350	400	1 050	42.0
3,000	1 200	1 100	1 050	700	850	450	400	450	1 150	38.3
3,500	1 250	1 150	1 100	700	900	450	400	450	1 250	35.7
4,000	1 300	1 200	1 200	750	900	500	450	450	1 350	33.8
5,000	1 450	1 300	1 250	800	1 000	500	500	500	1 500	30.0
7,000	1 650	1 500	1 450	900	1 150	600	550	600	1 700	24.3
10,000	1 850	1 700	1 600	1 050	1 300	700	700	700	2 000	20.0
15,000	2 150	1 950	1 800	1 200	1 500	850	1 000	850	2 350	15.7
20,000	2 400	2 200	1 950	1 350	1 650	1 000	1 250	1 000	2 550	12.8
30,000	2 800	2 550	2 250	1 550	1 900	1 250	1 800	1 250	2 900	9.7
40,000	3 100	2 800	2 500	1 800	2 100	1 500	2 250	1 500	3 150	7.9
50,000	3 350	3 050	2 750	2 000	2 300	1 700	2 700	1 650	3 400	6.8
100,000	4 250	4 000	3 750	3 000	3 400	2 400	4 650	2 250	4 300	4.3
150,000	5 000	4 850	4 600	3 850	4 450	2 850	6 400	2 500	5 000	3.3
200,000	5 750	5 650	5 400	4 550	5 350	3 200	8 000	2 650	5 600	2.8
300,000	7 250	7 250	6 850	5 550	6 750	3 700	10 900	2 800	6 650	2.2
500,000	10 150	10 050	9 250	7 000	8 600	4 250	. .	2 800	8 350	1.7
1,000,000	15 100	15 250	13 200	8 900	10 950	4 850	. .	. .	11 750	1.2
2,000,000	20 350	22 550	17 700	10 600	12 700	. .	. .	. .	17 050	0.9
. . not applicable

T2 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.
25% RSE
Mean duration of unemployment	11 200	9 500	8 600	4 400	6 200	2 300	1 600	2 400	14 700
Median duration of unemployment	29 800	25 700	22 600	12 100	18 100	8 100	5 000	6 700	29 000
All other estimates	6 300	5 400	5 100	2 600	3 500	1 400	1 100	1 400	6 800
50% RSE
Mean duration of unemployment	3 700	3 100	3 000	1 500	2 100	800	500	1 000	4 400
Median duration of unemployment	9 900	8 600	8 400	4 100	6 200	2 800	1 700	2 400	10 000
All other estimates	2 000	1 800	1 700	800	1 200	500	300	600	1 600
(a) Refers to the number of persons contributing to the estimate.