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 enable readers 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 1 shows that the estimated number of people in Australia who were discouraged job seekers was 106,600. Since the estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 5,100 and 6,050 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 101,400 to 111,800 and about 19 chances in 20 that the value will fall within the range 96,200 to 117,000. This example is illustrated in the following diagram.

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.**0.4), 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%.


PROPORTIONS AND PERCENTAGES

6 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.



7 Considering the example from paragraph 3, of the 106,600 people who were discouraged job seekers, 56,300 or 52.8% were females. The SE of 56,300 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 4,000/56,300=7.1%. The SE for 106,600 was calculated previously as 5,200 which converted to an RSE is 5,200/106,600=4.9%. Applying the above formula, the RSE of the proportion is:



8 Therefore, the SE for the proportion of discouraged job seekers who were females is 2.7 percentage points (=(52.8/100)x5.1). Therefore, there are about two chances in three that the proportion of females who were discouraged job seekers was between 50.1% and 55.5% and 19 chances in 20 that the proportion is within the range 47.4% to 58.2%.


DIFFERENCES

9 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:



10 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	SE	RSE
Size of Estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	160	170	150	150	160	110	90	90	110	110.0
200	270	270	240	220	240	160	130	160	200	100.0
300	350	340	310	280	310	200	150	200	270	90.0
500	470	460	430	360	410	250	190	270	390	78.0
700	580	560	520	420	490	290	230	320	490	70.0
1,000	710	680	640	490	580	340	270	370	620	62.0
1,500	880	830	800	590	700	400	330	430	790	52.7
2,000	1 030	960	930	670	800	440	380	470	930	46.5
2,500	1 150	1 050	1 050	750	900	500	450	500	1 050	42.0
3,000	1 250	1 150	1 150	800	950	500	450	500	1 150	38.3
3,500	1 350	1 250	1 200	850	1 000	550	500	550	1 250	35.7
4,000	1 450	1 350	1 300	900	1 050	550	550	550	1 350	33.8
5,000	1 600	1 450	1 400	1 000	1 150	600	650	650	1 550	31.0
7,000	1 850	1 700	1 650	1 100	1 350	700	850	750	1 800	25.7
10,000	2 150	1 950	1 900	1 250	1 500	850	1 150	950	2 100	21.0
15,000	2 500	2 300	2 200	1 500	1 750	1 050	1 600	1 250	2 500	16.7
20,000	2 800	2 550	2 400	1 700	2 000	1 250	2 050	1 500	2 800	14.0
30,000	3 200	2 900	2 750	2 100	2 500	1 550	2 800	1 850	3 250	10.8
40,000	3 550	3 200	3 150	2 450	3 000	1 750	3 450	2 050	3 550	8.9
50,000	3 850	3 550	3 500	2 750	3 400	2 000	4 000	2 200	3 850	7.7
100,000	5 400	5 100	5 100	3 900	5 000	2 700	6 250	2 500	5 100	5.1
150,000	6 850	6 550	6 450	4 700	6 150	3 250	7 850	2 500	6 050	4.0
200,000	8 200	7 800	7 600	5 350	7 050	3 650	. .	. .	6 950	3.5
300,000	10 350	9 900	9 300	6 300	8 500	4 250	. .	. .	8 450	2.8
500,000	13 350	13 300	11 800	7 550	10 500	5 050	. .	. .	11 050	2.2
1,000,000	17 850	19 600	15 450	9 400	13 600	. .	. .	. .	16 350	1.6
2,000,000	22 250	28 350	19 200	11 200	16 950	. .	. .	. .	23 700	1.2
5,000,000	26 700	45 150	23 500	. .	. .	. .	. .	. .	34 200	0.7
10,000,000	28 300	63 050	. .	. .	. .	. .	. .	. .	41 050	0.4
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	44 050	0.3
. . not applicable

T2 levels at which estimates have a relative standard errors of 25% and 50%(a)
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Australia
Percentage	no.	no.	no.	no.	no.	no.	no.	no.	no.
RSE of 25%	7 700	6 600	6 300	3 300	4 500	1 700	1 200	1 800	7 300
RSE of 50%	2 100	1 800	1 700	1 000	1 300	500	300	600	1 700
(a) Refers to the number of people contributing to the estimate