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 ERRORS

3 An example of the calculation and the use of SEs in relation to estimates of people is as follows. Table 2 shows that the estimated number of people who were part-time employees in their main job in Australia was 2,487,400. Since this estimate is between 2,000,000 and 5,000,000, table T1 shows the SE for Australia will be between 17,550 and 29,350 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 in the range 2,467,900 to 2,506,900, and about 19 chances in 20 that the value will fall within the range 2,448,400 to 2,526,400. 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.**0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less. Table T2 presents the levels at which estimates have RSEs of 25% and 50%.


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 above, of the 2,487,400 people who were part-time employees, 646,300 or 26% were men. The SE of 646,300 may be calculated by interpolation as 9,600. To convert this to an RSE we express the SE as a percentage of the estimate, or 9,600/646,300 = 1.5%. The SE for 2,487,400 was calculated previously as 19,500, which converted to an RSE is 19,500/2,487,400 = 0.8%. Applying the above formula, the RSE of the proportion is



8 Therefore, the SE for the proportion of men who were part time employees, is 0.3 percentage points (=(26/100)x1.3). Therefore, there are about two chances in three that the proportion of men who were part time employees, is between 25.7% and 26.3% and 19 chances in 20 that the proportion is within the range 25.4% to 26.6%.


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	Aust.
Size of estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	300	290	230	180	220	110	80	100	110	110.0
200	410	390	330	240	300	160	120	170	200	100.0
300	480	460	400	290	350	200	150	220	270	90.0
500	600	560	520	350	430	240	200	280	390	78.0
700	680	640	600	400	490	280	230	310	500	71.4
1,000	790	730	700	460	560	320	270	350	630	63.0
1,500	930	850	830	540	660	370	310	370	800	53.3
2,000	1 040	950	940	600	740	410	350	400	950	47.5
2,500	1 150	1 050	1 000	650	800	450	400	400	1 050	42.0
3,000	1 200	1 100	1 100	700	850	450	400	450	1 200	40.0
3,500	1 300	1 200	1 150	750	900	500	400	450	1 300	37.1
4,000	1 350	1 250	1 200	800	950	500	450	500	1 350	33.8
5,000	1 500	1 350	1 300	850	1 050	550	500	550	1 500	30.0
7,000	1 700	1 550	1 450	950	1 150	600	600	600	1 750	25.0
10,000	1 900	1 750	1 650	1 100	1 350	700	750	700	2 050	20.5
15,000	2 250	2 050	1 850	1 250	1 550	850	1 000	850	2 400	16.0
20,000	2 500	2 250	2 050	1 350	1 700	1 000	1 300	1 000	2 650	13.3
30,000	2 900	2 600	2 300	1 600	1 950	1 300	1 800	1 300	3 000	10.0
40,000	3 200	2 900	2 600	1 850	2 150	1 550	2 250	1 500	3 250	8.1
50,000	3 450	3 150	2 800	2 050	2 400	1 750	2 700	1 700	3 500	7.0
100,000	4 400	4 100	3 850	3 100	3 500	2 500	4 700	2 300	4 400	4.4
150,000	5 200	5 000	4 750	4 000	4 600	2 950	6 500	2 600	5 150	3.4
200,000	5 950	5 800	5 550	4 650	5 550	3 300	8 100	2 750	5 750	2.9
300,000	7 500	7 450	7 050	5 750	6 950	3 800	11 050	2 850	6 850	2.3
500,000	10 500	10 350	9 500	7 200	8 850	4 350	. .	2 900	8 600	1.7
1,000,000	15 550	15 750	13 600	9 200	11 300	5 000	. .	. .	12 100	1.2
2,000,000	20 950	23 250	18 300	10 900	13 100	. .	. .	. .	17 550	0.9
5,000,000	26 700	37 200	24 650	12 300	13 650	. .	. .	. .	29 350	0.6
10,000,000	28 650	51 300	28 850	. .	. .	. .	. .	. .	39 150	0.4
. . 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.
RSE of 25%	6 600	5 700	5 400	2 700	3 700	1 500	1 100	1 500	7 200
RSE of 50%	2 100	1 900	1 800	900	1 200	500	300	600	1 800
(a) Refers to the number of people contributing to the estimate.