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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 3 shows that the estimated number of migrants was 1,362,600. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows the SE for Australia will be between 12,150 and 16,050, 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 in the range 1,349,000 to 1,376,200, and about 19 chances in 20 that the value will fall within the range 1,335,400 to 1,389,800. This example is illustrated in the diagram below.

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 1,362,600 who were migrants, 625,300 or 46% were males. The SE of 625,300 may be calculated by interpolation as 10,000. To convert this to an RSE we express the SE as a percentage of the estimate, or 10,000/625,300 = 1.6%. The SE for 1,362,600 was calculated previously as 13,600, which converted to an RSE is 13,600/1,362,600 = 1.0%. Applying the above formula, the RSE of the proportion is

8 Therefore, the SE for the proportion of male migrants is 0.6 percentage points (=(46/100)x1.2). Therefore, there are about two chances in three that the proportion of male migrants is between 45.4% and 46.6% and 19 chances in 20 that the proportion is within the range 44.8% to 47.2%.

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
									AUST.
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	SE	RSE
Size of estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	100	110	190	170	160	110	100	140	80	80.0
200	170	180	270	220	230	150	140	170	140	70.0
300	230	240	330	270	280	180	160	190	200	66.7
500	340	340	420	330	350	220	200	230	290	58.0
700	430	420	490	380	410	250	230	250	370	52.9
1,000	550	530	580	440	480	290	270	280	470	47.0
1,500	720	670	690	520	570	340	310	330	610	40.7
2,000	860	790	790	590	650	380	350	360	730	36.5
2,500	1,000	900	850	650	700	400	400	400	850	34.0
3,000	1,100	1,000	950	700	750	450	400	400	950	31.7
3,500	1,200	1,050	1,000	750	800	500	450	450	1,050	30.0
4,000	1,300	1,150	1,100	800	850	500	450	450	1,100	27.5
5,000	1,450	1,250	1,200	850	950	550	500	500	1,250	25.0
7,000	1,700	1,500	1,400	1,000	1,100	650	550	600	1,550	22.1
10,000	2,050	1,750	1,600	1,150	1,250	700	650	650	1,850	18.5
15,000	2,450	2,100	1,900	1,350	1,500	850	750	800	2,250	15.0
20,000	2,800	2,350	2,200	1,500	1,650	950	850	900	2,600	13.0
30,000	3,300	2,750	2,600	1,800	1,950	1,100	1,000	1,050	3,150	10.5
40,000	3,650	3,100	2,900	2,000	2,200	1,250	1,100	1,150	3,550	8.9
50,000	3,950	3,300	3,200	2,200	2,350	1,350	1,150	1,300	3,900	7.8
100,000	4,950	4,200	4,250	2,900	3,050	1,750	1,500	1,750	5,100	5.1
150,000	5,600	4,850	5,050	3,400	3,500	2,000	1,750	2,100	5,900	3.9
200,000	6,150	5,450	5,650	3,800	3,900	2,250	. .	2,400	6,550	3.3
300,000	7,200	6,450	6,650	4,450	4,450	2,600	. .	2,850	7,650	2.6
500,000	8,900	8,100	8,150	5,450	5,300	3,100	. .	. .	9,300	1.9
1,000,000	12,450	11,350	10,700	7,150	6,600	. .	. .	. .	12,150	1.2
2,000,000	18,300	16,450	13,950	9,350	8,150	. .	. .	. .	16,050	0.8
5,000,000	32,850	28,350	19,650	. .	. .	. .	. .	. .	24,600	0.5
10,000,000	54,050	. .	. .	. .	. .	. .	. .	. .	43,150	0.4
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	66,850	0.4
20,000,000	. .	. .	. .	. .	. .	. .	. .	. .	95,800	0.5
. . 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%	6,800	5,200	4,600	2,600	3,200	1,300	1,100	1,200	5,100
RSE of 50%	1,300	1,100	1,300	800	900	400	400	400	800
(a) Refers to the number of people contributing to the estimate.