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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 2 shows that the estimated number of people in Australia who were discouraged job seekers was 56,100. Since this estimate is between 50,000 and 100,000, table T1 shows the SE for Australia will be between 3,750 and 4,800, 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 52,200 to 60,000, and about 19 chances in 20 that the value will fall within the range 48,300 to 63,900. 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 56,100 people in Australia who were discouraged job seekers, 20,400 or 36.4% were males. The SE of 20,400 may be calculated by interpolation as 2,600. To convert this to an RSE we express the SE as a percentage of the estimate, or 2,600/20,400 = 12.8%. The SE for 56,100 was calculated previously as 3,900, which converted to an RSE is 3,900/56,100 = 7.0%. Applying the above formula, the RSE of the proportion is

8 Therefore, the SE for the proportion of discouraged job seekers who were male is 3.9 percentage points (=(36.4/100)x10.7). Therefore, there are about two chances in three that the proportion of males who were discouraged job seekers is between 32.5% and 40.3% and 19 chances in 20 that the proportion is within the range 28.6% to 44.2%.

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.

11 SEs contained in table T1 are applicable to all estimates from this survey.

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	120	170	160	100	120	100	120	90	120	120.0
200	210	260	240	170	190	150	160	140	200	100.0
300	280	330	300	220	240	190	200	180	260	86.7
500	400	430	400	300	330	240	250	230	370	74.0
700	500	520	480	360	400	280	290	270	450	64.3
1000	630	620	580	430	480	320	350	320	560	56.0
1500	800	750	710	530	590	380	430	370	710	47.3
2000	930	870	820	600	670	420	500	410	830	41.5
2500	1 050	950	900	650	750	450	550	450	950	38.0
3000	1 150	1 050	1 000	700	800	450	600	450	1 050	35.0
3500	1 250	1 100	1 050	750	850	500	700	500	1 150	32.9
4000	1 350	1 200	1 150	800	900	500	750	500	1 200	30.0
5000	1 500	1 300	1 250	850	1 000	550	850	550	1 350	27.0
7000	1 700	1 500	1 450	950	1 100	650	1 100	650	1 600	22.9
10000	2 000	1 750	1 650	1 150	1 250	850	1 450	800	1 900	19.0
15000	2 350	2 050	1 950	1 350	1 450	1 050	2 050	1 050	2 300	15.3
20000	2 600	2 250	2 150	1 550	1 650	1 300	2 600	1 250	2 600	13.0
30000	3 000	2 650	2 500	1 850	2 100	1 600	3 550	1 550	3 050	10.2
40000	3 350	2 900	2 800	2 150	2 550	1 850	4 400	1 750	3 450	8.6
50000	3 700	3 200	3 100	2 450	2 900	2 100	5 200	1 900	3 750	7.5
100000	5 150	4 650	4 700	3 550	4 300	2 950	8 400	2 350	4 800	4.8
150000	6 400	5 950	6 150	4 400	5 350	3 500	10 900	2 500	5 600	3.7
200000	7 550	7 050	7 300	5 050	6 150	3 900	. .	. .	6 350	3.2
300000	9 700	8 800	9 050	6 000	7 450	4 550	. .	. .	7 800	2.6
500000	13 250	11 500	11 300	7 150	9 300	5 350	. .	. .	10 550	2.1
1000000	18 800	16 000	14 000	8 450	12 150	. .	. .	. .	16 600	1.7
2000000	24 450	21 600	15 650	9 300	15 250	. .	. .	. .	24 250	1.2
5000000	30 400	30 450	15 550	. .	. .	. .	. .	. .	35 250	0.7
10000000	32 450	37 950	. .	. .	. .	. .	. .	. .	42 450	0.4
15000000	. .	. .	. .	. .	. .	. .	. .	. .	45 550	0.3
. . 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	5 400	5 000	2 700	3 400	1 500	2 000	1 500	5 900
RSE of 50%	1 700	1 500	1 400	700	900	500	500	400	1 300
(a) Refers to the number of people contributing to the estimate.