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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 1 shows that the estimated number of people in Australia who were discouraged job seekers was 76,600. Since this estimate is between 50,000 and 100,000, table T1 shows the SE for Australia will be between 3,450 and 4,550, 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 72,600 to 80,600, and about 19 chances in 20 that the value will fall within the range 68,600 to 84,600. 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 76,600 people in Australia who were discouraged job seekers, 28,000 or 36.6% were males. The SE of 28,000 may be calculated by interpolation as 2,800. To convert this to an RSE we express the SE as a percentage of the estimate, or 2,800/28,000 = 10%. The SE for 76,600 was calculated previously as 4,000, which converted to an RSE is 4,000/76,600 = 5.2%. 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 3.1 percentage points (=(36.6/100)x 8.5). Therefore, there are about two chances in three that the proportion of males who were discouraged job seekers is between 33.5% and 39.7% and 19 chances in 20 that the proportion is within the range 30.4% to 42.8%.

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	150	160	130	140	130	100	140	80	100	100.0
200	240	240	210	200	200	150	190	130	180	90.0
300	320	310	270	250	250	190	220	180	240	80.0
500	440	420	370	320	330	240	290	230	350	70.0
700	530	500	460	380	400	280	340	280	440	62.9
1,000	650	610	560	450	480	320	400	320	550	55.0
1,500	810	750	700	530	580	370	490	370	710	47.3
2,000	940	860	810	610	660	410	560	400	840	42.0
2,500	1 050	950	900	650	700	450	650	400	950	38.0
3,000	1 150	1 050	1 000	700	800	450	700	450	1 050	35.0
3,500	1 250	1 100	1 050	750	850	500	750	450	1 150	32.9
4,000	1 300	1 200	1 100	800	900	500	850	500	1 250	31.3
5,000	1 450	1 300	1 250	900	950	550	950	550	1 350	27.0
7,000	1 700	1 500	1 400	1 000	1 100	650	1 250	650	1 600	22.9
10,000	1 950	1 750	1 650	1 150	1 250	800	1 650	800	1 900	19.0
15,000	2 300	2 050	1 900	1 350	1 450	1 000	2 400	1 100	2 250	15.0
20,000	2 550	2 250	2 100	1 500	1 650	1 150	3 000	1 300	2 500	12.5
30,000	2 950	2 600	2 400	1 900	2 050	1 450	4 150	1 550	2 900	9.7
40,000	3 250	2 900	2 700	2 200	2 450	1 650	. .	1 750	3 200	8.0
50,000	3 550	3 150	3 000	2 500	2 800	1 850	. .	1 900	3 450	6.9
100,000	4 950	4 600	4 450	3 550	4 100	2 550	. .	2 100	4 550	4.6
150,000	6 300	5 900	5 600	4 250	5 050	3 000	. .	. .	5 450	3.6
200,000	7 550	7 000	6 600	4 800	5 800	3 400	. .	. .	6 250	3.1
300,000	9 500	8 900	8 100	5 650	6 950	. .	. .	. .	7 600	2.5
500,000	12 300	11 900	10 250	6 800	8 600	. .	. .	. .	9 900	2.0
1,000,000	16 450	17 500	13 400	. .	. .	. .	. .	. .	14 700	1.5
2,000,000	20 450	25 350	. .	. .	. .	. .	. .	. .	21 250	1.1
5,000,000	. .	. .	. .	. .	. .	. .	. .	. .	30 650	0.6
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	36 750	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%	6 700	5 400	4 900	2 800	3 200	1 500	2 600	1 500	6 000
RSE of 50%	1 800	1 500	1 300	800	900	500	600	400	1 300
(a) Refers to the number of people contributing to the estimate.