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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 ERROR

3 An example of the calculation and the use of SEs in relation to estimates of people is as follows. Table 3 shows the estimated number of employed men in Australia, whose main location of work in their main job was at their own home, to be 277,400. Since this estimate is between 200,000 and 300,000, table T1 shows that the SE for Australia will lie between 5,300 and 6,350 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 within the range 271,300 to 283,500 and about 19 chances in 20 that the value will fall within the range 265,200 to 289,600. This example is illustrated in the diagram below.

MEANS

6 The RSEs of estimates of mean actual hours worked at home in main or second job is obtained by first finding the RSE of the estimate of the total number of people contributing to the mean (see table T1) and then multiplying the resulting number by the following factors:

• mean actual hours worked: 0.8

8 The RSE of the estimate of mean actual hours worked at home in second job for men, who did some work at home, is calculated by multiplying this number (4.3%) by the appropriate factor shown in the previous paragraph (in this case 0.8): 4.3 x 0.8 = 3.4%. The SE of this estimate of mean actual hours worked at home in second job for males, who did some work at home, is therefore 3.4% of 9.6, i.e. 0.3 of one hour. Therefore, there are two chances in three that the mean actual hours worked at home in second job for men, who did some work at home, that would have been obtained if all dwellings had been included in the survey would have been within the range 9.3 hours to 9.9 hours, and about 19 chances in 20 that it would have been within the range 9.0 hours to 10.2 hours.

PROPORTIONS AND PERCENTAGES

9 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.

10 Considering the example from the previous page, of the 277,400 employed men whose main location of work was at their own home, 92,200 or 33.2% had child(ren) under the age of 15. The SE of 92,200 may be calculated by interpolation as 3,900. To convert this to an RSE we express the SE as a percentage of the estimate, or 3,900/92,200 = 4.2%. The SE for 277,400 was calculated previously as 6,100, which converted to an RSE is 6,100/277,400 = 2.2%. Applying the above formula, the RSE of the proportion is

11 Therefore, the SE for the proportion of employed men whose main location of work was at their own home who had child(ren) under the age of 15 is 1.2 percentage points (=(33.2/100)x3.6). Therefore, there are about two chances in three that the proportion of employed men, whose main location of work was at their own home, who had child(ren) under the age of 15 is between 32.0% and 34.4%, and 19 chances in 20 that the proportion is within the range 30.8% to 35.6%.

DIFFERENCES

12 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:

13 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	290	250	250	150	160	100	100	140	100	100.0
200	380	330	330	210	220	140	150	180	180	90.0
300	440	390	390	250	260	180	190	200	240	80.0
500	540	470	470	300	330	220	260	230	350	70.0
700	620	540	540	350	380	260	300	260	430	61.4
1,000	710	620	610	400	440	300	360	280	540	54.0
1,500	830	730	710	470	520	340	420	320	690	46.0
2,000	920	810	790	530	590	370	470	340	820	41.0
2,500	1 000	900	850	550	650	400	500	350	900	36.0
3,000	1 100	950	900	600	700	400	550	400	1 000	33.3
3,500	1 150	1 000	950	650	750	450	550	400	1 100	31.4
4,000	1 200	1 050	1 000	700	750	450	600	400	1 200	30.0
5,000	1 300	1 150	1 100	750	850	500	650	450	1 300	26.0
7,000	1 500	1 300	1 250	850	950	550	750	500	1 550	22.1
10,000	1 700	1 500	1 400	950	1 100	650	950	600	1 800	18.0
15,000	2 000	1 750	1 600	1 100	1 250	800	1 300	750	2 100	14.0
20,000	2 200	1 950	1 800	1 200	1 400	950	1 600	850	2 300	11.5
30,000	2 600	2 300	2 050	1 450	1 600	1 250	2 200	1 100	2 650	8.8
40,000	2 850	2 550	2 250	1 700	1 750	1 500	2 800	1 350	2 900	7.3
50,000	3 100	2 800	2 450	1 900	1 950	1 750	3 350	1 500	3 100	6.2
100,000	4 050	3 600	3 400	2 900	3 050	2 600	5 950	2 050	4 000	4.0
150,000	4 800	4 350	4 250	3 700	4 100	3 200	8 450	2 350	4 700	3.1
200,000	5 550	5 200	5 100	4 400	4 950	3 650	10 900	2 450	5 300	2.7
300,000	7 100	6 800	6 800	5 450	6 250	4 300	15 750	2 550	6 350	2.1
500,000	9 950	9 300	9 550	6 900	7 950	5 150	. .	2 550	8 100	1.6
1,000,000	14 950	13 700	13 500	9 000	10 050	6 250	. .	. .	11 600	1.2
2,000,000	21 350	19 350	16 550	11 000	11 400	. .	. .	. .	17 150	0.9
5,000,000	31 500	28 550	17 350	13 000	11 500	. .	. .	. .	29 250	0.6
10,000,000	39 750	36 450	15 250	. .	. .	. .	. .	. .	39 200	0.4
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	44 050	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.
25% RSE
Mean hours actually worked at home	3 400	2 900	2 600	1 400	1 700	800	800	800	3 200
All other estimates	5 400	4 400	4 100	2 200	2 600	1 300	1 800	1 200	5 500
50% RSE
Mean hours actually worked at home	1 100	900	800	400	500	200	200	300	600
All other estimates	1 800	1 400	1 400	700	800	400	500	400	1 200
(a) Refers to the number of people contributing to the estimate.