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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 persons is as follows. Table 5 shows the estimated number of female part-time employees in main job was 1,929,000. Since this estimate is between 1,000,000 and 2,000,000, table T1 shows that the SE for Australia will lie between 10,550 and 15,300 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 1,914,000 to 1,944,000 and about 19 chances in 20 that the value will fall within the range 1,899,000 to 1,959,000. 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 less than 25%.


MEANS AND MEDIANS

6 The RSEs of estimates of mean and median weekly earnings (see paragraphs 18 and 19 of the Explanatory Notes) are obtained by first finding the RSE of the estimate of the total number of persons contributing to the estimate (see table T1) and then multiplying the resulting number by the following factors:

mean weekly earnings: 0.9
median weekly earnings: 1.0

T1 STANDARD ERRORS OF ESTIMATES
									Aust.
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	SE	RSE
Size of estimates (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	270	260	190	160	180	100	110	90	100	100.0
200	360	340	280	210	240	150	160	140	170	85.0
300	430	400	340	250	280	180	200	180	240	80.0
500	530	490	440	310	340	220	260	230	340	68.0
700	610	550	510	350	390	250	310	260	430	61.4
1,000	700	640	590	400	450	290	360	290	550	55.0
1,500	830	740	700	470	520	340	420	310	700	46.7
2,000	930	830	790	530	580	370	470	330	830	41.5
2,500	1 000	900	850	550	650	400	500	350	950	38.0
3,000	1 100	950	900	600	700	400	550	350	1 050	35.0
3,500	1 150	1 050	1 000	650	700	450	550	400	1 100	31.4
4,000	1 200	1 100	1 050	700	750	450	600	400	1 200	30.0
5,000	1 300	1 150	1 100	750	800	500	650	450	1 350	27.0
7,000	1 500	1 350	1 250	850	950	550	750	500	1 550	22.1
10,000	1 700	1 500	1 400	950	1 050	650	1 000	600	1 800	18.0
15,000	2 000	1 750	1 550	1 100	1 200	800	1 350	700	2 100	14.0
20,000	2 200	1 950	1 700	1 200	1 350	900	1 750	850	2 300	11.5
30,000	2 550	2 250	1 950	1 400	1 550	1 150	2 400	1 050	2 600	8.7
40,000	2 850	2 500	2 200	1 600	1 700	1 400	3 050	1 250	2 850	7.1
50,000	3 100	2 750	2 400	1 800	1 900	1 600	3 650	1 450	3 050	6.1
100,000	3 950	3 550	3 250	2 700	2 750	2 250	6 300	1 900	3 850	3.9
150,000	4 600	4 350	4 000	3 450	3 650	2 700	. .	2 150	4 500	3.0
200,000	5 300	5 050	4 700	4 050	4 400	3 000	. .	2 300	5 050	2.5
300,000	6 700	6 500	5 950	5 000	5 500	. .	. .	. .	5 950	2.0
500,000	9 350	9 000	8 050	6 250	7 000	. .	. .	. .	7 500	1.5
1,000,000	13 900	13 700	11 500	8 000	8 950	. .	. .	. .	10 550	1.1
2,000,000	18 750	20 250	15 450	. .	. .	. .	. .	. .	15 300	0.8
5,000,000	23 900	32 400	. .	. .	. .	. .	. .	. .	25 550	0.5
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	34 100	0.3
. . not applicable

T2 LEVELS AT WHICH ESTIMATES HAVE RSE'S 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 weekly earnings	4 900	4 200	3 200	1 600	2 200	1 000	800	1 000	4 900
Median weekly earnings	5 500	4 600	4 100	2 100	2 700	1 200	1 100	1 200	6 000
All other estimates	5 500	4 500	4 200	2 200	2 600	1 300	1 800	1 200	5 600
50% RSE
Mean weekly earnings	1 600	1 400	1 000	500	700	300	200	400	1 000
Median weekly earnings	1 800	1 500	1 300	700	900	400	300	400	1 400
All other estimates	1 800	1 500	1 300	700	800	400	600	400	1 300
(a) Refers to the number of people contributing to the estimate.