TECHNICAL NOTE DATA QUALITY


INTRODUCTION

1 Estimates in this publication are based on information obtained from occupants of a sample of dwellings, and 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 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 11 shows that 366,600 people involuntarily ceased their last job during the year and their duration in that job was less than 12 months. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,150 and 9,000 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 358,800 to 374,400 and about 19 chances in 20 that the value will fall within the range 351,000 to 382,200. This example is illustrated in the following diagram.

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.*3.2) 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%.


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 previous example from Table 11, of the 366,600 people who ceased their last job involuntarily during the year ending February 2013, and their duration of last job was less than 12 months, 210,900 or 57.5% gave their reason as 'Job was temporary or seasonal'. The SE of 210,900 may be calculated by interpolation as 6,200. To convert this to an RSE we express the SE as a percentage of the estimate, or 6,200/210,900 = 2.9%. The SE for 366,600 was calculated previously as 7,800, which converted to an RSE 7,800/366,600=2.1%. Applying the above formula, the RSE of the proportion is:



8 Therefore, the SE for the proportion of people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months is 1.2 percentage points (=(57.5/100)x2.0). Therefore, there are about two chances in three that the proportion of people who reported their reason for ceasing their last job as 'Job was temporary or seasonal' and their duration of last job was less than 12 months or more was between 56.3% and 58.7% and 19 chances in 20 that the proportion is within the range 55.1% to 59.9%.


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 sub populations, 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
	NSW	Vic.	Qld.	SA	WA	Tas.	NT	ACT	SE	RSE
Size of Estimate (persons)	no.	no.	no.	no.	no.	no.	no.	no.	no.	%
100	320	310	240	190	230	120	90	110	120	120.0
200	430	410	340	260	310	170	130	180	210	105.0
300	510	480	420	300	370	210	160	230	290	96.7
500	620	580	540	370	450	260	210	290	410	82.0
700	720	670	630	420	510	290	250	330	520	74.3
1,000	830	770	740	490	590	340	290	360	660	66.0
1,500	970	900	870	570	690	390	340	390	840	56.0
2,000	1 090	1 000	980	630	770	430	380	420	990	49.5
2,500	1 200	1 100	1 050	700	850	450	400	450	1 100	44.0
3,000	1 250	1 150	1 150	750	900	500	450	450	1 250	41.7
3,500	1 350	1 250	1 200	800	950	500	450	500	1 350	38.6
4,000	1 400	1 300	1 250	800	1 000	550	450	500	1 450	36.3
5,000	1 550	1 400	1 400	900	1 100	550	500	550	1 600	32.0
7,000	1 750	1 600	1 550	1 000	1 250	650	600	650	1 850	26.4
10,000	2 000	1 850	1 750	1 150	1 400	750	800	750	2 150	21.5
15,000	2 350	2 150	1 950	1 300	1 600	900	1 100	900	2 500	16.7
20,000	2 600	2 350	2 100	1 450	1 800	1 050	1 400	1 050	2 750	13.8
30,000	3 000	2 750	2 450	1 700	2 050	1 350	1 950	1 350	3 150	10.5
40,000	3 350	3 050	2 700	1 950	2 250	1 600	2 450	1 600	3 400	8.5
50,000	3 600	3 300	2 950	2 150	2 500	1 800	2 950	1 800	3 650	7.3
100,000	4 600	4 300	4 050	3 250	3 650	2 600	5 100	2 400	4 650	4.7
150,000	5 400	5 200	4 950	4 150	4 800	3 100	7 000	2 700	5 400	3.6
200,000	6 250	6 100	5 800	4 900	5 800	3 450	8 750	2 850	6 050	3.0
300,000	7 850	7 800	7 400	6 000	7 300	4 000	11 950	3 000	7 150	2.4
500,000	11 000	10 850	9 950	7 550	9 300	4 600	. .	3 000	9 000	1.8
1,000,000	16 300	16 500	14 250	9 600	11 850	5 250	. .	. .	12 700	1.3
2,000,000	21 950	24 350	19 150	11 450	13 700	. .	. .	. .	18 400	0.9
5,000,000	28 000	39 000	25 850	12 900	14 300	. .	. .	. .	30 700	0.6
10,000,000	30 000	53 750	30 200	. .	. .	. .	. .	. .	41 000	0.4
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	46 250	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.
Relative Standard Error of 25%	7 100	6 100	5 800	2 900	4 000	1 600	1 300	1 600	7 800
Relative Standard Error of 50%	2 300	2 000	1 900	1 000	1 300	500	400	600	2 000
(a) Refers to the number of people contributing to the estimate