• Summary
• Downloads
• Explanatory Notes
• Related Information
• Past Releases

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 1 shows that the estimated number of people in Australia who were discouraged job seekers was 117,200. Since the estimate is between 100,000 and 150,000, table T1 shows that the SE for Australia will lie between 6,050 and 7,250 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 110,700 to 123,700 and about 19 chances in 20 that the value will fall within the range 104,200 to 130,200. This example is illustrated in the following diagram.

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 from paragraph 3, of the 117,200 people who were discouraged job seekers, 55,000 or 46.9% were females. The SE of 55,000 may be calculated by interpolation as 4,700. To convert this to an RSE we express the SE as a percentage of the estimate, or 4,700/55,000=8.5%. The SE for 117,200 was calculated previously as 6,500 which converted to an RSE is 6,500/117,200=5.5%. Applying the above formula, the RSE of the proportion is:

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.

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	180	150	200	170	170	110	80	120	140	140.0
200	300	230	330	250	260	160	110	210	240	120.0
300	390	290	440	310	330	200	130	270	320	106.7
500	530	400	600	400	440	250	170	370	460	92.0
700	650	480	730	470	520	290	200	430	580	82.9
1,000	800	580	900	560	620	340	240	500	730	73.0
1,500	990	710	1 120	670	760	400	290	580	940	62.7
2,000	1 150	820	1 300	760	860	440	330	630	1 120	56.0
2,500	1 300	900	1 450	850	950	450	350	650	1 250	50.0
3,000	1 400	1 000	1 600	900	1 050	500	400	700	1 400	46.7
3,500	1 500	1 050	1 700	950	1 100	550	450	750	1 500	42.9
4,000	1 600	1 150	1 800	1 000	1 150	550	500	750	1 650	41.3
5,000	1 800	1 250	2 000	1 100	1 250	600	550	850	1 800	36.0
7,000	2 100	1 450	2 300	1 250	1 450	700	750	1 000	2 150	30.7
10,000	2 400	1 650	2 650	1 400	1 600	850	1 000	1 300	2 500	25.0
15,000	2 800	1 950	3 050	1 650	1 900	1 050	1 400	1 700	3 000	20.0
20,000	3 150	2 150	3 350	1 900	2 150	1 200	1 800	2 000	3 350	16.8
30,000	3 600	2 500	3 900	2 350	2 700	1 500	2 450	2 450	3 850	12.8
40,000	4 000	2 750	4 400	2 750	3 200	1 750	3 000	2 750	4 250	10.6
50,000	4 350	3 000	4 850	3 100	3 650	1 950	3 500	2 950	4 600	9.2
100,000	6 050	4 350	7 150	4 450	5 350	2 700	5 450	3 350	6 050	6.1
150,000	7 700	5 600	9 050	5 350	6 600	3 200	6 900	3 350	7 250	4.8
200,000	9 200	6 650	10 600	6 050	7 600	3 600	. .	. .	8 300	4.2
300,000	11 600	8 450	13 050	7 100	9 100	4 200	. .	. .	10 100	3.4
500,000	15 000	11 350	16 500	8 550	11 300	5 000	. .	. .	13 200	2.6
1,000,000	20 050	16 750	21 650	10 600	14 600	. .	. .	. .	19 550	2.0
2,000,000	24 950	24 200	26 850	12 650	18 250	. .	. .	. .	28 300	1.4
5,000,000	30 000	38 550	32 900	. .	. .	. .	. .	. .	40 800	0.8
10,000,000	31 800	53 850	. .	. .	. .	. .	. .	. .	49 000	0.5
15,000,000	. .	. .	. .	. .	. .	. .	. .	. .	52 550	0.4

T2 levels at which estimates have a relative standard errors of 25% and 50%(a)
	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Australia
Percentage	no.	no.	no.	no.	no.	no.	no.	no.	no.
RSE of 25%	9 400	5 000	10 900	4 100	5 100	1 600	900	2 700	10 100
RSE of 50%	2 700	1 300	3 300	1 200	1 500	500	200	1 000	2 600