6227.0 - Education and Work, Australia, May 2001

ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 22/03/2002

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Explanatory Notes
Glossary
Data Quality (Technical Note)

ESTIMATION PROCEDURE

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 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 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 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 persons is as follows. Table 3 shows the estimated number of females enrolled to study for a bachelor degree was 320,400. Since this estimate is between 300,000 and 500,000, table T1 shows that the SE for Australia will lie between 7,650 and 9,300 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 312,600 to 328,200 and about 19 chances in 20 that the value will fall within the range 304,800 to 336,000. 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 so 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 aterisk (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%.

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 the previous page, the 320,400 females enrolled to study for a bachelor degree, represent 29% of the 1,108,400 females currently enrolled for a qualification. The SE of 320,400 was calculated previously as 7,800. To convert this to a RSE we express the SE as a percentage of the estimate, so the RSE is 7,800/320,400 = 2.4%. The SE for 1,108,400 may be calculated by interpolation as 12,600, which converted to a RSE is 12,600/1,108,400 = 1.1%. Applying the above formula, the RSE of the proportion is:

8 Therefore, the SE for the proportion (29%) is 0.6 percentage points (=(29/100)X2.1). Therefore, there are about two chances in three that the proportion of females currently enrolled for a qualification was between 28.4% and 29.6%, and 19 chances in 20 that the proportion is within the range 27.8% to 30.2%.

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

									AUST.

	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	SE	RSE

	no.	no.	no.	no.	no.	no.	no.	no.	no.	%

100	100	. .	. .	. .	. .	. .	. .	. .	80	80.0
200	170	180	. .	. .	. .	150	150	170	140	70.0
300	230	240	. .	270	280	180	180	190	200	66.7
500	340	340	420	330	350	220	220	230	290	58.0
700	430	420	490	380	410	250	260	250	370	52.9
1,000	550	530	580	440	480	290	290	280	470	47.0
1,500	720	670	690	520	570	340	350	330	610	40.7
2,000	860	790	790	590	650	380	390	360	730	36.5
2,500	1,000	900	850	650	700	400	400	400	850	34.0
3,000	1,100	1,000	950	700	750	450	450	400	950	31.7
3,500	1,200	1,050	1,000	750	800	500	500	450	1,050	30.0
4,000	1,300	1,150	1,100	800	850	500	500	450	1,100	27.5
5,000	1,450	1,250	1,200	850	950	550	550	500	1,250	25.0
7,000	1,700	1,500	1,400	1,000	1,100	650	650	600	1,550	22.1
10,000	2,050	1,750	1,600	1,150	1,250	700	700	650	1,850	18.5
15,000	2,450	2,100	1,900	1,350	1,500	850	850	800	2,250	15.0
20,000	2,800	2,350	2,200	1,500	1,650	950	950	900	2,600	13.0
30,000	3,300	2,750	2,600	1,800	1,950	1,100	1,050	1,050	3,150	10.5
40,000	3,650	3,100	2,900	2,000	2,200	1,250	1,200	1,150	3,550	8.9
50,000	3,950	3,300	3,200	2,200	2,350	1,350	1,300	1,300	3,900	7.8
100,000	4,950	4,200	4,250	2,900	3,050	1,750	1,650	1,750	5,100	5.1
150,000	5,600	4,850	5,050	3,400	3,500	2,000	1,900	2,100	5,900	3.9
200,000	6,150	5,450	5,650	3,800	3,900	2,250	2,100	2,400	6,550	3.3
300,000	7,200	6,450	6,650	4,450	4,450	2,600	. .	2,850	7,650	2.6
500,000	8,900	8,100	8,150	5,450	5,300	3,100	. .	. .	9,300	1.9
1,000,000	12,450	11,350	10,700	7,150	6,600	. .	. .	. .	12,150	1.2
2,000,000	18,300	16,450	13,950	9,350	8,150	. .	. .	. .	16,050	0.8
5,000,000	32,850	28,350	19,650	. .	. .	. .	. .	. .	24,600	0.5
10,000,000	. .	. .	. .	. .	. .	. .	. .	. .	43,150	0.4

. . not applicable