6360.0 - Superannuation: Coverage and Financial Characteristics, Australia, Jun 2000

ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 17/09/2001

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TECHNICAL NOTE - SAMPLING VARIABILITY

MEASURING SAMPLING VARIABILITY

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. A table of SEs and RSEs for estimates of numbers of persons included in this publication appears at the end of this Technical note. These values do not give a precise measure of the SE or RSE for a particular estimate but will provide an indication of its magnitude.

CALCULATION OF STANDARD ERRORS

3. An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Consider the estimate for Australia of pre-retired persons with no superannuation, which is 2,836,200. Since this estimate is between 2,000,000 and 5,000,000 in the SE table, the SE for the estimate will be between 30,580 and 45,310 and can be approximated by interpolation as 34,700 (rounded to the nearest 100). 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 34,700 persons of the survey estimate, i.e. in the range 2,801,500 to 2,870,900, and about 19 chances in 20 that the value will fall within 69,400 persons of the survey estimate, i.e. in the range 2,766,800 to 2,905,600. This example is illustrated in the diagram below.

4. As can be seen from the SE table at the end of this note, the smaller the estimate the higher the RSE. Very small estimates are subject to very high SEs (relative to the size of the estimate). This detracts significantly from their value for most reasonable uses.

5. In the tables in this publication, only estimates with RSEs of less than 25%, and percentages based on such estimates, are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included. Estimates with RSEs between 25% and 50% are preceded by an asterisk (*) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (**) to indicate that they are considered too unreliable for general use.

6. The standard error can be calculated from the relative standard error and the estimate using the following formula.

SE =RSE x Estimate

PROPORTIONS AND PERCENTAGES

7. 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:

8. Consider the example above of the number of pre-retired persons with no superannuation (2,836,200). Of these, 1,304,400 or 46.0% were estimated to be male. The SE of 2,836,200 is approximately 34,700 so the RSE is 1.2%. The RSE for 1,304,400 is 1.9%. Applying the formula above, the RSE of the proportion is 1.5% giving a SE for the proportion (46.0%) of 0.68 percentage points. Therefore there are about two chances in three that the proportion of pre-retired persons with no superannuation who were male is between 45.3% and 46.7% and 19 chances in 20 the proportion is within the range 44.6% and 47.4%

9. Published estimates may also be used to calculate the difference between two survey estimates (numbers or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between the 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 be exact only for differences between separate and uncorrelated characteristics of subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.

11. The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by interviewers and respondents and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error and they may occur in any enumeration, whether it be a full count or a sample.

STANDARD ERRORS OF ESTIMATES
	Standard Error								Australia
Size of estimate (persons)	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Standard error	Relative standard error
	no.	no.	no.	no.	no.	no.	no.	no.	no.	%

400	0	0	0	0	0	0	0	230	460	115
500	0	0	0	0	0	320	0	260	520	104
600	0	0	0	0	0	350	400	290	570	95
700	0	0	0	0	0	370	430	310	620	89
800	0	0	0	0	0	400	460	330	670	84
900	0	0	0	0	0	420	480	350	710	79
1,000	0	0	0	0	0	440	510	370	750	75
1,100	0	0	0	0	0	460	530	390	790	72
1,200	0	0	0	650	700	480	550	410	830	69
1,300	0	0	0	680	730	500	570	420	870	67
1,400	0	0	0	710	760	520	590	440	900	64
1,500	0	0	0	730	780	530	610	460	940	63
1,600	0	0	950	760	810	550	620	470	970	61
1,700	0	0	980	780	840	570	640	480	1,000	59
1,800	0	1,080	1,010	800	860	580	660	500	1,030	57
1,900	0	1,110	1,030	830	890	600	670	510	1,060	56
2,000	0	1,140	1,060	850	910	610	690	520	1,090	55
2,100	0	1,170	1,090	870	930	630	700	530	1,120	53
2,200	0	1,200	1,120	890	960	640	720	550	1,150	52
2,300	0	1,230	1,140	910	980	660	730	560	1,170	51
2,400	0	1,250	1,170	930	1,000	670	750	570	1,200	50
2,500	1,440	1,280	1,190	950	1,020	680	760	580	1,230	49
3,000	1,580	1,410	1,310	1,040	1,120	740	830	630	1,350	45
3,500	1,710	1,530	1,420	1,120	1,210	800	880	680	1,460	42
4,000	1,830	1,640	1,520	1,200	1,300	850	940	720	1,570	39
4,500	1,940	1,740	1,620	1,270	1,370	900	990	760	1,670	37
5,000	2,050	1,840	1,710	1,340	1,450	950	1,040	800	1,760	35
6,000	2,240	2,020	1,870	1,460	1,590	1,040	1,120	860	1,940	32
8,000	2,590	2,330	2,160	1,680	1,830	1,190	1,280	980	2,240	28
10,000	2,890	2,600	2,420	1,860	2,040	1,320	1,410	1,080	2,510	25
20,000	4,050	3,650	3,400	2,560	2,860	1,840	1,920	1,430	3,560	18
30,000	4,930	4,420	4,140	3,070	3,470	2,230	2,300	1,680	4,360	15
40,000	5,650	5,050	4,760	3,480	3,980	2,560	2,620	1,880	5,020	13
50,000	6,280	5,590	5,290	3,840	4,420	2,850	2,890	2,040	5,590	11
100,000	8,700	7,630	7,320	5,130	6,080	3,970	3,940	2,610	7,810	8
200,000	11,970	10,300	10,070	6,790	8,310	5,530	5,360	3,300	10,820	5
300,000	14,400	12,200	12,090	7,960	9,950	6,710	0	3,750	13,070	4
400,000	16,390	13,740	13,740	8,880	11,280	7,700	0	0	14,910	4
500,000	18,120	15,040	15,160	9,660	12,430	0	0	0	16,510	3
1,000,000	24,620	19,760	20,490	12,440	16,700	0	0	0	22,540	2
2,000,000	33,280	25,680	27,490	15,830	22,280	0	0	0	30,580	2
5,000,000	49,130	35,680	40,100	0	0	0	0	0	45,310	1
10,000,000	0	0	0	0	0	0	0	0	60,540	1
15,000,000	0	0	0	0	0	0	0	0	71,500	0

ESTIMATES WITH RELATIVE STANDARD ERRORS OF 25% AND 50%
Size of estimate (persons)	NSW	Vic.	Qld	SA	WA	Tas.	NT	ACT	Aust.
	no.	no.	no.	no.	no.	no.	no.	no.	no.

Estimates with RSEs of 25%	13277	10825	9356	5705	6718	2956	3566	2175	10115
Estimates with RSEs of 50%	3348	2638	2272	1429	1643	784	1022	551	2405