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