TECHNICAL NOTE RELIABILITY OF ESTIMATES
RELIABILITY OF THE ESTIMATES
1 As the estimates in this publication are based on information obtained from a sample of households and persons, they are subject to sampling variability. That is, they may differ from the figures that would have been produced if all households and persons in Australia 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 households and persons was included. There are about 2 chances in 3 that a sample estimate will differ by less than one SE from the figure that would have been obtained if all households and persons had been included in the survey, and about 19 chances in 20 that the difference will be less than two SEs.
2 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.
3 In the tables in this publication, only estimates (numbers and percentages) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are annotated to indicate they are subject to higher SEs and should be used with caution. Estimates with RSEs of 10% to less than 25% are preceded by a ^, and estimates with RSEs of 25% to 50% are preceded by an asterix (*) to indicate that they 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.
4 To assist readers of this publication to ascertain the approximate levels of reliability of estimates throughout this publication, tables of SEs and RSEs for certain estimates of population counts for the data appear at the end of this Technical Note. These values do not give a precise measure of the SEs or RSEs for a particular estimate but will provide an indication of their magnitude.
USING STANDARD ERRORS FOR POPULATION ESTIMATES
5 An example of the use of SEs in relation to estimates is as follows.
6 From table 4.1, it is estimated that 4,730,000 households accessed the Internet using a home computer in 2005-06. This estimate has a SE around 39,000. This means there are about two chances in three that the value that would have been obtained from a complete census is within the range 4,691,000 to 4,769,000 households and about 19 chances in 20 that the true value is in the range 4,652,000 to 4,808,000 households.
7 Particular care should be taken when comparing figures over time. It is not correct to assume that an apparent difference between figures is actually significant. Such an estimate is subject to sampling error. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:
8 The estimated increase in the number of households with home internet access from the previous year was 337,000 (from 4,393,000 in 2004-05 to 4,730,000 in 2005-06). The SE on the movement is around 55,000. There are 2 chances in 3 that the true value is within the range 282,000 to 392,000 households and 19 chances in 20 that the true value is in the range 227,000 to 447,000 households.
9 Improved modelling techniques have resulted in some differences between SEs for states and territories in 2005-06 with those from 2004-05. The ABS considers 2005-06 estimates for SEs to be more accurate.
TABLES OF STANDARD ERRORS AND RELATIVE STANDARD ERRORS
Standard errors of household estimates-2005-06 |
| |
| | STANDARD ERROR | AUSTRALIA | |
| | NSW | Vic. | Qld | SA | WA | Tas. | NT | ACT | Standard error | Relative standard error | |
| | no. | no. | no. | no. | no. | no. | no. | no. | no. | % | |
| |
Size of estimate | | | | | | | | | | | |
| 100 | 140 | 180 | 160 | 110 | 140 | 120 | 130 | 120 | 180 | 180 | |
| 200 | 250 | 280 | 260 | 200 | 240 | 190 | 210 | 190 | 280 | 140 | |
| 300 | 330 | 370 | 340 | 270 | 310 | 240 | 280 | 240 | 360 | 120 | |
| 500 | 480 | 510 | 460 | 380 | 440 | 320 | 380 | 320 | 490 | 98 | |
| 700 | 610 | 620 | 570 | 480 | 550 | 390 | 460 | 390 | 600 | 86 | |
| 1,000 | 780 | 770 | 710 | 610 | 690 | 470 | 560 | 480 | 740 | 74 | |
| 1,500 | 1 020 | 980 | 900 | 780 | 870 | 580 | 680 | 580 | 930 | 62 | |
| 2,000 | 1 220 | 1 150 | 1 070 | 920 | 1 020 | 670 | 780 | 670 | 1 100 | 55 | |
| 2,500 | 1 400 | 1 300 | 1 200 | 1 050 | 1 150 | 750 | 850 | 750 | 1 250 | 50 | |
| 3,000 | 1 550 | 1 450 | 1 350 | 1 150 | 1 300 | 800 | 950 | 800 | 1 400 | 47 | |
| 3,500 | 1 700 | 1 550 | 1 450 | 1 250 | 1 400 | 900 | 1 000 | 850 | 1 500 | 43 | |
| 4,000 | 1 850 | 1 700 | 1 550 | 1 350 | 1 500 | 950 | 1 050 | 900 | 1 600 | 40 | |
| 5,000 | 2 100 | 1 900 | 1 750 | 1 500 | 1 650 | 1 050 | 1 150 | 1 000 | 1 850 | 37 | |
| 7,000 | 2 550 | 2 250 | 2 100 | 1 750 | 1 950 | 1 200 | 1 300 | 1 150 | 2 200 | 31 | |
| 10,000 | 3 050 | 2 700 | 2 500 | 2 050 | 2 300 | 1 350 | 1 450 | 1 300 | 2 650 | 27 | |
| 15,000 | 3 750 | 3 300 | 3 050 | 2 450 | 2 700 | 1 600 | 1 600 | 1 450 | 3 250 | 22 | |
| 20,000 | 4 350 | 3 750 | 3 500 | 2 750 | 3 050 | 1 750 | 1 700 | 1 600 | 3 800 | 19 | |
| 30,000 | 5 250 | 4 500 | 4 250 | 3 150 | 3 550 | 2 000 | 1 900 | 1 800 | 4 650 | 16 | |
| 40,000 | 5 950 | 5 100 | 4 800 | 3 500 | 3 950 | 2 200 | 1 950 | 1 900 | 5 350 | 13 | |
| 50,000 | 6 550 | 5 650 | 5 300 | 3 700 | 4 250 | 2 350 | 2 050 | 2 000 | 5 950 | 12 | |
| 100,000 | 8 600 | 7 450 | 7 050 | 4 500 | 5 250 | 2 800 | 2 200 | 2 300 | 8 200 | 8 | |
| 150,000 | 10 000 | 8 750 | 8 250 | 4 900 | 5 850 | 3 050 | 2 230 | 2 450 | 9 850 | 7 | |
| 200,000 | 11 000 | 9 700 | 9 150 | 5 200 | 6 250 | 3 250 | 2 240 | 2 500 | 11 200 | 6 | |
| 300,000 | 12 550 | 11 200 | 10 600 | 5 550 | 6 850 | 3 500 | - | 2 600 | 13 350 | 5 | |
| 500,000 | 14 550 | 13 300 | 12 600 | 5 900 | 7 500 | 3 750 | - | - | 16 550 | 3 | |
| 1,000,000 | 17 300 | 16 450 | 15 600 | 6 200 | 8 250 | - | - | - | 21 900 | 2 | |
| 2,000,000 | 20 000 | 19 950 | 18 950 | 6 300 | 8 800 | - | - | - | 28 550 | 1 | |
| 5,000,000 | 23 050 | 24 950 | 23 750 | - | - | - | - | - | 39 750 | 1 | |
| 10,000,000 | - | - | - | - | - | - | - | - | 50 300 | 1 | |
| |
- nil or rounded to zero (including null cells) |
Household estimates with relative standard errors of 25% to 50%-2005-06 |
| |
| | NSW | Vic. | Qld | SA | WA | Tas. | NT | ACT | Aust. | |
| | no. | no. | no. | no. | no. | no. | no. | no. | no. | |
| |
Size of estimate | | | | | | | | | | |
| Estimate with RSEs of 25% | 15 158 | 11 595 | 10 104 | 7 068 | 8 495 | 3 515 | 4 332 | 3 392 | 11 312 | |
| Estimate with RSEs of 30% | 10 472 | 8 088 | 6 990 | 4 981 | 6 041 | 2 505 | 3 205 | 2 451 | 7 704 | |
| Estimate with RSEs of 35% | 7 549 | 5 912 | 5 069 | 3 643 | 4 470 | 1 860 | 2 454 | 1 840 | 5 528 | |
| Estimate with RSEs of 40% | 5 615 | 4 473 | 3 807 | 2 738 | 3 408 | 1 424 | 1 926 | 1 420 | 4 124 | |
| Estimate with RSEs of 45% | 4 278 | 3 477 | 2 938 | 2 100 | 2 657 | 1 117 | 1 541 | 1 120 | 3 170 | |
| Estimate with RSEs of 50% | 3 322 | 2 761 | 2 317 | 1 636 | 2 110 | 892 | 1 252 | 899 | 2 496 | |
| |
STANDARD ERRORS OF PERSON ESTIMATES-2005-06 |
| |
| | STANDARD ERROR | AUSTRALIA | |
| | NSW | VIC | Qld | SA | WA | Tas. | NT | ACT | Standard error | Relative standard error | |
| | no. | no. | no. | no. | no. | no. | no. | no. | no. | % | |
| |
Size of estimate | | | | | | | | | | | |
| 100 | 210 | 210 | 230 | 120 | 150 | 120 | 130 | 140 | 170 | 170 | |
| 200 | 360 | 350 | 380 | 230 | 270 | 210 | 230 | 240 | 290 | 145 | |
| 300 | 490 | 460 | 500 | 310 | 370 | 290 | 320 | 320 | 390 | 130 | |
| 500 | 700 | 650 | 690 | 470 | 540 | 420 | 470 | 450 | 560 | 112 | |
| 700 | 880 | 820 | 860 | 600 | 690 | 530 | 600 | 550 | 710 | 101 | |
| 1,000 | 1 120 | 1 030 | 1 080 | 780 | 890 | 670 | 760 | 690 | 910 | 91 | |
| 1,500 | 1 470 | 1 340 | 1 380 | 1 030 | 1 170 | 870 | 980 | 870 | 1 190 | 79 | |
| 2,000 | 1 770 | 1 600 | 1 640 | 1 250 | 1 400 | 1 030 | 1 150 | 1 020 | 1 440 | 72 | |
| 2,500 | 2 050 | 1 850 | 1 850 | 1 450 | 1 600 | 1 200 | 1 300 | 1 150 | 1 650 | 66 | |
| 3,000 | 2 300 | 2 050 | 2 100 | 1 600 | 1 800 | 1 300 | 1 450 | 1 250 | 1 850 | 62 | |
| 3,500 | 2 500 | 2 250 | 2 250 | 1 800 | 2 000 | 1 450 | 1 550 | 1 350 | 2 050 | 59 | |
| 4,000 | 2 700 | 2 400 | 2 450 | 1 900 | 2 150 | 1 550 | 1 650 | 1 450 | 2 250 | 56 | |
| 5,000 | 3 100 | 2 750 | 2 800 | 2 200 | 2 450 | 1 750 | 1 850 | 1 600 | 2 550 | 51 | |
| 7,000 | 3 800 | 3 350 | 3 350 | 2 650 | 2 900 | 2 050 | 2 150 | 1 900 | 3 150 | 45 | |
| 10,000 | 4 650 | 4 050 | 4 050 | 3 200 | 3 500 | 2 450 | 2 500 | 2 200 | 3 900 | 39 | |
| 15,000 | 5 800 | 5 050 | 5 000 | 3 950 | 4 300 | 3 000 | 2 900 | 2 600 | 4 900 | 33 | |
| 20,000 | 6 750 | 5 850 | 5 800 | 4 550 | 4 950 | 3 400 | 3 150 | 2 850 | 5 750 | 29 | |
| 30,000 | 8 350 | 7 200 | 7 150 | 5 500 | 5 900 | 4 050 | 3 550 | 3 300 | 7 200 | 24 | |
| 40,000 | 9 650 | 8 300 | 8 200 | 6 200 | 6 650 | 4 500 | 3 850 | 3 600 | 8 400 | 21 | |
| 50,000 | 10 750 | 9 200 | 9 150 | 6 800 | 7 300 | 4 900 | 4 000 | 3 850 | 9 400 | 19 | |
| 100,000 | 14 900 | 12 650 | 12 550 | 8 800 | 9 400 | 6 250 | 4 550 | 4 600 | 13 300 | 13 | |
| 150,000 | 17 900 | 15 100 | 15 050 | 10 100 | 10 700 | 7 050 | 4 750 | 5 000 | 16 150 | 11 | |
| 200,000 | 20 250 | 17 050 | 17 000 | 11 000 | 11 650 | 7 650 | 4 850 | 5 300 | 18 450 | 9 | |
| 300,000 | 23 950 | 20 050 | 20 150 | 12 300 | 13 050 | 8 500 | - | 5 650 | 22 100 | 7 | |
| 500,000 | 29 300 | 24 400 | 24 650 | 13 900 | 14 700 | 9 550 | - | - | 27 500 | 6 | |
| 1,000,000 | 37 750 | 31 250 | 32 050 | 15 900 | 16 850 | - | - | - | 36 350 | 4 | |
| 2,000,000 | 47 550 | 39 200 | 40 850 | 17 550 | 18 550 | - | - | - | 47 100 | 2 | |
| 5,000,000 | 62 400 | 51 200 | 54 850 | - | - | - | - | - | 64 250 | 1 | |
| 10,000,000 | - | - | - | - | - | - | - | - | 79 400 | 1 | |
| 15,000,000 | - | - | - | - | - | - | - | - | 89 000 | 1 | |
| 20,000,000 | - | - | - | - | - | - | - | - | 96 150 | 1 | |
| |
- nil or rounded to zero (including null cells) |
Person estimates with relative standard errors of 25% to 50%-2005-06 |
| |
| | NSW no. | Vic no. | Qld no. | SA no. | WA no. | Tas. no. | NT no. | ACT no. | Aust. no. | |
| |
Size of estimate | | | | | | | | | | |
| Estimate with RSEs of 25% | 37 183 | 27 628 | 27 148 | 16 728 | 19 497 | 9 741 | 9 923 | 7 974 | 27 433 | |
| Estimate with RSEs of 30% | 25 635 | 19 081 | 18 803 | 11 610 | 13 780 | 6 767 | 7 300 | 5 747 | 18 321 | |
| Estimate with RSEs of 35% | 18 521 | 13 816 | 13 672 | 8 376 | 10 130 | 4 894 | 5 547 | 4 302 | 12 861 | |
| Estimate with RSEs of 40% | 13 855 | 10 361 | 10 307 | 6 216 | 7 666 | 3 647 | 4 316 | 3 312 | 9 369 | |
| Estimate with RSEs of 45% | 10 648 | 7 984 | 7 991 | 4 712 | 5 932 | 2 780 | 3 418 | 2 605 | 7 023 | |
| Estimate with RSEs of 50% | 8 361 | 6 288 | 6 335 | 3 631 | 4 670 | 2 157 | 2 745 | 2 084 | 5 386 | |
| |
Standard errors of number of children aged 5-14 years estimate, 2006 |
| |
| | STANDARD ERROR | AUSTRALIA | |
| | NSW | Vic. | Qld. | SA | WA | Tas. | NT | ACT | Standard error | Relative standard error | |
| | no. | no. | no. | no. | no. | no. | no. | no. | no. | % | |
| |
Size of estimate | | | | | | | | | | | |
| 300 | 430.0 | 360.0 | 370.0 | 270.0 | 300.0 | 210.0 | 210.0 | 220.0 | 300.0 | 100.0 | |
| 500 | 550.0 | 470.0 | 460.0 | 340.0 | 400.0 | 270.0 | 270.0 | 280.0 | 400.0 | 80.0 | |
| 700 | 640.0 | 560.0 | 540.0 | 400.0 | 470.0 | 320.0 | 330.0 | 330.0 | 480.0 | 68.6 | |
| 1000 | 760.0 | 670.0 | 640.0 | 470.0 | 560.0 | 370.0 | 390.0 | 390.0 | 580.0 | 58.0 | |
| 1500 | 920.0 | 810.0 | 760.0 | 560.0 | 690.0 | 450.0 | 470.0 | 460.0 | 720.0 | 48.0 | |
| 2000 | 1 050.0 | 940.0 | 870.0 | 640.0 | 790.0 | 510.0 | 540.0 | 520.0 | 840.0 | 42.0 | |
| 2500 | 1 150.0 | 1 050.0 | 950.0 | 700.0 | 900.0 | 550.0 | 600.0 | 580.0 | 950.0 | 38.0 | |
| 3000 | 1 250.0 | 1 150.0 | 1 050.0 | 750.0 | 950.0 | 600.0 | 650.0 | 620.0 | 1 050.0 | 35.0 | |
| 3500 | 1 350.0 | 1 200.0 | 1 100.0 | 800.0 | 1 050.0 | 650.0 | 700.0 | 650.0 | 1 100.0 | 31.4 | |
| 4000 | 1 450.0 | 1 300.0 | 1 200.0 | 850.0 | 1 100.0 | 700.0 | 750.0 | 700.0 | 1 200.0 | 30.0 | |
| 5000 | 1 600.0 | 1 450.0 | 1 300.0 | 950.0 | 1 200.0 | 750.0 | 800.0 | 750.0 | 1 350.0 | 27.0 | |
| 7000 | 1 900.0 | 1 700.0 | 1 550.0 | 1 100.0 | 1 400.0 | 850.0 | 900.0 | 900.0 | 1 600.0 | 22.9 | |
| 10000 | 2 250.0 | 2 000.0 | 1 800.0 | 1 300.0 | 1 650.0 | 950.0 | 1 050.0 | 1 000.0 | 1 900.0 | 19.0 | |
| 15000 | 2 700.0 | 2 350.0 | 2 200.0 | 1 550.0 | 1 950.0 | 1 100.0 | 1 200.0 | 1 200.0 | 2 350.0 | 15.7 | |
| 20000 | 3 050.0 | 2 700.0 | 2 500.0 | 1 750.0 | 2 200.0 | 1 200.0 | 1 300.0 | 1 350.0 | 2 700.0 | 13.5 | |
| 30000 | 3 700.0 | 3 200.0 | 3 000.0 | 2 050.0 | 2 650.0 | 1 350.0 | 1 500.0 | 1 550.0 | 3 250.0 | 10.8 | |
| 40000 | 4 200.0 | 3 600.0 | 3 450.0 | 2 300.0 | 2 950.0 | 1 450.0 | 1 650.0 | 1 750.0 | 3 750.0 | 9.4 | |
| 50000 | 4 650.0 | 3 950.0 | 3 800.0 | 2 550.0 | 3 250.0 | 1 550.0 | - | 1 900.0 | 4 150.0 | 8.3 | |
| 100000 | 6 350.0 | 5 200.0 | 5 250.0 | 3 400.0 | 4 200.0 | 1 850.0 | - | - | 5 750.0 | 5.8 | |
| 150000 | 7 600.0 | 6 100.0 | 6 300.0 | 4 000.0 | 4 900.0 | - | - | - | 6 950.0 | 4.6 | |
| 200000 | 8 650.0 | 6 800.0 | 7 200.0 | 4 500.0 | 5 450.0 | - | - | - | 7 900.0 | 4.0 | |
| 300000 | 10 350.0 | 7 900.0 | 8 700.0 | - | 6 300.0 | - | - | - | 9 450.0 | 3.2 | |
| 500000 | 13 000.0 | 9 500.0 | 11 050.0 | - | - | - | - | - | 11 850.0 | 2.4 | |
| 1000000 | 17 600.0 | 12 150.0 | 15 250.0 | - | - | - | - | - | 15 950.0 | 1.6 | |
| 2000000 | - | - | - | - | - | - | - | - | 21 350.0 | 1.1 | |
| 5000000 | - | - | - | - | - | - | - | - | 31 000.0 | 0.6 | |
| 10000000 | - | - | - | - | - | - | - | - | - | . . | |
| |
. . not applicable |
- nil or rounded to zero (including null cells) |
Estimates with relative standard errors of 25% to 50%, number of children aged 5-14 years, 2006 |
| |
| | NSW | Vic. | Qld | SA | WA | Tas. | NT | ACT | Aust. | |
| | no. | no. | no. | no. | no. | no. | no. | no. | no. | |
| |
Size of Estimates | | | | | | | | | | |
| Estimate with RSEs of 25% | 8 077 | 6 522 | 5 545 | 3 102 | 4 729 | 2 078 | 2 302 | 2 173 | 5 819 | |
| Estimate with RSEs of 30% | 5 752 | 4 655 | 3 964 | 2 236 | 3 372 | 1 502 | 1 650 | 1 572 | 4 015 | |
| Estimate with RSEs of 35% | 4 313 | 3 487 | 2 986 | 1 693 | 2 522 | 1 133 | 1 233 | 1 191 | 2 924 | |
| Estimate with RSEs of 40% | 3 359 | 2 707 | 2 336 | 1 329 | 1 955 | 881 | 951 | 935 | 2 216 | |
| Estimate with RSEs of 45% | 2 692 | 2 160 | 1 882 | 1 073 | 1 557 | 702 | 752 | 753 | 1 731 | |
| Estimate with RSEs of 50% | 2 208 | 1 762 | 1 551 | 885 | 1 267 | 571 | 606 | 620 | 1 386 | |
| |