4602.0 - Environmental Issues: People's Views and Practices, Mar 2004
Previous ISSUE Released at 11:30 AM (CANBERRA TIME) 24/11/2004
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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 2 chances in 3 (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, tables of SEs are provided to enable readers to determine the SE for an estimate from the size of that estimate (see tables T1 and T2). Each SE table is derived from a mathematical model, referred to as the "SE model", which is created using the data collected in this survey. 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.

3 This publication contains estimates for persons and households. Table T1 gives SEs for estimates of households, while SEs for estimates of persons are presented in T2. Tables containing estimates of households are found in Chapters 3 and 4, while Chapters 2 and 5 contains estimates of persons.

CALCULATION OF STANDARD ERROR

4 An example of the calculation and the use of SEs in relation to estimates of persons is as follows. Table 2.15 shows that the estimated number of persons in Australia who used signed petition as a means of registering an environmental concern was 390,700. Since this estimate is between 300,000 and 500,000, table T2 shows that the SE for Australia will lie between 18,550 and 23,550 and can be approximated by interpolation using the following general formula:

5 Therefore, there are about 2 chances in 3 that the value that would have been produced if all persons had been included in the survey will fall within the range 369,900 to 411,500 and about 19 chances in 20 that the value will fall within the range 349,100 to 432,300. This example is illustrated in the diagram below.

6 Similarly, SEs are calculated for household level estimates using table T1 instead of table T2. For example, table 3.23 shows that the estimated number of households in Victoria who have mains/town water as main source of water for gardening was 1,180,500. This estimate is between 1,000,000 and 2,000,000, so the SE for this estimate will be between 16,800 and 18,100, and can be approximated using the same interpolation formula as above, with the resulting SE being 17,000 (rounded to the nearest 100).

7 Therefore, there are about 2 chances in 3 that the value that would have been produced if all households in the population had been included in the survey will fall within the range 1,163,500 to 1,197,500 and about 19 chances in 20 that the value will fall within the range 1,146,500 to 1,214,500.

8 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% are preceded by an asterisk (e.g. *1.8) to indicate they are subject to high SEs and should be used with caution.

PROPORTIONS AND PERCENTAGES

9 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.

10 For example, in table 2.15, the estimate for the total number of persons aged 18 years and over, who registered an environmental concern in Australia was 1,090,800. The estimated number of persons who used signed petition as a means of registering that concern was 390,700, so the proportion of persons in Australia who registered an environmental concern by signed petition is 390,700/1,090,800 or 35.8%. The SE of the total number of persons in Australia registering an environmental concern may be calculated by interpolation as 33,026 or 33,000 rounded to the nearest 100. To convert this to a RSE we express the SE as a percentage of the estimate, or 33,000/1,090,800 = 3.1%. The SE for the number of persons in Australia who registerd environmental concerns by signed petition was calculated above as 20,800, which converted to a RSE is 20,800/ 390,700 = 5.3%. Applying the above formula, the RSE of the proportion is ; giving a SE for the proportion (35.8%) of 1.5 percentage points (=35.8**0.043).

11 Therefore, there are about 2 chances in 3 that the proportion of persons in Australia who registered an environmental concern by means of signed petition is between 34.3% and 37.3% and 19 chances in 20 that the proportion is within the range 32.8% to 38.8%.

12 Similarly, SEs can be calculated for household level estimates using the same formula.

DIFFERENCES

13 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:

14 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.

NON-SAMPLING ERROR

15 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfect reporting by respondents, errors made in collection such as in recording and coding data, and errors made in processing the 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. It is not possible to quantify non-sampling error, but every effort is made to reduce it to a minimum. This is done by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.

 T1 STANDARD ERRORS FOR HOUSEHOLD LEVEL ESTIMATES NSW Vic. Qld. SA WA Tas. NT ACT Aust. Size of estimate no. no. no. no. no. no. no. no. no. 100 90 50 100 90 130 60 90 70 100 200 180 100 170 170 210 110 160 140 170 300 250 150 240 230 270 160 220 190 220 500 380 250 360 330 380 240 310 280 320 700 500 340 460 420 480 310 390 350 400 1,000 650 470 590 540 590 410 490 450 500 1,500 880 670 790 700 760 540 630 570 650 2,000 1,080 850 950 840 900 650 740 680 770 2,500 1,250 1,000 1,100 950 1,000 750 850 750 900 3,000 1,450 1,150 1,250 1,050 1,150 850 900 850 1,000 3,500 1,600 1,300 1,350 1,150 1,250 900 1,000 900 1,100 4,000 1,750 1,450 1,500 1,250 1,350 1,000 1,050 1,000 1,200 5,000 2,000 1,700 1,700 1,450 1,500 1,100 1,200 1,100 1,350 7,000 2,500 2,150 2,100 1,700 1,800 1,300 1,400 1,250 1,650 10,000 3,100 2,750 2,550 2,050 2,150 1,550 1,650 1,450 2,000 15,000 3,900 3,500 3,200 2,500 2,650 1,850 1,900 1,700 2,500 20,000 4,550 4,150 3,700 2,850 3,000 2,050 2,150 1,850 2,950 30,000 5,650 5,200 4,500 3,400 3,600 2,350 2,450 2,050 3,650 40,000 6,550 6,000 5,200 3,800 4,100 2,550 2,650 2,200 4,250 50,000 7,300 6,700 5,750 4,150 4,550 2,750 2,850 2,300 4,750 100,000 9,950 9,000 7,750 5,300 6,000 3,150 3,400 2,600 6,700 150,000 11,800 10,500 9,050 6,000 7,000 3,350 3,700 2,700 8,150 200,000 13,150 11,550 10,100 6,500 7,750 3,450 3,850 2,700 9,300 300,000 15,250 13,000 11,600 7,200 8,900 3,550 - 2,750 11,200 500,000 18,100 14,750 13,650 8,050 10,500 3,550 - - 14,000 1,000,000 22,050 16,800 16,550 9,100 12,850 - - - 18,650 2,000,000 26,050 18,100 19,400 9,950 15,350 - - - 24,500 5,000,000 30,750 18,500 22,850 - - - - - 34,200 10,000,000 - - - - - - - - 43,150 - nil or rounded to zero (including null cells)
 T2 STANDARD ERRORS FOR PERSON LEVEL ESTIMATES NSW Vic. Qld. SA WA Tas. NT ACT Aust. Size of estimate no. no. no. no. no. no. no. no. no. 100 260 240 210 160 130 110 110 160 120 200 400 370 340 260 230 190 220 250 200 300 520 480 440 350 310 260 320 310 270 500 720 670 600 490 450 370 480 420 400 700 880 820 740 600 570 470 620 500 510 1,000 1,090 1,010 910 750 730 590 790 610 650 1,500 1,390 1,290 1,160 960 960 760 1,020 760 860 2,000 1,640 1,520 1,370 1,140 1,150 910 1,210 890 1,050 2,500 1,850 1,700 1,550 1,300 1,350 1,050 1,350 1,000 1,200 3,000 2,050 1,900 1,700 1,450 1,500 1,150 1,500 1,100 1,350 3,500 2,250 2,100 1,850 1,550 1,650 1,250 1,600 1,200 1,500 4,000 2,450 2,250 2,000 1,650 1,750 1,350 1,700 1,250 1,650 5,000 2,750 2,550 2,250 1,900 2,000 1,500 1,850 1,400 1,900 7,000 3,350 3,050 2,700 2,250 2,450 1,800 2,100 1,650 2,350 10,000 4,050 3,650 3,300 2,700 2,950 2,100 2,400 2,000 2,950 15,000 5,000 4,550 4,050 3,250 3,650 2,550 2,650 2,400 3,750 20,000 5,800 5,250 4,700 3,700 4,250 2,900 2,800 2,750 4,450 30,000 7,150 6,400 5,700 4,450 5,150 3,400 3,000 3,300 5,600 40,000 8,250 7,400 6,550 5,000 5,900 3,800 3,050 3,800 6,550 50,000 9,200 8,200 7,300 5,500 6,500 4,100 3,100 4,150 7,400 100,000 12,850 11,350 10,000 7,150 8,700 5,100 3,050 5,600 10,750 150,000 15,500 13,600 12,000 8,250 10,150 5,750 2,900 6,650 13,200 200,000 17,700 15,450 13,550 9,100 11,300 6,200 2,800 7,450 15,250 300,000 21,200 18,350 16,050 10,350 12,950 6,800 - 8,750 18,550 500,000 26,450 22,650 19,750 12,000 15,250 7,500 - - 23,550 1,000,000 35,300 29,850 25,850 14,350 18,500 - - - 32,050 2,000,000 46,450 38,650 33,250 16,750 21,800 - - - 42,800 5,000,000 65,500 53,300 45,400 - - - - - 60,950 10,000,000 - - - - - - - - 77,950 - nil or rounded to zero (including null cells)