4602.0 - Environmental Issues: People's Views and Practices, Mar 2004

ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 24/11/2004

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Explanatory Notes
Technical Note

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:
Equation: SE formula rev
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)