TECHNICAL NOTE
RELIABILITY OF THE ESTIMATES
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 occupants of 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 (or occupants) was included. There are about two chances in three (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.
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 Limited space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this release, only those for Table 3 have been included in Table T.1 at the end of these Technical Notes.
4 In the tables in this publication, only estimates (numbers, percentages, means and medians) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *3.4) 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 (e.g. **2.1) to indicate that they are considered too unreliable for general use.
CALCULATION OF STANDARD ERRORS
5 SEs can be calculated using the estimates (counts or means) and the corresponding RSEs. For example Table 3 shows that the estimated number of persons aged 15 years or over with household internet access was 10,587,000 in 2007-08. In the corresponding RSE table (Table T.1), the RSE for this estimate is shown to be 0.7%. The SE calculated as:
6 The standard error for this estimate is therefore 74,000 (rounded to nearest 1,000).
7 Therefore there are about two chances in three that the value that would have been produced if all persons had been included in the survey will fall within the range 10,513,000 to 10,661,000 and about 19 chances in 20 that the value will fall within the range 10,439,000 to 10,735,000.
PROPORTIONS AND PERCENTAGES
8 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.
9 For example in Table 3 the estimate for the proportion of persons aged 65 years or older with Broadband access in terms of those with Internet access is 69%.
10 From the RSEs published for this table in Table T.1, the RSE of the estimated number of persons aged 65 years or older with Broadband access is 4.6%, and the estimated number of persons aged 65 years or older with Internet access is 3.3%.
11 Applying the above formula, the RSE of the proportion is:
12 This then gives an SE for the proportion (69%) of (3.2/100) x 69 = 2 percentage points.
13 Therefore there are about two chances in three that the proportion of persons aged 65 years and over with Broadband access is between 67% and 71%, and 19 chances in 20 that the proportion is within the ranges 65% and 73%.
DIFFERENCES
14 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:
15 From table 3, it is estimated that 10,587,000 persons aged 15 years or over with household internet access was 10,587,000 in 2007-08. This estimate has a RSE of 0.7 (see Table T.1 below), which corresponds to a standard error of around 74,000 (see paragraph 5 above). The corresponding figure for 2006-07 was 9,922,000, with a standard error of around 69,000. The estimated increase in the number of persons aged 15 years or over with household internet access was 665,000. Substituting the SEs for 2005-06 and 2006-07 in the above formula the SE on the movement is around 101,000. There are 2 chances in 3 that the true value is within the range 564,000 to 766,000 persons and 19 chances in 20 that the true value is in the range 463,000 to 867,000 persons.
16 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.
SIGNIFICANCE TESTING
17 The statistical significance test for any of the comparisons between estimates was performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 14. This standard error is then used to calculate the following test statistic :
18 If the value of this test statistic is greater than 1.96 then we may say there is good evidence of a real difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations.
19 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 respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error, and they occur in any enumeration, whether it be a full count or sample. Every effort is made to reduce non-sampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.
T1: Type of Internet Connection, Selected Personal Characteristics, 2007-08, RSEs |
| |
| | | Number of persons accessing the internet at home | Dial-up access | Broadband | Both | Don't know | |
| | | % | % | % | % | % | |
| |
Age group (years) | | | | | | |
| 15 - 17 | 2.2 | 13.2 | 3.1 | 103.4 | 34.9 | |
| 18 - 24 | 1.7 | 9.6 | 2.4 | 63.2 | 29.6 | |
| 25 - 34 | 1.4 | 7.5 | 1.8 | 100.3 | 29.8 | |
| 35 - 44 | 1.1 | 5.4 | 1.5 | 28.3 | 28.9 | |
| 45 - 54 | 2.0 | 6.4 | 2.4 | 40.0 | 28.8 | |
| 55 - 64 | 1.9 | 6.3 | 2.8 | 37.1 | 39.8 | |
| 65 or over | 3.3 | 5.9 | 4.6 | 72.3 | 47.8 | |
Sex | | | | | | |
| Male | 1.1 | 4.3 | 1.2 | 31.5 | 21.1 | |
| Female | 1.0 | 3.2 | 1.5 | 22.2 | 16.3 | |
Personal income(a) | | | | | | |
| $0 to $39,999 | 1.4 | 4.4 | 1.9 | 28.1 | 17.0 | |
| $40,0000 to $79,999 | 2.0 | 5.4 | 2.5 | 34.1 | 32.3 | |
| $80,0000 to $119,999 | 4.1 | 16.0 | 4.5 | 100.5 | 69.6 | |
| $120,0000 plus | 7.9 | 25.0 | 8.6 | 52.4 | - | |
| Could not be determined | 3.4 | 8.8 | 3.1 | 84.9 | 32.4 | |
Labour Force Status(b) | | | | | | |
| Employed | 1.0 | 3.7 | 1.2 | 20.9 | 20.9 | |
| Not Employed | 1.8 | 3.7 | 2.4 | 37.1 | 17.0 | |
Indigenous Status | | | | | | |
| Indigenous | 17.3 | 30.4 | 20.7 | - | 100.8 | |
| Non Indigenous | 0.8 | 3.0 | 1.1 | 17.2 | 13.3 | |
Country of Birth(c) | | | | | | |
| Born in Australia | 1.0 | 3.5 | 1.1 | 17.8 | 19.1 | |
| Born Overseas | | | | | | |
| | Born in main English-speaking Countries | 3.0 | 8.0 | 2.6 | 78.3 | 35.1 | |
| | Born in other countries | 3.7 | 8.0 | 4.2 | 59.3 | 25.8 | |
Highest Level of Educational Attainment(d) | | | | | | |
| Bachelor degree or above | 2.1 | 7.1 | 2.0 | 36.1 | 38.4 | |
| Advanced diploma or diploma | 4.7 | 10.2 | 5.2 | 54.8 | 35.8 | |
| Certificate | 3.0 | 6.8 | 3.1 | 58.4 | 51.7 | |
| Year 12 or below | 1.1 | 4.7 | 1.7 | 26.3 | 14.8 | |
Total | 0.7 | 3.0 | 1.0 | 17.2 | 13.2 | |
| |
- nil or rounded to zero (including null cells) |
(a) Includes those persons with income less than zero. |
(b) Labour force status in the week before the survey. |
(c) Excludes persons whose country of birth was not stated and/or inadequately described. |
(d) Excludes those persons who had no educational attendance/attainment and where level was not determined. |
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