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10 The ASCED spans all sectors of the formal Australian education system; that is, School, Vocational Education and Training and Higher Education. From 2001 ASCED replaces a number of classifications used in administrative and statistical systems, including the ABSCQ. The ASCED comprises two classifications: Level of Education and Field of Education. See Australian Standard Classification of Education (ASCED), 2001 (Cat. no. 1272.0).
11 Information Paper: Implementing the Redesigned Labour Force Survey Questionnaire (Cat. no. 6295.0) contains further information about the questionnaire changes.
SCOPE OF THE SURVEY
12 Only those businesses which employ less than 20 people and their operators are included in the survey results. Business size
13 All businesses identified were classified according to the Australian and New Zealand Standard Industrial Classification (ANZSIC), a detailed description of which appears in Australian and New Zealand Standard Industrial Classification 1993 (Cat. no. 1292.0).
14 The survey included businesses in the following industries: Mining Manufacturing Construction Wholesale trade Retail trade Accommodation, cafes and restaurants Transport and storage Communication services Finance and insurance Property and business services Education Health and community services Cultural and recreational services Personal and other services.
15 The survey covered both rural and urban areas in all States and Territories, excluding some 175,000 persons living in remote and sparsely settled parts of Australia. The exclusion of these persons will have only a minor impact on any aggregate estimates that are produced for individual States or Territories, with the exception of the Northern Territory where such persons account for over 20% of the population.
16 The population for the survey includes all persons aged 15 or over except:
17 While these categories of people have an effect on the measurement of labour force levels, their exclusion is not expected to have significant impact on the identification of small businesses.
18 As the Characteristics of Small Business survey is a supplementary survey to the Labour Force Survey, it has the same basic design. The survey was based on a multi-stage area sample of private dwellings (about 30,000 houses and flats), and covered about one-half of one per cent of the population of Australia.
COVERAGE OF THE SURVEY
19 Coverage rules are applied which aim to ensure that each person is associated with only one dwelling, and hence has only one chance of selection. The chance of a person being enumerated at two separate dwellings in the one survey is considered to be negligible.
20 Persons who are away from their usual residence for six weeks or less at the time of the interview are enumerated at their usual residence.
21 Where comparative data are available, this publication presents estimates from the November 1999 Characteristics of Small Business Survey. Data from the February 1997 Survey are also presented in the commentary in some sections.
RELIABILITY OF ESTIMATES
22 The estimates provided in this publication are subject to two types of error: sampling error and non-sampling error.
23 As 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, the estimates may differ from those that would have been produced if all dwellings had been included in the survey.
24 One measure of the likely difference is given by the standard errors (SEs) (see Appendix tables A1.1 and A1.2 ), which indicate 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 (67%) that a sample estimate will vary by less than one SE from the estimate that would have been obtained if all dwellings had been included, and about nineteen chances in twenty (95%) that the difference will be less than two SEs.
25 Another measure of the sampling variability is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate to which it refers. The RSE is a useful measure in that it provides an immediate indication of the percentage of error likely to have occurred due to sampling.
26 As the Appendix tables A1.1 and A1.2 of SEs show, the size of the SE increases with the size of the estimate. However, the smaller the estimate the higher the RSE. Thus, larger estimates will be relatively more reliable than smaller estimates.
27 Very small estimates are subject to large 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% but less than or equal to 50% 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 of greater than 50%, preceded by a double asterisk (e.g. **0.3), are considered too unreliable for general use and should only be used to aggregate with other estimates to provide derived estimates with RSEs of 25% or less.
28 Space does not allow for separate indication of the standard errors of all estimates in this publication. As a guide, the Appendix provides an average
29 If the actual value for a particular estimate is not shown in the Appendix table an approximate SE can be derived by taking the SEs shown for estimates on either side of the required value and interpolating a figure within that range.
CALCULATIONS OF STANDARD ERROR (SE )
30 An example of the calculation and the use of SEs in relation to estimates of the number of small business operators is as follows. The table 2.1 shows that the estimated number of male small business operators in New South Wales is 356,000. Since this estimate is between 300,000 and 400,000, Appendix table A1.1 shows that the SE for New South Wales will be between 12,200 and 14,300, and can be approximated by interpolation using the following general formula:
31 SE of estimate = lower SE + (((size of estimate - lower estimate) / (upper estimate - lower estimate))x(upper SE - lower SE))
32 = 12,200 + (((356,000 - 300,000) / (400,000 - 300,000)) x (14,300 - 12,200))
33 = 13,376
34 = 13,400 (rounded to the nearest 100)
35 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 in the range 342,600 to 369,400 and about 19 chances in 20 that the value will fall in the range 329,200 to 382,800.
36 Similarly, SEs are calculated for estimates of the number of small businesses using Appendix A1.2 instead of Appendix A1.1. For example, table 3.1 shows that the estimated total number of small businesses in Australia is 1,162,000. This estimate is between 1,000,000 and 2,000,000, so the SE for this estimate will be between 17,800 and 25,100, and can be approximated using the same interpolation formula as above, with the resulting SE being 19,000 (rounded to the nearest 100).
PROPORTIONS AND PERCENTAGES
37 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.
38 For example, in table 2.1, the estimate for the total number of small business operators in NSW is 515,200. The estimated number of male small business operators in NSW is 356,000, so the proportion of small business operators in NSW who are male is 356,000/515,200 or 69.1%. The SE of the total number of small business operators in NSW may be calculated by interpolation as 16,300. To convert this to a RSE we express the SE as a percentage of the estimate, or 16,300/515,200 = 3.2%. The SE for the number of male small business operators in NSW was calculated above as 13,300, which converted to a
RSE is 13,300/356,000 = 3.7%. Applying the above formula, the RSE of the proportion is
39 giving a SE for the proportion (69.1%) of 1.3 percentage points (=(69.1/100)*1.9).
40 Therefore, there are about two chances in three that the proportion of small business operators in NSW who are male is between 67.8% and 70.4% and 19 chances in 20 that the proportion is within the range 66.5% to 71.7%.
41 Similarly, SEs can be calculated for estimates of the number of small businesses using the same formula.
42 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:
43 While this formula will only be exact for differences between separate and uncorrelated characteristics or sub-populations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
44 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur due to non-sampling errors.
45 Non-sampling errors can occur whether the estimates are derived from a sample or from a complete enumeration. Three major sources of non-sampling error are:
46 Non-sampling errors are difficult to measure in any collection. However, every effort was made to minimise these errors. In particular, the effect of the reporting and processing errors described above was minimised by careful questionnaire design, intensive training and supervision of interviewers, asking respondents to refer to records whenever possible and extensive editing and quality control checking at all stages of data processing.
SURVEY ESTIMATION AND WEIGHTING PROCEDURES
47 Estimates derived from the survey are obtained by using a calibrated weighting procedure which ensures that the survey estimates conform to an independently estimated distribution of the population by area of residence, age and sex.
48 Two separate weights were used for the survey:
49 Each person in the sample is assigned a ‘weight’ which takes into account their probability of selection in the sample from their region, with adjustments to account for under-enumeration (for example, non-response) at the age and sex level.
50 The ‘weights’ are also adjusted to reduce the bias introduced by varying levels of non- response in different sub-groups of the population.
51 Business weights are derived from the person weights using partner per business information.
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