Disability, Ageing and Carers, Australia: First Results methodology

Latest release
Reference period
2015
Released
29/04/2016
Next release Unknown
First release

Explanatory notes

Introduction

1 This publication presents first results from the 2015 Survey of Disability, Ageing and Carers (SDAC), conducted throughout Australia by the Australian Bureau of Statistics (ABS). This is the eighth comprehensive national survey conducted by the ABS to measure disability, following similar surveys in 1981, 1988, 1993, 1998, 2003, 2009 and 2012. This publication contains a subset of the items that will be provided in the main release of data which will be available later in 2016.

2 The aims of the survey are to:

  • measure the prevalence of disability in Australia
  • measure the need for support of older people and those with disability
  • provide a demographic and socio-economic profile of people with disability, older people and carers compared with the general population
  • estimate the number of and provide information about people who provide care to people with disability, long-term health conditions and older people.


3 The main concepts for this first release publication are defined separately within the Glossary. These are:

  • disability
  • long-term health condition
  • specific limitation or restriction
  • core activity limitation and levels of restriction.


4 The survey collected detailed information from three target populations:

  • people with disability
  • older people (i.e. those aged 65 years and over)
  • people who care for people with disability, long-term health conditions or older people

Scope and coverage of the survey

5 The scope of SDAC was people in both urban and rural areas in all states and territories, living in private dwellings, self-care retirement villages and establishments providing long-term cared accommodation. The survey excluded the following:

  • certain diplomatic personnel of overseas governments, customarily excluded from the Census and estimated resident population
  • persons whose usual place of residence was outside Australia
  • members of non-Australian defence forces (and their dependents) stationed in Australia
  • persons living in very remote areas, and
  • discrete Aboriginal and Torres Strait Islander communities.


6 Since 2012, the survey has excluded discrete Aboriginal and Torres Strait Islander communities from its estimates. These communities are found in Queensland, South Australia, Western Australia and the Northern Territory. This exclusion has minimal impact on Australia level estimates. However, it could have an impact on Northern Territory estimates, as around 10% of Northern Territory households that were included before 2012 are now excluded. Most of the discrete Aboriginal and Torres Strait Islander communities are located in very remote areas of Australia.

7 The survey also collected a small amount of information about people not in the target populations, allowing for comparison of demographic and socio-economic characteristics of the target populations with the general population.

8 The coverage of SDAC was the same as the scope. 

9 Rules were applied to maximise the likelihood that each person in coverage was associated with only one dwelling and thus had one chance of selection.

10 Usual residents of private dwellings and self-care retirement villages were included in the survey unless they were away on the night of enumeration and were likely to be away for the remainder of the enumeration period. 

11 Visitors to private dwellings and self-care retirement villages were excluded from coverage as the expectation was that most would have their chance of selection at their usual residence.

12 Occupants of long-term cared-accommodation establishments in scope of the survey were enumerated if they had been, or were expected to be, a usual resident of an establishment for three months or more.

Sample design

13 Multi-stage sampling techniques were used to select the sample for the survey. Private dwellings and self-care retirement village units, collectively referred to as the household component, included approximately 25,500 private dwellings and 250 self-care retirement village dwellings, after sample loss. The cared-accommodation sample included approximately 1,000 health establishments

Table 1.1 Household component (private dwellings), response rates

 Number%
Fully responding25 55580.0
Non response.  
 Refusal1 1723.7
 Non response4 98715.6
 Part response2430.8
Total 6 40220.0
    
Total 31 957100.0

 

 

Table 1.2 Household component (self-care retirement villages), response rates

 Number%
Fully responding25187.2
Non response  
 Refusal113.8
 Non response258.7
 Part response10.3
Total 3712.8
    
Total 288100.0

 

 

Table 1.3 Cared-accommodation component, response rates

 Number%
Responding establishments1 00989.4
Non-responding establishments12010.6
   
Total1 129100.0

 

 

14 After exclusions due to scope and coverage, the final combined sample was 75,211 persons, comprised of 63,515 persons from the household component and 11,696 persons from the cared-accommodation component.

Household component

15 Private dwellings were selected at random using a multi-stage area sample of private dwellings to ensure that all sections of the population living within the geographic scope of the survey were represented. 

16 Self-care retirement villages were selected separately from the private dwellings based on a list of all non private dwellings in Australia. While the list included hotels, motels, boarding houses and short term caravan parks, only self-care retirement villages were chosen for the household component as the inclusion of the other types of accommodation would have minimal impact on estimates. 

17 Similar to the private dwelling selection process, the list of self-care retirement villages was first amended to meet the scope and coverage requirements of the survey, which excluded dwellings in very remote areas, collection districts containing a discrete Aboriginal or Torres Strait Islander community, boarding schools, gaols and correctional institutions. 

Cared-accommodation component

18 The cared-accommodation establishment sample was chosen separately from other samples. A frame was constructed which included all Australian businesses which may provide adequate facilities to support long-term cared-accommodation. 

19 A census was then conducted of those establishments on the frame to ensure they provided long-term cared-accommodation. This process is explained further in the Data Collection section of these Explanatory Notes. 

20 Each in-scope establishment was given a chance of selection proportional to the average number of persons it accommodated. In order to identify the occupants to be included in the survey, they were ordered by the respondent (a representative of the establishment) and a random selection technique was applied.

Data collection

21 Similar to the 2003, 2009 and 2012 surveys, the 2015 survey collected information about people living in households as well as those in cared-accommodation to ensure the survey represented a comprehensive picture of disability in Australia. This was achieved by conducting the survey in two separate parts: the household component and the cared-accommodation component, using different methods for data collection and processing.

22 The household component covered persons in private dwellings such as houses, flats, home units and townhouses and self-care components of retirement villages.

23 In this publication, persons in the household component of the survey are referred to as 'living in households'.

24 The cared-accommodation component covered residents of hospitals, nursing homes, hostels and other homes, who had been, or were expected to be, living there or in another health establishment for a period of three months or more.

Household component

25 Data for the household component of the survey were collected by trained interviewers, who conducted computer-assisted personal interviews. The interviews were conducted from 5 July to 19 December 2015.

26 Households containing people with disability or those aged 65 years and over, were determined through a series of screening questions asked of a responsible adult in the selected household.

27 Households containing people who were carers of persons with a core activity limitation, living either in the same household or elsewhere, or who provided any care to persons living elsewhere, were identified using two methods: 

  • through a series of screening questions asked of a responsible adult in the household and, when applicable,
  • through information provided by recipients of care during their personal interview.


28 Where possible, a personal interview was conducted with people identified in the above populations. Proxy interviews were conducted for: 

  • children aged less than 15 years
  • those aged 15 to 17 years whose parent or guardian did not consent to them being personally interviewed 
  • those incapable of answering for themselves due to illness, impairment, injury or language problems.

 

29 People with disability were asked questions relating to: 

  • help and assistance needed and received for mobility, self-care, communication, cognitive or emotional tasks, health care, household chores, property maintenance, meal preparation, reading and writing tasks, and transport activities 
  • use of aids and equipment  
  • schooling restrictions, for those aged 5 to 20 years
  • employment restrictions 
  • satisfaction with the quality of services received and range of services available 
  • accessibility and discrimination related to disability
  • National Disability Insurance Scheme (NDIS) participation
  • internet use 
  • self-perception of health and well-being
  • access and barriers to health care 
  • social, community and civic participation 
  • feelings of safety.
     

30 People aged 65 years and over without disability were asked questions relating to: 

  • self-perception of health and well-being
  • help and assistance needed and received for health care, cognitive or emotional tasks, household chores, property maintenance, meal preparation, reading and writing tasks, and transport activities 
  • employment restrictions 
  • satisfaction with the quality of services received and range of services available 
  • internet use 
  • social, community and civic participation 
  • feelings of safety 


31 A set of modules was also asked of persons who confirmed they were the primary carer of a person with a disability; however, data items related to primary carers are not included in this release. Data items about primary carers will be available in the main release of SDAC data due later in 2016. 

32 Basic demographic and socio-economic information was collected for all people in the household. This information was generally provided by a responsible adult in the household, or if preferred, by personal interview of each respondent.

Cared-accommodation component

33 The cared-accommodation component was enumerated in two stages using both web and mail-based methodologies directed to administrators of selected health establishments.

34 The first stage involved a census of all known health establishments in Australia. These establishments were sent an approach letter from the ABS, detailing their selection and the requirement for a suitable employee of their establishment to complete a web-based Contact Information Form. This form collected the name and role of a contact officer for the establishment, whether the establishment offered cared-accommodation to occupants on a long-term basis (i.e. for a period of three months or more), the current number of occupants within the cared-accommodation component, and the type of establishment.

35 The second stage, conducted from 25 May to 31 July 2015, was based on a sample of the health establishments that indicated their ability to provide long-term cared-accommodation in stage one. Each establishment was given a likelihood of selection relative to the number of long-term occupants they had reported. If a health establishment was selected, the nominated contact officer was required to select a sample of occupants in their establishment, following the instructions provided. The contact officer then completed a separate questionnaire for each selected occupant.

36 The range of data collected in the cared-accommodation component was narrower than in the household component as some topics were not suitable for collection through a proxy or were irrelevant to those residing in cared-accommodation.

Processing procedures

Collection

37 A number of editing techniques were implemented within the computer-assisted survey instrument to assist with processing data collected by the personal interviews, such as: 

  • the programming of 'edits' relating to the range and consistency of answers, which would prompt interviewers to check the correctness of responses and would not allow implausible results to be accepted 
  • the inclusion of pick lists and coders, resulting in a high proportion of coding being automated at the time of data collection.
     

Coding of long-term health conditions

38 The majority of reported long-term health conditions were automatically coded to a list of approximately 1,000 health conditions, within the computer-assisted personal interview. Those conditions that could not be automatically coded at the time of data collection were reviewed on a case by case basis by ABS employees during post-collection editing.

39 The code list used for the 2015 SDAC was similar to that used in previous surveys, with some minor updates. Conditions classified at the full level of detail are not generally available for output from the survey, however, they can be regrouped in various ways for output. The output classification, developed for the SDAC, is based on the International Classification of Diseases: 10th Revision (ICD-10). 

Editing

40 An extensive range of edits and quality checks were performed on the aggregated data file, after the completion of data collection. These included: 

  • ensuring there were no contradictory responses and that relationships between items were within acceptable limits 
  • identifying cases which, although not necessarily errors, were sufficiently unusual or close to specified limits as to warrant examination 
  • a review of incomplete data and responses that could not be automatically coded at the time of collection, to determine if these responses could be coded or categorised appropriately.
     

Weighting, benchmarking and estimation

41 Weighting is a process of adjusting results from a sample survey to infer results for the in-scope total population. To do this, a weight is allocated to each sample unit; for example, a household or a person. The weight is a value which indicates how many population units are represented by the sample unit. 

42 The first step in calculating weights for each person was to assign an initial weight, which was equal to the inverse of the probability of being selected in the survey. For example, if the probability of a person being selected in the survey was 1 in 300, then the person would have an initial weight of 300 (that is, they represent 300 others). An adjustment was then made to these initial weights to account for the time period in which a person was assigned to be enumerated.

43 The cared-accommodation component of the survey was weighted separately from the household component.  These two components together represent the entire in-scope population.

44 The weights of the household component were calibrated to align with independent estimates of the population of interest, referred to as 'benchmarks', in designated categories of sex by age by area of usual residence.  The weights of the cared-accommodation component were calibrated to benchmarks in categories by state.  Weights calibrated against population benchmarks ensure that the survey estimates conform to the distribution of the population rather than to the distribution within the sample itself. Calibration to population benchmarks helps to compensate for over or under-enumeration of particular categories of persons which may occur due to either the random nature of sampling or non-response.

45 The household component of the survey was benchmarked to the estimated resident population (ERP) in each state and territory, excluding those living in very remote areas of Australia and living in a collection district in a non-very remote area containing one or more discrete Aboriginal or Torres Strait Islander communities, as at 30th September 2015.  The cared-accommodation component of the survey was benchmarked to population counts derived from the census of this component, incorporating a non-response adjustment. The SDAC estimates do not (and are not intended to) match estimates for the total Australian population obtained from other sources (which may include persons living in very remote parts of Australia and persons living in discrete Aboriginal or Torres Strait Islander communities).

46 Survey estimates of counts of persons are obtained by summing the weights of persons with the characteristic of interest. Estimates of non-person counts (for example, number of health conditions) are obtained by multiplying the characteristic of interest with the weight of the reporting person and aggregating.

47 Age standardisation is a way of allowing comparisons between two or more populations with different age structures, in order to remove age as a factor when examining relationships between variables. For example, the age structure of the population of Australia is changing over time. As the prevalence of a particular disability may be related to age, any increase in the proportion of people with that health condition over time may be due to real increases in prevalence or to changes in the age structure of the population over time or to both. Age standardising removes the effect of age in assessing change over time or between different populations.

48 For this publication the direct age standardisation method was used. The standard population used was the 30 June 2001 Estimated Resident Population. The age categories used in the standardisation for this publication were five year age groups, to 75 years and over. Totals presented in Tables 1 and 4 comparing rates over time are shown as age-standardised percentages.

Reliability of estimates

49 All sample surveys are subject to sampling and non-sampling error.

50 Sampling error is the difference between estimates, derived from a sample of persons, and the value that would have been produced if all persons in scope of the survey had been included. Indications of the level of sampling error are given by the Relative Standard Error (RSE) and 95% Margin of Error (MOE). For more information refer to the Technical Note - Data quality.

51 In this publication, estimates with an RSE of 25% to 50% are flagged to indicate that the estimate has a high level of sampling error relative to the size of the estimate, and should be used with caution. Estimates with an RSE over 50% are also flagged and are generally considered too unreliable for most purposes.

52 Margins of Error are provided for proportions to assist users in assessing the reliability of these data. The proportion combined with the MOE defines a range which is expected to include the true population value with a given level of confidence. This is known as the confidence interval. This range should be considered by users to inform decisions based on the proportion.

53 Non-sampling error may occur in any data collection, whether it is based on a sample or a full count such as a census. Non-sampling errors occur when survey processes work less effectively than intended. Sources of non-sampling error include non-response, errors in reporting by respondents or in recording of answers by interviewers, and errors in coding and processing data.

54 Non-response occurs when people are unable to or do not respond, or cannot be contacted. Non-response can affect the reliability of results and can introduce a bias. The magnitude of any bias depends on the rate of non-response and the extent of the difference between the characteristics of those people who responded to the survey and those who did not. 

55 The following methods were adopted to reduce the level and impact of non-response: 

  • face-to-face interviews with respondents;
  • the use of proxy interviews in cases where language difficulties were encountered, noting the interpreter was typically a family member; 
  • follow-up of respondents if there was initially no response; and 
  • weighting to population benchmarks to reduce non-response bias.
     

Interpretation of results

Measuring disability

56 Disability is a difficult concept to measure because it depends on a respondent's perception of their ability to perform a range of activities associated with daily living. Factors discussed below should also be considered when interpreting the estimates contained in this publication. 

57 Information in the survey was based, wherever possible, on the personal response given by the respondent. However, in cases where information was provided by another person, some answers may differ from those the selected person would have provided. In particular, interpretation of the concepts of 'need' and 'difficulty' may be affected by the proxy-interview method. 

58 A number of people may not have reported certain conditions because of: 

  • the sensitive nature of the condition (e.g. alcohol and drug-related conditions, schizophrenia, other mental health conditions) 
  • the episodic or seasonal nature of the condition (e.g. asthma, epilepsy) 
  • a lack of awareness of the presence of the condition on the part of the person reporting (e.g. mild diabetes) or a lack of knowledge or understanding of the correct medical terminology for the condition 
  • the lack of comprehensive medical information kept by their cared-accommodation establishment.
     

59 As certain conditions may not have been reported, data collected from the survey may have underestimated the number of people with one or more disabilities. 

60 The need for help may have been underestimated as some people may not have admitted needing help because of such things as a desire to remain independent, or may not have realised help was needed with a task because help had always been received with that task. 

61 The criteria by which people assessed whether they had difficulty performing tasks may have varied. Comparisons may have been made with the ability of others of a similar age, or with the respondent's own ability when younger. 

62 The criteria used to identify disability and disability status has changed between 2012 and 2015. New modules were added to identify people with social and behavioural difficulties, memory loss and periods of confusion and dementia.

63 The different collection methods used (personal interview for households, and administrator completed forms for cared-accommodation) may have had some effect on the reporting of need for assistance with core activities. As a result there may have been some impact on measures such as disability status. If so, this would have more impact on the older age groups because of their increased likelihood of being in cared-accommodation.

Comparability with previous Surveys of Disability, Ageing and Carers

64 Much of the content of the eight disability surveys conducted by the ABS in 1981, 1988, 1993, 1998, 2003, 2009, 2012 and 2015 is comparable. There are differences, however, as later surveys have attempted to obtain better coverage of disability and of specific tasks and activities previously considered too sensitive for a population survey.  A list of output data items available in the first release of data from the 2015 survey can be accessed on the ABS website, under the Data downloads section of this release.

65 Data for the 2015 SDAC is comparable with earlier surveys, with some exceptions:

  • Older persons aged 65 years and over: this group of people were included in Self-Perception of Health and Well-being and Employment Limitations and excluded from Patient Experience in 2015.
  • Definition of whether has a disability has changed in 2015: three new modules were added to the disability identification module including: social and behavioural difficulties, memory loss and periods of confusion, and dementia. A data item is available which uses the 2012 definition to enable time series comparisons.
  • Labour Force: A number of minor changes were made to labour force data items in order to align this survey with the standard outputs from the Labour Force Survey (cat. no. 6202.0).
  • Removal of some non-private dwellings from coverage:  Some non-private dwellings, including, hotels, motels, boarding houses and short term caravan parks were removed from the sample due to the difficulty in enumeration for the relatively small number of fully responding participants. The only non-private dwellings enumerated were establishments offering long term cared-accommodation.   
  • Classification of self-care retirement villages: Self-care retirement village units, previously considered non-private dwellings, were reclassified in 2015 to private dwellings to align with Census classifications.
  • Addition of discrimination and accessibility data items: The inclusion of this data is in response to a growing interest by a number of government departments.
  • National Disability Insurance Scheme (NDIS) participation: The 2015 survey includes a question to measure the number of  people who are participating in the NDIS, with the intention of this acting as a baseline for future surveys as the rollout of NDIS continues. 
  • Experience of Homelessness: this module was included in the 2012 survey but removed in the 2015 survey.
  • Self perception of health and well-being:  The Short Form 12 questions used in 2012 were replaced with the Kessler Psychological Distress Scale questions.
     

Classifications

66 Long-term health conditions described in this publication were categorised to an output classification developed for the SDAC, based on the International Classification of Diseases: 10th Revision (ICD-10). This classification, with some minor amendments, has been used since the 2003 survey.

67 Country of birth was classified according to the Standard Australian Classification of Countries (SACC), 2016 (cat. no. 1269.0).

68 Main language spoken at home was classified according to the Australian Standard Classification of Languages (ASCL), 2016 (cat. no. 1267.0).

69 Education data were classified according to the Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0). 

70 Occupation data were classified according to the Australian and New Zealand Standard Classification of Occupations (ANZSCO) 2013 (cat.no. 1220.0).

71 Industry data were classified according to the Australian and New Zealand Standard Industrial Classification (ANZSIC), 2006 (cat.no. 1292.0).

72 In 2015, remoteness areas were classified according to the Statistical Geography: Volume 1 - Australian Standard Geography Standard (ASGS), 2011 (cat. no. 1270.0.55.001). 

Rounding

73 Estimates presented in this publication have been rounded. 

74 Proportions presented in this publication are based on unrounded estimates. Calculations using rounded estimates may differ from those published.

Confidentiality

75 The Census and Statistics Act,1905 provides the authority for the ABS to collect statistical information, and requires that statistical output shall not be published or disseminated in a manner that is likely to enable the identification of a particular person or organisation. This requirement means that the ABS must take care and make assurances that any statistical information about individual respondents cannot be derived from published data.

76 To minimise the risk of identifying individuals in aggregate statistics, a technique known as perturbation is used to randomly adjust cell values. Perturbation involves a small random adjustment of the statistics and is considered the most satisfactory technique for avoiding the release of identifiable statistics while maximising the range of information that can be released. These adjustments have a negligible impact on the underlying pattern of the statistics. After perturbation, a given published cell value will be consistent across all tables. However, adding up cell values to derive a total will not necessarily give the same result as published totals. 

77 Perturbation has been applied to 2015 data, similar to 2012 data. SDAC data from previous surveys presented in this publication have not been perturbed, but have been confidentialised if required using suppression of cells.

Acknowledgements

78 ABS publications draw extensively on information provided freely by individuals, businesses, governments and other organisations. Their continued cooperation is very much appreciated; without it, the wide range of statistics published by the ABS would not be available. Information received by the ABS is treated in strict confidence as required by the Census and Statistics Act,1905.

Products and services

79 It is planned that results from the 2015 SDAC will be available in the form of:

  • this first release publication of data containing a subset of the data items that will be available in the main release of data later in 2016. 
  • the main release later in 2016 which will contain a Summary of Findings publication, including a set of data cubes (spreadsheet format) containing a broad selection of national estimates
  • a set of data cubes containing a broad selection of estimates for each state and territory
  • a Confidentialised Unit Record File (CURF)
  • a TableBuilder product
  • a number of supplementary themed publications, and
  • tables produced on request to meet specific information requirements from the survey.
     

80 A set of tables in a spreadsheet format will be produced for each state and territory (subject to standard error and confidentiality constraints and excluding time series tables). These tables will be available from the ABS website www.abs.gov.au later in 2016.

81 It is expected that a basic CURF and TableBuilder will be produced from the SDAC, subject to the approval of the Australian Statistician.  Further details about these releases will be provided with the main release of SDAC data later in 2016.

82 A set of themed publications using the 2015 SDAC data will be released progressively following the release of the Summary of Findings publication.

83 Customised tabulations are available on request. Subject to confidentiality and sampling variability constraints, tabulations can be produced from the survey incorporating data items, populations and geographic areas selected to meet individual requirements. 

84 The first release publication and these Explanatory Notes are available free of charge on the ABS website www.abs.gov.au.

Related publications

85 Current publications and other products released by the ABS are listed on the ABS website. The ABS also issues a daily Release Advice on the website which details products to be released in the week ahead.

Appendix - limitations and restrictions

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Appendix - disability groups

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Technical note - data quality

Reliability of estimates

1 Two types of error are possible in an estimate based on a sample survey: sampling error and non-sampling error. The sampling error is a measure of the variability that occurs by chance because a sample, rather than the entire population, is surveyed. 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 the figures 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). There are about two chances in three that a sample estimate will differ by less than one SE from the figure that would have been obtained if all dwellings had been included, 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. The RSE is a useful measure in that it provides an immediate indication of the percentage errors likely to have occurred due to sampling, and thus avoids the need to refer also to the size of the estimate.

\(\large{R S E \%=\left(\frac{S E}{\text {estimate}}\right) \times 100}\)


3 RSEs for published estimates are supplied in Excel data tables, available via the Data downloads section.

4 The smaller the estimate the higher is the RSE. Very small estimates are subject to such high SEs (relative to the size of the estimate) as to detract seriously from their value for most reasonable uses. In the tables in this publication, only estimates with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs, between 25% and less than 50% have been included and are flagged to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs of 50% or more have also been flagged and are considered unreliable for most purposes.

5 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 interviewers and respondents and errors made in coding and processing of data. Inaccuracies of this kind are referred to as the non-sampling error, and they may occur in any enumeration, whether it be in a full count or only a sample. In practice, the potential for non-sampling error adds to the uncertainty of the estimates caused by sampling variability. However, it is not possible to quantify the non-sampling error.

Standard errors of proportions and percentages

6 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. For proportions where the denominator is an estimate of the number of persons in a group and the numerator is the number of persons in a sub-group of the denominator group, the formula to approximate the RSE is given below. The formula is only valid when x is a subset of y.

\(\large{R S E\left(\frac{x}{y}\right) \approx \sqrt{[R S E(x)]^{2}-[R S E(y)]^{2}}}\)

Comparison of estimates

7 Published estimates may also be used to calculate the difference between two survey estimates. 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:

\(\large{\mathrm{SE}(\mathrm{x}-\mathrm{y})=\sqrt{[\mathrm{SE}(\mathrm{x})]^{2}+[\mathrm{SE}(\mathrm{y})]^{2}}}\)

8 While the above formula will be exact only for differences between separate and uncorrelated (unrelated) characteristics of sub-populations, it is expected that it will provide a reasonable approximation for all differences likely to be of interest in this publication.

9 Another measure is the Margin of Error (MOE), which describes the distance from the population value that the sample estimate is likely to be within, and is specified at a given level of confidence. Confidence levels typically used are 90%, 95% and 99%. For example, at the 95% confidence level the MOE indicates that there are about 19 chances in 20 that the estimate will differ by less than the specified MOE from the population value (the figure obtained if all dwellings had been enumerated). The 95% MOE is calculated as 1.96 multiplied by the SE.

10 The 95% MOE can also be calculated from the RSE by:

\(\large{M O E(y) \approx \frac{R S E(y) \times y}{100} \times 1.96}\)

11 The MOEs in this publication are calculated at the 95% confidence level. This can easily be converted to a 90% confidence level by multiplying the MOE by:

\(\Large\frac{1.645}{1.96}\)

or to a 99% confidence level by multiplying by a factor of:

\(\Large\frac{2.576}{1.96}\)

12 A confidence interval expresses the sampling error as a range in which the population value is expected to lie at a given level of confidence. The confidence interval can easily be constructed from the MOE of the same level of confidence by taking the estimate plus or minus the MOE of the estimate.

Significance testing

13 For comparing estimates between surveys or between populations within a survey it is useful to determine whether apparent differences are 'real' differences between the corresponding population characteristics or simply the product of differences between the survey samples. One way to examine this is to determine whether the difference between the estimates is statistically significant. This is done by calculating the standard error of the difference between two estimates (x and y) and using that to calculate the test statistic using the formula below:

\(\Large{ \left(\frac{|x-y|}{S E(x-y)}\right)}\)

where

\(\large{S E(y)=\frac{R S E(y) \times y}{100}}\)

14 If the value of the statistic is greater than 1.96 then we may say there is good evidence of a statistically significant difference at 95% confidence levels between the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations.

Glossary

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Quality declaration - summary

Institutional environment

Relevance

Timeliness

Accuracy

Coherence

Interpretability

Accessibility

I-Notes - data cubes

An issue has been identified with the preparation of data on schooling or employment restrictions. A small number of people who are permanently unable to work were included as having a schooling or employment restriction, a category limited to those who are able to work. Revisions have been made to Schooling or employment restriction and All with specific limitations or restrictions to correct the previously published data. Also, an improvement to the method used to calculate relative standard errors (RSE) for cared accommodation will mean a small number of RSEs will differ from those shown in the original release of this publication.

Abbreviations

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