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- Articles and reports: 12-001-X201800154925Description:
This paper develops statistical inference based on super population model in a finite population setting using ranked set samples (RSS). The samples are constructed without replacement. It is shown that the sample mean of RSS is model unbiased and has smaller mean square prediction error (MSPE) than the MSPE of a simple random sample mean. Using an unbiased estimator of MSPE, the paper also constructs a prediction confidence interval for the population mean. A small scale simulation study shows that estimator is as good as a simple random sample (SRS) estimator for poor ranking information. On the other hand it has higher efficiency than SRS estimator when the quality of ranking information is good, and the cost ratio of obtaining a single unit in RSS and SRS is not very high. Simulation study also indicates that coverage probabilities of prediction intervals are very close to the nominal coverage probabilities. Proposed inferential procedure is applied to a real data set.
Release date: 2018-06-21 - Articles and reports: 75F0002M2008006Geography: Province or territoryDescription:
Comparisons of low income between regions may have impacts on policy choices. However, it is often argued that rankings of distributions are not robust and that they are also quite sensitive to methods of defining low income. This paper avoids these problems by using a stochastic dominance approach to compare regional low income profiles in Canada without arbitrarily specifying a low-income line. This analysis is carried out for the 10 provinces using the Survey of Labour and Income Dynamics for 2000. Robustness of the results is also verified with respect to different choices of spatial price deflators and equivalence scales. The extent to which the findings are sensitive to the choice of an absolute or a relative concept of low income is also examined. We show that, in most cases, dominance relations can be determined and regional low income can be ordered for a wide range of low-income lines. We also show that dominance results are robust to the choice of equivalence scales, while rank reversal occurs when alternative cost-of-living deflators are used. Switching from an absolute to a relative low-income concept only affects low-income rankings for Ontario, Quebec and the Prairie provinces, but not in the case of other provinces. Nevertheless, for all scales, we find that low income is greatest in British Columbia.
Release date: 2008-10-09 - 3. Making Sense of Health Rankings ArchivedSurveys and statistical programs – Documentation: 82-582-XDescription:
This special methodological paper will help readers understand and assess reports that rank the health status or health system performance of a country, province or jurisdiction. The report outlines the components and processes that underlie health rankings, explores why such rankings can be difficult to interpret and includes a plain-language checklist to use as a critical evaluative resource when reading health-ranking reports.
Release date: 2008-09-16 - Surveys and statistical programs – Documentation: 11-522-X20050019476Description:
The paper will show how, using data published by Statistics Canada and available from member libraries of the CREPUQ, a linkage approach using postal codes makes it possible to link the data from the outcomes file to a set of contextual variables. These variables could then contribute to producing, on an exploratory basis, a better index to explain the varied outcomes of students from schools. In terms of the impact, the proposed index could show more effectively the limitations of ranking students and schools when this information is not given sufficient weight.
Release date: 2007-03-02 - Articles and reports: 11F0019M1999105Geography: CanadaDescription:
This paper outlines the growth in advanced technology use that has taken place over the last decade in Canadian manufacturing establishments. It presents the percentage of plants that use any one of the advanced technologies studied and how this has changed between 1989 and 1998. It also investigates how growth rates in the 1990s have varied across different technologies in specific functional areas, such as design and engineering, fabrication, communications, and integration and control. In an attempt to discover how changes in technology use are related to certain plant characteristics, the paper then investigates whether the growth in technology use varies across plants that differ by size, nationality and industry. Multivariate analysis is used to investigate the joint effects of plant size, foreign ownership and industry on the incidence of technology adoption and how these effects have changed over the last decade.
Release date: 1999-12-14 - Articles and reports: 12-001-X199600114390Description:
Data are often available only as a set of group or area means. However, it is well known that statistical analysis based on such data will often produce results very different from those obtained from analysing the corresponding individual or household data. If the results of area level analyses are thought to apply to the individual level then we risk committing the ecological fallacy. Aggregation or ecological effects arise in part because geographic areas are not comprised of random groupings of people or households but exhibit strong socio-economic differences between areas. The population structure must be incorporated into the statistical model underpinning the analysis if aggregation effects are to be understood. A simple general model is proposed to achieve this and the consequences of the model and its implications for the estimation of population means and covariance matrices are obtained. Furthermore, methods are suggested which can provide unbiased estimates of individual level parameters from aggregated data and so avoid the ecological fallacy. These methods rely on identifying the “grouping variables” that characterise the process that led to the population structure, or at least characterise the area differences. An estimate of the unit level covariance matrix of the grouping variables is required from some source. Data from the 1991 Census of the United Kingdom have been analysed to identify the important grouping variables and evaluate the effectiveness of the proposed adjustment methods for the estimation of covariance matrices and correlation coefficients. These results lead to a suggested strategy for the analysis of aggregated data.
Release date: 1996-06-14
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- Articles and reports: 12-001-X201800154925Description:
This paper develops statistical inference based on super population model in a finite population setting using ranked set samples (RSS). The samples are constructed without replacement. It is shown that the sample mean of RSS is model unbiased and has smaller mean square prediction error (MSPE) than the MSPE of a simple random sample mean. Using an unbiased estimator of MSPE, the paper also constructs a prediction confidence interval for the population mean. A small scale simulation study shows that estimator is as good as a simple random sample (SRS) estimator for poor ranking information. On the other hand it has higher efficiency than SRS estimator when the quality of ranking information is good, and the cost ratio of obtaining a single unit in RSS and SRS is not very high. Simulation study also indicates that coverage probabilities of prediction intervals are very close to the nominal coverage probabilities. Proposed inferential procedure is applied to a real data set.
Release date: 2018-06-21 - Articles and reports: 75F0002M2008006Geography: Province or territoryDescription:
Comparisons of low income between regions may have impacts on policy choices. However, it is often argued that rankings of distributions are not robust and that they are also quite sensitive to methods of defining low income. This paper avoids these problems by using a stochastic dominance approach to compare regional low income profiles in Canada without arbitrarily specifying a low-income line. This analysis is carried out for the 10 provinces using the Survey of Labour and Income Dynamics for 2000. Robustness of the results is also verified with respect to different choices of spatial price deflators and equivalence scales. The extent to which the findings are sensitive to the choice of an absolute or a relative concept of low income is also examined. We show that, in most cases, dominance relations can be determined and regional low income can be ordered for a wide range of low-income lines. We also show that dominance results are robust to the choice of equivalence scales, while rank reversal occurs when alternative cost-of-living deflators are used. Switching from an absolute to a relative low-income concept only affects low-income rankings for Ontario, Quebec and the Prairie provinces, but not in the case of other provinces. Nevertheless, for all scales, we find that low income is greatest in British Columbia.
Release date: 2008-10-09 - Articles and reports: 11F0019M1999105Geography: CanadaDescription:
This paper outlines the growth in advanced technology use that has taken place over the last decade in Canadian manufacturing establishments. It presents the percentage of plants that use any one of the advanced technologies studied and how this has changed between 1989 and 1998. It also investigates how growth rates in the 1990s have varied across different technologies in specific functional areas, such as design and engineering, fabrication, communications, and integration and control. In an attempt to discover how changes in technology use are related to certain plant characteristics, the paper then investigates whether the growth in technology use varies across plants that differ by size, nationality and industry. Multivariate analysis is used to investigate the joint effects of plant size, foreign ownership and industry on the incidence of technology adoption and how these effects have changed over the last decade.
Release date: 1999-12-14 - Articles and reports: 12-001-X199600114390Description:
Data are often available only as a set of group or area means. However, it is well known that statistical analysis based on such data will often produce results very different from those obtained from analysing the corresponding individual or household data. If the results of area level analyses are thought to apply to the individual level then we risk committing the ecological fallacy. Aggregation or ecological effects arise in part because geographic areas are not comprised of random groupings of people or households but exhibit strong socio-economic differences between areas. The population structure must be incorporated into the statistical model underpinning the analysis if aggregation effects are to be understood. A simple general model is proposed to achieve this and the consequences of the model and its implications for the estimation of population means and covariance matrices are obtained. Furthermore, methods are suggested which can provide unbiased estimates of individual level parameters from aggregated data and so avoid the ecological fallacy. These methods rely on identifying the “grouping variables” that characterise the process that led to the population structure, or at least characterise the area differences. An estimate of the unit level covariance matrix of the grouping variables is required from some source. Data from the 1991 Census of the United Kingdom have been analysed to identify the important grouping variables and evaluate the effectiveness of the proposed adjustment methods for the estimation of covariance matrices and correlation coefficients. These results lead to a suggested strategy for the analysis of aggregated data.
Release date: 1996-06-14
Reference (2)
Reference (2) ((2 results))
- 1. Making Sense of Health Rankings ArchivedSurveys and statistical programs – Documentation: 82-582-XDescription:
This special methodological paper will help readers understand and assess reports that rank the health status or health system performance of a country, province or jurisdiction. The report outlines the components and processes that underlie health rankings, explores why such rankings can be difficult to interpret and includes a plain-language checklist to use as a critical evaluative resource when reading health-ranking reports.
Release date: 2008-09-16 - Surveys and statistical programs – Documentation: 11-522-X20050019476Description:
The paper will show how, using data published by Statistics Canada and available from member libraries of the CREPUQ, a linkage approach using postal codes makes it possible to link the data from the outcomes file to a set of contextual variables. These variables could then contribute to producing, on an exploratory basis, a better index to explain the varied outcomes of students from schools. In terms of the impact, the proposed index could show more effectively the limitations of ranking students and schools when this information is not given sufficient weight.
Release date: 2007-03-02
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