Statistical methods

Skip to filters. View results.

Key indicators

Changing any selection will automatically update the page content.

Selected geographical area:Canada

Selected geographical area:Newfoundland and Labrador

Selected geographical area:Prince Edward Island

Selected geographical area:Nova Scotia

Selected geographical area:New Brunswick

Selected geographical area:Quebec

Selected geographical area:Ontario

Selected geographical area:Manitoba

Selected geographical area:Saskatchewan

Selected geographical area:Alberta

Selected geographical area:British Columbia

Selected geographical area:Yukon

Selected geographical area:Northwest Territories

Selected geographical area:Nunavut

Sort Help
entries

Results

All (2,478)

All (2,478) (10 to 20 of 2,478 results)

  • Articles and reports: 12-001-X202500200003
    Description: In this paper a model-based inference procedure based on a multivariate structural time series model is developed for the production of monthly figures about consumer confidence. The input for the model are five series of direct estimates for the indices that measure consumer confidence, which are derived from the Dutch Consumer Survey. The model improves the accuracy of the direct estimates, since it provides a better separation of measurement errors and sampling errors from estimated target parameters. The standard errors for the month-to-month changes are clearly smaller under the time series model. A second problem addressed in this paper is related to the transition to a new survey process in 2017. Structural time series models in combination with a parallel run are applied to estimate discontinuities induced by the redesign. An algorithm designed for the consumer confidence variables is developed to construct uninterrupted input series for the aforementioned structural time series model. This inference method facilitated a smooth transition to a new survey design and resulted in uninterrupted series about consumer confidence that date back to 1986. The method is implemented for the production of official monthly figures on consumer confidence in the Netherlands.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200004
    Description: The class of generalized linear models (GLM) is a flexible generalization of ordinary least squares regression that allows the linear model to be related to the response variable via a link function and assumes the magnitude of the variance of each measurement to be a function of its predicted value. Multicollinearity in GLMs can inflate variances of the estimated coefficients and cause poor prediction in certain regions of the regression space. It may also cause a nonsignificant Wald statistic even when the predictors are highly predictive in a model of the family of GLMs. Little previous research has closely investigated the diagnostics of multicollinearity in GLMs, especially when complex survey data are used. In this paper, we develop variance inflation factors (VIFs) that measure the amount that the variance of a parameter estimator is increased due to multicollinearity in GLMs. We also extend VIFs and condition indexes to apply to complex survey data, accounting for design features, e.g. weights, clusters, and strata. Illustrations of these methods are given using data from a household survey of health and nutrition.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200005
    Description: The use of non-probability data sources for statistical purposes and for official statistics has become increasingly popular in recent years. However, statistical inference based on non-probability samples is made more difficult by nature of their biasedness and lack of representativity. In this paper we propose quantile balancing inverse probability weighting estimator (QBIPW) for non-probability samples. We apply the idea of Harms and Duchesne (2006) allowing the use of quantile information in the estimation process to reproduce known totals and the distribution of auxiliary variables. We discuss the estimation of the QBIPW probabilities and its variance. Our simulation study has demonstrated that the proposed estimators are robust against model mis-specification and, as a result, help to reduce bias and mean squared error. Finally, we applied the proposed methods to estimate the share of job vacancies aimed at Ukrainian workers in Poland using an integrated set of administrative and survey data about job vacancies.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200006
    Description: National Statistical Institutes (NSIs) are directing resources into advancing the use of administrative data in official statistics. Administrative data, however, are not developed for the purpose of producing statistics rather as a result of an event or transaction relating to administrative procedures of organizations, public administrations and government agencies. Therefore, it is essential to check the quality of the administrative data with respect to sources of error, particularly representativeness to the target population. In this paper, we utilize the strength of probability-based reference samples or censuses that can be used to detect the lack of representativeness in administrative data and introduce quality indicators based on distance metrics and representativity indicators (R-indicators). We demonstrate their application with a simulation study and discuss a real application applied on a UK Office for National Statistics (ONS) administrative dataset.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200007
    Description: Although probability samples have been regarded as the gold standard to collect information for population-based study, non-probability samples have been used frequently in practice due to low cost, convenience, and the lack of the sampling frame for the survey. Naïve estimates based on non-probability samples without any adjustments may be misleading due to selection bias. Recently, a valid data integration approach that includes mass imputation, propensity score weighting, and calibration has been used to improve the representativeness of non-probability samples. The effectiveness of the mass imputation approach depends on the underlying model assumptions. In this paper, we propose using deep learning for the mass imputation in the combining of probability and non-probability samples and compare it with several modern machine learning-based mass imputation approaches, including generalized additive modeling, regression tree, random forest, and XG-boosting. In the simulation study, deep learning-based approaches have been shown to be more robust and effective than other mass imputation approaches against the failure of underlying model assumptions under non-linearity scenarios.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200008
    Description: Classical design-based survey estimation relies on a properly specified sampling design for valid inference. We consider the properties of regression estimation under a misspecified sample design, in which the nominal and true inclusion probabilities do not necessarily match. This general misspecified sample design setting encompasses many challenges in the modern survey environment. Under this setting, an asymptotic analysis of the regression estimator, an expression of the bias, and an expression of the variance are presented. Further, a consistent variance estimator is derived and an expression which estimates the bias in-part or in-whole is discussed. This later expression may be used as an indicator of the presence of bias due to misspecification by a practitioner. A simulation study is conducted to support the presented theory.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200009
    Description: We present and apply methodology to improve inference for small area parameters by using data from several sources. This work extends Cahoy and Sedransk (2023) who showed how to integrate summary statistics from several sources. Our methodology uses hierarchical global-local prior distributions to make inferences for the proportion of individuals in Florida’s counties who do not have health insurance. Results from an extensive simulation study show that this methodology will provide improved inference by using several data sources. Among the five model variants evaluated the ones using horseshoe priors for all variances have better performance than the ones using lasso priors for the local variances.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200010
    Description: In this paper, we study the performance of hierarchical Bayes (HB) small area estimators using noninformative and informative priors. We apply the Bayesian models of You and Chapman (2006) and You (2021) to the Canadian Labor Force Survey (LFS) data and evaluate the impact of the priors on the HB estimators. A Bayesian model comparison and simulation study are also conducted. Our results indicate that a correct informative prior can lead to very good results, and noninformative priors can also perform very well. Incorrect informative priors can lead to poor results in terms of large bias and large coefficient of variation (CV). Noninformative priors are recommended in practice for HB small area estimation unless correctly specified informative priors are available. Informative priors are particularly useful when the number of small areas is relatively small.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200011
    Description: We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function (NEF-QVF) in combining information from multiple sources to improve traditional survey estimates of finite population means for small areas. Unlike other Bayesian approaches in finite population sampling, we do not assume a model for all units of the finite population and do not require linking sampled units to the finite population frame. We assume a model only for the finite population units in which the outcome variable is observed; because, for these units, the assumed model can be checked using existing statistical tools. We do not posit an elaborate model on the true means for unobserved units. Instead, we assume that population means of cells with the same combination of factor levels are identical across small areas, and that the population mean for a cell is identical to the mean of the observed units in that cell. We apply our proposed methodology to a real-life survey, linking information from multiple disparate data sources. We also provide practical ways of model selection that can be applied to a wider class of models under similar setting but for a diverse range of scientific problems.
    Release date: 2025-12-23

  • Articles and reports: 12-001-X202500200012
    Description: The observed best prediction (OBP) under a nested-error regression (NER) model was previously proposed using a design-based mean squared prediction error (MSPE) as a tool to derive the best predictive estimator (BPE). A recent study showed the OBP under the NER model may suffer from numerical instability when computing the BPE. We propose several modifications of the OBP under the NER model, including ones using a model-based MSPE to derive the BPE, to improve the numerical stability and predictive performance. We compare the performance of the modified OBP strategies with the existing methods in a simulation study. A real-data example is discussed.
    Release date: 2025-12-23
Data (10)

Data (10) ((10 results))

  • Public use microdata: 89F0002X
    Description: The SPSD/M is a static microsimulation model designed to analyse financial interactions between governments and individuals in Canada. It can compute taxes paid to and cash transfers received from government. It is comprised of a database, a series of tax/transfer algorithms and models, analytical software and user documentation.
    Release date: 2026-02-12

  • Profile of a community or region: 46-26-0002
    Description: The National Address Register (NAR) is a list of commercial and residential addresses in Canada that are extracted from Statistics Canada's Building Register and deemed non-confidential.
    Release date: 2025-12-19

  • Table: 89-26-0006
    Description: PASSAGES is an open-source dynamic microsimulation model aimed at supporting policy analysis and research relating to Canadian retirement income system outcomes at the individual and family level. The publicly available version includes a synthetic starting database, a model, and documentation. A confidential starting database is also available.
    Release date: 2025-03-12

  • Data Visualization: 71-607-X2020010
    Description: The Canadian Statistical Geospatial Explorer empowers users to discover geo enabled data holdings of Statistics Canada at various levels of geography including at the neighbourhood level. Users are able to visualize, thematically map, spatially explore and analyze, export and consume data in various formats. Users can also view the data superimposed on satellite imagery, topographic and street layers.
    Release date: 2024-08-21

  • Table: 11-10-0074-01
    Geography: Census tract
    Frequency: Occasional
    Description:

    The divergence index (D-index) describes the degree that families with different income levels are mixing together in neighbourhoods. It compares neighbourhood (census tract, CT) discrete income distributions to a base distribution, which is the income quintiles of the neighbourhood’s census metropolitan area (CMA).

    Release date: 2020-06-22

  • Data Visualization: 71-607-X2019010
    Description: The Housing Data Viewer is a visualization tool that allows users to explore Statistics Canada data on a map. Users can use the tool to navigate, compare and export data.
    Release date: 2019-10-30

  • Table: 53-500-X
    Description:

    This report presents the results of a pilot survey conducted by Statistics Canada to measure the fuel consumption of on-road motor vehicles registered in Canada. This study was carried out in connection with the Canadian Vehicle Survey (CVS) which collects information on road activity such as distance traveled, number of passengers and trip purpose.

    Release date: 2004-10-21

  • Table: 13-220-X
    Description: In the 1997 edition, new and revised benchmarks were introduced for 1992 and 1988. The indicators are used to monitor supply, demand and employment for tourism in Canada on a timely basis. The annual tables are derived using the National Income and Expenditure Accounts (NIEA) and various industry and travel surveys. Tables providing actual data and percentage changes, for seasonally adjusted current and constant price estimates are included. In addition, an analytical section provides graphs, and time series of first differences, percentage changes, and seasonal factors for selected indicators. Data are published from 1987 and the publication will be available on the day of release. New data are included in the demand tables for non-tourism commodities produced by non-tourism industries and in the employment tables covering direct tourism employment generated by non-tourism industries. This product was commissioned by the Canadian Tourism Commission to provide annual updates for the Tourism Satellite Account.
    Release date: 2003-01-08

  • Table: 11-516-X
    Description:

    The second edition of Historical statistics of Canada was jointly produced by the Social Science Federation of Canada and Statistics Canada in 1983. This volume contains about 1,088 statistical tables on the social, economic and institutional conditions of Canada from the start of Confederation in 1867 to the mid-1970s. The tables are arranged in sections with an introduction explaining the content of each section, the principal sources of data for each table, and general explanatory notes regarding the statistics. In most cases, there is sufficient description of the individual series to enable the reader to use them without consulting the numerous basic sources referenced in the publication.

    The electronic version of this historical publication is accessible on the Internet site of Statistics Canada as a free downloadable document: text as HTML pages and all tables as individual spreadsheets in a comma delimited format (CSV) (which allows online viewing or downloading).

    Release date: 1999-07-29

  • Table: 82-567-X
    Description:

    The National Population Health Survey (NPHS) is designed to enhance the understanding of the processes affecting health. The survey collects cross-sectional as well as longitudinal data. In 1994/95 the survey interviewed a panel of 17,276 individuals, then returned to interview them a second time in 1996/97. The response rate for these individuals was 96% in 1996/97. Data collection from the panel will continue for up to two decades. For cross-sectional purposes, data were collected for a total of 81,000 household residents in all provinces (except people on Indian reserves or on Canadian Forces bases) in 1996/97.

    This overview illustrates the variety of information available by presenting data on perceived health, chronic conditions, injuries, repetitive strains, depression, smoking, alcohol consumption, physical activity, consultations with medical professionals, use of medications and use of alternative medicine.

    Release date: 1998-07-29
Analysis (2,036)

Analysis (2,036) (2,020 to 2,030 of 2,036 results)

  • Articles and reports: 12-001-X197500254829
    Description: J.N.K. Rao (1975) derived a general formula for estimating the variance in multistage sample designs. This general formula extends the previous results by Des Raj (1966) to the case where the conditional variance from a given primary sampling unit is a random variable. The authors reviewed Rao's paper for its application to Horvitz-Thompson and Yates-Grundy variance estimators as well as the variance estimator for the random group method by Rao, Hartley and Cochran (1962). The authors present an altered version of the Yates-Grundy variance estimators as a result of Rao's paper.
    Release date: 1975-12-15

  • Articles and reports: 12-001-X197500254830
    Description: This paper focuses on the improvement of sample survey estimates in the particular situation where the survey sample, or part of it, is included in a larger sample from which auxiliary information is available. The properties of a method of estimation - sometimes applied in specific circumstances - are investigated and the limitations of its application are found. The application of the method to rotation designs in continuing surveys is more closely studied in the context of composite estimation.
    Release date: 1975-12-15

  • Articles and reports: 12-001-X197500254831
    Description: This paper summarizes the results of a telephone experiment conducted in conjunction with the Canadian Labour Force Survey over the period June 1972 to November 1973. Included in the paper is a detailed outline of the purpose and design of the experiment. A discussion of the impact telephone interviewing had on the cost of enumeration, non-response and participation and unemployment rates is given. In addition, interviewer and respondent attitudes toward telephone interviewing are described. Finally, the paper summarizes the experiences gained from this experiment and indicates some areas where further examinations related to telephone interviewing can be carried out.
    Release date: 1975-12-15

  • Articles and reports: 12-001-X197500254832
    Description: A ratio estimate based on an auxiliary variable is considered for the case when the sample is post-stratified using information on another auxiliary variable. The variance of the ratio estimate is derived by the method of linearization [3,4]. An application to subprovincial estimation in the Canadian Labour Force Survey is discussed.
    Release date: 1975-12-15

  • Articles and reports: 12-001-X197500300001
    Description: Most sample surveys in the past have been "descriptive" in the sense that the main objective is the computation of means or totals of a number of characters of interest along with their standard errors. However, in recent years data produced from "descriptive" surveys are also being increasingly used for "analytical" purposes, i.e., for investigating relationships among variables. Also some sample surveys might have primary "analytical goals" in which case the "optimal" designing of such "analytical surveys" becomes important.

    These lecture notes present an account of some recent developments in the analytical studies of sample survey data. Many challenging problems remain to be solved and I hope these notes will provide stimulation for further research in this important area.
    Release date: 1975-12-15

  • Articles and reports: 12-001-X197500254824
    Description:

    Madow [1968] has proposed a two-phase sampling scheme under which response bias can be eliminated from sample surveys by obtaining “true” values for a subsample of the original sample. Often in cases of Censuses or ongoing surveys, the subsample data are not used to correct the main survey estimates but to assess their reliability. The main purpose of this paper is to present methods by which reliability estimates can be obtained when true values can be determined for a subsample of units.

    Release date: 1975-12-15

  • Articles and reports: 12-001-X197500254825
    Description:

    Random rounding is a technique to ensure confidentiality of aggregate statistics. By randomly rounding all the components of a total, independently, together with the random rounding of the total itself, substantial discrepancies may arise when aggregating the published data. This paper presents a procedure which avoids substantial discrepancies while still protecting the concept of confidentiality.

    Release date: 1975-12-15

  • Articles and reports: 12-001-X197500100001
    Description: Although a survey is designed to satisfy a specific set of survey constraints, some steps involved in designing a survey, such as stratification, sample allocation and sample selection are common to all surveys. The steps involved in the creation of survey design systems are to identify, develop and implement common methods and procedures for such stages which, when taken together, constitute a survey design. The paper describes some methodological considerations in the development of an automated system for three methods of ratio estimation.
    Release date: 1975-06-16

  • Articles and reports: 12-001-X197500100002
    Description: In 1962, Hartley and Rao derived an asymptotic formula for the joint probability selection for samples selected with unequal probability sampling. In 1966, Connor, derived an exact formula for this joint probability, however, his formulae were very involved. In the present paper the authors, using a modification of Connor's formula derive the exact joint probabilities using a specially designed computer algorithm.
    Release date: 1975-06-16

  • Articles and reports: 12-001-X197500100003
    Description: In order to monitor changes in expenditure patterns and, if necessary, provide information for a reweighting of the Consumer Price Index, family expenditure surveys have been carried out at approximately two year intervals since 1953.

    While all of the Family Expenditure Surveys have utilized the Canadian Labour Force Survey [1] frame, the particular survey in 1974 was designed somewhat differently from earlier surveys in that segments or city blocks were specially selected for the survey and there was strict control on the sample size not adhered to in earlier surveys.

    The sample design, from the considerations based on the broad requirements of the survey to the details of the sampling procedures, is described in this article.
    Release date: 1975-06-16
Reference (380)

Reference (380) (10 to 20 of 380 results)

  • Surveys and statistical programs – Documentation: 89-657-X2024009
    Description: The Survey on the Official Language Minority Population (SOLMP) user guide contains a description of the survey, along with survey concepts and definitions and an overview of the content development. The target and survey populations, the sample design and sample size are described in the Methodology section. Finally, in the Data Collection module, the collection period and instrument, modes of collection, collection and communications strategies and response rates are provided.
    Release date: 2024-12-16

  • Surveys and statistical programs – Documentation: 11-633-X2024004
    Description: The Longitudinal Immigration Database (IMDB) is a comprehensive source of data that plays a key role in the understanding of the economic behaviour of immigrants. It is the only annual Canadian dataset that allows users to study the characteristics of immigrants to Canada at the time of admission and their economic outcomes and regional (inter-provincial) mobility over a time span of more than 40 years.
    Release date: 2024-12-09

  • Surveys and statistical programs – Documentation: 11-633-X2024005
    Description: The Analytical Studies and Modelling Branch is the research (ASMB), modelling, training and access hub of Statistics Canada. It focuses on leveraging the agency’s vast data holdings to generate in-depth insights that support evidence-based policy making and to enable others to do so through analytical training and data access. The ASMB, like other program areas in the agency, works to support Statistics Canada’s overall mission of delivering insights through data for a better Canada.
    Release date: 2024-12-06

  • Surveys and statistical programs – Documentation: 98-303-X
    Description: The Coverage Technical Report will present the errors included in census data that result from persons who are either missed (not enumerated) or enumerated more than once. The population coverage error is one of the most important types of errors because it affects the accuracy of not only population counts, but also all the census data results that describe the characteristics of the population universe.
    Release date: 2024-10-23

  • Surveys and statistical programs – Documentation: 89-653-X2024002
    Description: This guide is intended to provide a detailed review of both the 2022 IPS and IPS–NIS with respect to subject matter and methodological approaches. It is designed to help data users by serving as a guide to the concepts and measures of the survey as well as the technical details of the survey’s design, field work and data processing. This guide is meant to provide users with helpful information on how to use and interpret survey results. The discussion on data quality also allows users to review the strengths and limitations of the data for their particular needs.

    Chapter 1 of this guide provides an overview of the 2022 IPS and IPS–NIS by introducing the survey background and objectives. Chapter 2 outlines the survey’s themes and explains the key concepts and definitions used for the survey. Chapters 3 to 6 cover important aspects of the survey methodology, sampling design, data collection and processing. Chapters 7 and 8 review issues of data quality and caution users about comparing 2022 IPS or IPS–NIS data with data from other sources. Chapter 9 outlines the survey products available to the public, including data tables, analytical articles and reference material. The appendices provide a comprehensive list of survey indicators, extra coding categories and standard classifications used on both the IPS and the IPS–NIS. Lastly, a glossary of survey terms and information on confidence intervals is also provided.
    Release date: 2024-08-14

  • Surveys and statistical programs – Documentation: 75-514-G
    Description: The Guide to the Job Vacancy and Wage Survey contains a dictionary of concepts and definitions, and covers topics such as survey methodology, data collection, processing, and data quality. The guide covers both components of the survey: the job vacancy component, which is quarterly, and the wage component, which is annual.
    Release date: 2024-06-18

  • Surveys and statistical programs – Documentation: 32-26-0007
    Description: Census of Agriculture data provide statistical information on farms and farm operators at fine geographic levels and for small subpopulations. Quality evaluation activities are essential to ensure that census data are reliable and that they meet user needs.

    This report provides data quality information pertaining to the Census of Agriculture, such as sources of error, error detection, disclosure control methods, data quality indicators, response rates and collection rates.
    Release date: 2024-02-06

  • Surveys and statistical programs – Documentation: 11-633-X2024001
    Description: The Longitudinal Immigration Database (IMDB) is a comprehensive source of data that plays a key role in the understanding of the economic behaviour of immigrants. It is the only annual Canadian dataset that allows users to study the characteristics of immigrants to Canada at the time of admission and their economic outcomes and regional (inter-provincial) mobility over a time span of more than 35 years.
    Release date: 2024-01-22

  • Surveys and statistical programs – Documentation: 75-005-M2023001
    Description: This document provides information on the evolution of response rates for the Labour Force Survey (LFS) and a discussion of the evaluation of two aspects of data quality that ensure the LFS estimates continue providing an accurate portrait of the Canadian labour market.
    Release date: 2023-10-30

  • Surveys and statistical programs – Documentation: 98-306-X
    Description:

    This report describes sampling, weighting and estimation procedures used in the Census of Population. It provides operational and theoretical justifications for them, and presents the results of the evaluations of these procedures.

    Release date: 2023-10-04