Analysis

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This presentation describes the important and urgent task of providing useful expressions for analytical statistics for complex sample designs. The following topics are discussed: effects of complex designs, sampling error for analytical statistics, subclasses involved in analytical statistics, comparisons of paired means, computation of analytical statistics and categorical data analysis.

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Univariate statistical models, linear regression models and generalized linear models are briefly reviewed. Examples of a two-way analysis of variance, a three-way analysis of variance and logistic regression for a three way layout are given.

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This paper proposes a modification to the method of Denton (1971) for adjusting sub-annual series to yearly totals. These totals originate from more reliable sources and constitute annual benchmarks. The benchmarked series derived according to the modified method is more parallel to the unbenchmarked series than this is the case with the original method. An additive and a proportional variant of the method are presented. These can easily be adapted for flow, stock and index series. Also presented are a few recommendations about the preliminary benchmarking of current data and the management of “historical” estimates of the series.

Description:

Using data from the Family Expenditures Surveys over time, consumer expenditures on in-home and transportation energy from 1969 to 1982 are being studied. This article briefly summarizes some of the procedures being used to explore the data, summarize it and develop insights into shifts in consumption for policy implications purposes. With such a complex data set and such a complex, multi-faceted subject for analysis some effort must be made to reduce information flows and at the same time increase the information content of each factor of both input and output in the analyses.

Description:

Standard chisquared (X^2) or likelihood ratio (G^2) tests for logistic regression analysis, involving a binary response variable, are adjusted to take account of the survey design. The adjustments are based on certain generalized design effects. The adjusted statistics are utilized to analyse some data from the October 1980 Canadian Labour Force Survey (LFS). The Wald statistic, which also takes the survey design into account, is also examined for goodness-of-fit of the model and for testing hypotheses on the parameters of the assumed model. Logistic regression diagnostics to detect any outlying cell proportions in the table and influential points in the factor space are applied to the LFS data, after making necessary adjustments to account for the survey design.

Description:

Most sample surveys conducted by organizations such as Statistics Canada or the U.S. Bureau of the Census employ complex designs. The design-based approach to statistical inference, typically the institutional standard of inference for simple population statistics such as means and totals, may be extended to parameters of analytic models as well. Most of this paper focuses on application of design-based inferences to such models, but rationales are offered for use of model-based alternatives in some instances, by way of explanation for the author’s observation that both modes of inference are used in practice at his own institution.

Within the design-based approach to inference, the paper briefly describes experience with linear regression analysis. Recently, variance computations for a number of surveys of the Census Bureau have been implemented through “replicate weighting”; the principal application has been for variances of simple statistics, but this technique also facilitates variance computation for virtually any complex analytic model. Finally, approaches and experience with log-linear models are reported.

Description:

The paper shows different estimation methods for complex survey designs. Among others, estimation of mean, ratio and regression coefficient is presented. The standard errors are estimated by different methods: the ordinary least squares procedure, the stratified weighted sample procedure, the stratified unit weight procedure, etc. Theory of large samples and conditions to apply it are also presented.

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Cost models to determine an optimum allocation of the sample among stages in cluster samples are considered. Results from a proposed cost model, which directly considers the implications of follow-up visits to sample clusters as well as other travel to and from the field by data collectors, are compared with results from existing cost models. The proposed model generally calls for fewer clusters with more elements selected per cluster than the existing models.

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This study considers the suitability of composite estimation techniques for the Canadian Labour Force Survey. The performance of a class of AK composite estimators introduced initially by Gurney and Daly is investigated for several characteristics. While the ordinary composite estimate has a large bias, the AK composite estimate is capable of reducing the bias. Composite estimates having minimum variance and minimum mean square error are compared.

Description:

The oil crisis of the mid-1970’s triggered a new awareness among Canadians of the importance of energy conservation. The resulting government programs in the transportation sector demanded basic data about on-the-road fuel consumption by motor vehicles operating in Canadian conditions. This paper describes the Passenger Car Fuel Consumption Survey which was developed jointly by Statistics Canada and Transport Canada to meet this need. The methodology of the survey is described and some examples of the results are presented. The paper concludes with some speculation about future directions for the survey and for vehicle-usage statistics in general.

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Obtaining a work permit enables foreign nationals to work in Canada temporarily, and for many individuals, this serves as a stepping stone toward obtaining permanent residency (PR). This article examines the recent changes in the transition to PR across work permit programs and immigration pathways for individuals who have made the transition. The analysis focuses on work permit holders who are in Canada for work purposes under either the Temporary Foreign Worker Program (TFWP) or the International Mobility Program (IMP).

Description: Retaining and recruiting young skilled workers are important for any community, but perhaps even more so for communities where the main language spoken is a minority official language. This article informs the issue by calculating the share of youth who grew up in a province and eventually obtained a postsecondary education, but who left to work in another part of the country (termed “skill loss”). Likewise, the article also looks at young postsecondary graduates who entered a province to work, as a share of that province’s initial population of homegrown young postsecondary graduates (termed “skill gain”).

Description: Businesses have faced numerous challenges since the beginning of the COVID-19 pandemic. Public health restrictions on business and personal activities aimed at stopping the spread of the virus were associated with a slowing of economic activity. This article examines how new businesses that entered after the beginning of the pandemic fared compared with previous entry cohorts.

Description: On average, individuals who own their dwelling report higher satisfaction with their dwelling, neighbourhood and life than renters. These differences may reflect a positive causal impact of ownership on satisfaction. However, these differences could also reflect compositional effects, such as differences in household, dwelling and neighbourhood characteristics. Using the 2021 Canadian Housing Survey, this study provides a comparison of renters’ and owners’ reported dwelling, neighbourhood and life satisfaction accounting for compositional effects.

Description: Approximately one in four individuals in Canada is currently or has been a landed immigrant or permanent resident. From 2016 to 2021, about 1.3 million new immigrants arrived in Canada and accounted for 80% of the growth in the labour force. Alongside increases in immigrants, there has been a rise in same-sex couples within Canada. This study explores select sociodemographic and economic characteristics of immigrants in same-sex couples compared with their counterparts in opposite-sex couples from 2000 to 2020.

Description: This study presents an updated sociodemographic profile of children aged 0 to 14 years with affirmative responses largely based on parent reports to the questions on the 2021 Census long-form questionnaire about difficulties with activities of daily living.

Description: Inspired by the two excellent discussions of our paper, we offer some new insights and developments into the problem of estimating participation probabilities for non-probability samples. First, we propose an improvement of the method of Chen, Li and Wu (2020), based on best linear unbiased estimation theory, that more efficiently leverages the available probability and non-probability sample data. We also develop a sample likelihood approach, similar in spirit to the method of Elliott (2009), that properly accounts for the overlap between both samples when it can be identified in at least one of the samples. We use best linear unbiased prediction theory to handle the scenario where the overlap is unknown. Interestingly, our two proposed approaches coincide in the case of unknown overlap. Then, we show that many existing methods can be obtained as a special case of a general unbiased estimating function. Finally, we conclude with some comments on nonparametric estimation of participation probabilities.

Description: We provide comparisons among three parametric methods for the estimation of participation probabilities and some brief comments on homogeneous groups and post-stratification.

Description: Beaumont, Bosa, Brennan, Charlebois and Chu (2024) propose innovative model selection approaches for estimation of participation probabilities for non-probability sample units. We focus our discussion on the choice of a likelihood and parameterization of the model, which are key for the effectiveness of the techniques developed in the paper. We consider alternative likelihood and pseudo-likelihood based methods for estimation of participation probabilities and present simulations implementing and comparing the AIC based variable selection. We demonstrate that, under important practical scenarios, the approach based on a likelihood formulated over the observed pooled non-probability and probability samples performed better than the pseudo-likelihood based alternatives. The contrast in sensitivity of the AIC criteria is especially large for small probability sample sizes and low overlap in covariates domains.

Description: Non-probability samples are being increasingly explored in National Statistical Offices as an alternative to probability samples. However, it is well known that the use of a non-probability sample alone may produce estimates with significant bias due to the unknown nature of the underlying selection mechanism. Bias reduction can be achieved by integrating data from the non-probability sample with data from a probability sample provided that both samples contain auxiliary variables in common. We focus on inverse probability weighting methods, which involve modelling the probability of participation in the non-probability sample. First, we consider the logistic model along with pseudo maximum likelihood estimation. We propose a variable selection procedure based on a modified Akaike Information Criterion (AIC) that properly accounts for the data structure and the probability sampling design. We also propose a simple rank-based method of forming homogeneous post-strata. Then, we extend the Classification and Regression Trees (CART) algorithm to this data integration scenario, while again properly accounting for the probability sampling design. A bootstrap variance estimator is proposed that reflects two sources of variability: the probability sampling design and the participation model. Our methods are illustrated using Statistics Canada’s crowdsourcing and survey data.

Description: The fact sheets in this series provide an "at-a-glance" overview of particular aspects of education in Canada and summarize key data trends in selected tables published as part of the Pan-Canadian Education Indicators Program (PCEIP).

The PCEIP mission is to publish a set of statistical measures on education systems in Canada for policy makers, practitioners and the general public to monitor the performance of education systems across jurisdictions and over time. PCEIP is a joint venture of Statistics Canada and the Council of Ministers of Education, Canada (CMEC).

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The articles published in EnviroStats use statistics to illustrate topical environmental issues. The publication is intended for a general readership rather than an expert audience.

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The documents in this collection are based on data from the Longitudinal and International Study of Adults, a survey that examines a variety of topics on the well-being of Canadians and measures the effect of changes in certain areas on people's lives. The survey covers several topics, such as jobs, health, adult education and training, income and earnings, as well as the family dynamic. Reports on the survey content, concepts, methodology and data quality are also available.

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This report helps users understand how we balance protecting confidentiality and meeting needs for data. It provides information at a high level for major variables such as those related to gender, Indigenous peoples, visible minority, ethnocultural diversity, instruction in the official minority language and religious groups.

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Human Activity and the Environment (16-201-X) focuses on current environmental issues. The latest information and statistics are gathered from many sources to produce an in-depth analytical article.

Description: Health fact sheets will include short, focused, single-theme analysis documents. Over the course of the series, analysis will include topics on: Health conditions, lifestyle, well-being, disability, prevention and detection of disease, deaths, pregnancy and birth, health care services and environmental factors.

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The Report on the Demographic Situation in Canada analyses recent demographic patterns at the national, provincial and subprovincial levels. Trends in population growth and the evolution of the various components of Canada's population growth - fertility, mortality and migration (interprovincial and international) - as well as marital status, are examined. The Report on the Demographic Situation in Canada has been published annually or biennially since 1985. Beginning in 2011, the Report is available as a dynamic, internet-only publication in order to provide the most recent data and analyses on Canadian demographics as soon as they are available.

Description: Articles in the Economic Insights series highlight issues related to the growth and development of Canada's economy. In some cases, these articles highlight new insights or synthesize the results of previous research carried out by Statistics Canada; in others, they provide contextual information that accompanies the release of new data or updates from previous papers. The Economic Insights series features concise examinations of economic events, research results, trends, and important structural changes in the economy.

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Over 80 indicators measure the health of the Canadian population and the effectiveness of the health care system. Designed to provide comparable information at the health region and provincial/territorial levels, these data are produced from a wide range of the most recently available sources.

This Internet publication is produced by Statistics Canada and the Canadian Institute for Health Information.

Description:

The Geography working paper series is intended to stimulate discussion on a variety of topics covering conceptual, methodological or technical work to support the development and dissemination of the division's data, products and services. Readers of the series are encouraged to contact the Geography Division with comments and suggestions.