Analysis

Description:

A finite population of size N is supposed to contain M (unknown) units of a specified category A (say) constituting a domain with mean \mu. A procedure which involves drawing units using simple random sampling without replacement till a preassigned number of members of the domain is reached is proposed. An unbiased estimator of \mu is also derived. This is seen to be superior to the corresponding possibly biased estimator based on a comparable SRSWOR scheme with a fixed number of draws. The proposed scheme is also shown to admit unbiased estimators of M and the domain total T.

Description:

In response to a need for data on disabled persons in Canada, Statistics Canada undertook a program to create a disability database. This includes using supplements to the Canadian Labour Force Survey in the Fall of 1983 and the Spring of 1984, as well as including questions on the 1986 Census of Population. A general discussion of the background and content of the survey is presented. A comparison of screening methodologies conducted by Statistics Canada in November 1982 and January 1983 is presented and the results are compared.

Description:

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.

Description:

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.

Description:

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.

Description:

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.

Description: This video is part of a series that is designed to give you a basic understanding of the Census of Population web pages. The purpose of this video is to explain where to find the most popular standard data product of the Census of Population, the 2021 Census Profile, and how to filter the data.

Description: This video is part of a series that is designed to give you a basic understanding of the Census of Population web pages. The purpose of this video is to explain how to add geographies in the 2021 Census Profile and to present the various downloading options to see the data.

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: 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: In this rejoinder, I address the comments from the discussants, Dr. Takumi Saegusa, Dr. Jae-Kwang Kim and Ms. Yonghyun Kwon. Dr. Saegusa’s comments about the differences between the conditional exchangeability (CE) assumption for causal inferences versus the CE assumption for finite population inferences using nonprobability samples, and the distinction between design-based versus model-based approaches for finite population inference using nonprobability samples, are elaborated and clarified in the context of my paper. Subsequently, I respond to Dr. Kim and Ms. Kwon’s comprehensive framework for categorizing existing approaches for estimating propensity scores (PS) into conditional and unconditional approaches. I expand their simulation studies to vary the sampling weights, allow for misspecified PS models, and include an additional estimator, i.e., scaled adjusted logistic propensity estimator (Wang, Valliant and Li (2021), denoted by sWBS). In my simulations, it is observed that the sWBS estimator consistently outperforms or is comparable to the other estimators under the misspecified PS model. The sWBS, as well as WBS or ABS described in my paper, do not assume that the overlapped units in both the nonprobability and probability reference samples are negligible, nor do they require the identification of overlap units as needed by the estimators proposed by Dr. Kim and Ms. Kwon.

Description: In some of non-probability sample literature, the conditional exchangeability assumption is considered to be necessary for valid statistical inference. This assumption is rooted in causal inference though its potential outcome framework differs greatly from that of non-probability samples. We describe similarities and differences of two frameworks and discuss issues to consider when adopting the conditional exchangeability assumption in non-probability sample setups. We also discuss the role of finite population inference in different approaches of propensity scores and outcome regression modeling to non-probability samples.

Description: Pseudo weight construction for data integration can be understood in the two-phase sampling framework. Using the two-phase sampling framework, we discuss two approaches to the estimation of propensity scores and develop a new way to construct the propensity score function for data integration using the conditional maximum likelihood method. Results from a limited simulation study are also presented.

Description: Nonprobability samples emerge rapidly to address time-sensitive priority topics in different areas. These data are timely but subject to selection bias. To reduce selection bias, there has been wide literature in survey research investigating the use of propensity-score (PS) adjustment methods to improve the population representativeness of nonprobability samples, using probability-based survey samples as external references. Conditional exchangeability (CE) assumption is one of the key assumptions required by PS-based adjustment methods. In this paper, I first explore the validity of the CE assumption conditional on various balancing score estimates that are used in existing PS-based adjustment methods. An adaptive balancing score is proposed for unbiased estimation of population means. The population mean estimators under the three CE assumptions are evaluated via Monte Carlo simulation studies and illustrated using the NIH SARS-CoV-2 seroprevalence study to estimate the proportion of U.S. adults with COVID-19 antibodies from April 01-August 04, 2020.

Description: Papers in this series provide background discussions of the methods used to develop data for economic, health, and social analytical studies at Statistics Canada. They are intended to provide readers with information on the statistical methods, standards and definitions used to develop databases for research purposes. All papers in this series have undergone peer and institutional review to ensure that they conform to Statistics Canada's mandate and adhere to generally accepted standards of good professional practice.

Description: This article presents results from the first Survey of Sexual Misconduct in the Canadian Armed Forces. Namely, the prevalence of general sexualized behaviour in the workplace; discrimination on the basis of sex, sexual orientation, or gender identity; personal experiences of discrimination or sexualized behaviour; the prevalence of sexual assault; and knowledge of policies on sexual misconduct and perceptions of responses to sexual misconduct are examined. Where possible, results are analyzed by sex, environmental command, type of service, age, rank, and number of years of service.

Description: This publication features short, informative articles focusing on specific justice-related issues. For more in-depth articles on justice in Canada, see also Juristat, Catalogue no. 85-002-X.

Description:

Each issue contains a short article highlighting statistical insights on themes relating to agriculture, food and rural issues.

Description: This publication presents energy balance sheets in natural units and heat equivalents in primary and secondary forms, by province. Each balance sheet shows data on production, trade, interprovincial movements, conversion and consumption by sector. Analytical tables and details on non-energy products are also included. It includes explanatory notes, a historical energy summary table and data analysis. The publication also presents data on natural gas liquids, electricity generated from fossil fuels, solid wood waste and spent pulping liquor.

Description: The Departmental Sustainable Development Strategy (DSDS) outlines departmental actions, with measurable performance indicators, that support the implementation strategies of the 2022-2026 Federal Sustainable Development Strategy. The DSDS further outlines Statistics Canada’s sustainable development vision to produce data to help track whether Canada is moving toward a more sustainable future and highlights projects with links to supporting sustainable development goals.

Description: This series provides detailed documentation on the issues, concepts, methodology, data quality and other relevant research related to household expenditures from the Survey of Household Spending, the Homeowner Repair and Renovation Survey and the Food Expenditure Survey.

Description: This report summarizes the annual achievements of the Methodology Research and Development Program (MRDP) sponsored by the Modern Statistical Methods and Data Science Branch at Statistics Canada. This program covers research and development activities in statistical methods with potentially broad application in the agency’s statistical programs; these activities would otherwise be less likely to be carried out during the provision of regular methodology services to those programs. The MRDP also includes activities that provide support in the application of past successful developments in order to promote the use of the results of research and development work. Selected prospective research activities are also presented.

Description: The series covers environment accounts and indicators, environmental surveys, spatial environmental information and other research related to environmental statistics. The technical paper series is intended to stimulate discussion on a range of environmental topics.

Description: This series of analytical articles provides insights on the socio-economic environment in rural communities in Canada. New articles will be released periodically.