Analysis

Description:

The Canadian Health and Disability Survey, administered as a supplement to the Canadian Labour Force Survey in October 1983, collected data on potentially disabled persons by means of a screening questionnaire and a follow-up questionnaire for those screened-in. The data from the screening questionnaire, consisting of a set of activities of daily living, were used to group respondents according to identifiable characteristics. A description of the groups of respondents is provided along with an evaluation of the methods used in their determination. An incompletely ordered severity scale is proposed.

Description:

The seasonal adjustment of a time series is not a straightforward procedure particularly when the level of a series nearly doubles in just one year. The 1981-82 recession had a very sudden great impact not only on the structure of the series but on the estimation of the trend- cycle and seasonal components at the end of the series. Serious seasonal adjustment problems can occur. For instance: the selection of the wrong decomposition model may produce underadjustment in the seasonally high months and overadjustment in the seasonally low months. The wrong decomposition model may also signal a false turning point. This article analyses these two aspects of the interplay between a severe recession and seasonal adjustment.

Description:

Nearly all surveys and censuses are subject to two types of nonresponse: unit (total) and item (partial). Several methods of compensating for nonresponse have been developed in an attempt to reduce the bias associated with nonresponse. This paper summarizes the nonresponse adjustment procedures used at the U.S. Census Bureau, focusing on unit nonresponse. Some discussion of current and future research in this area is also included.

Description:

From an annual sample of U.S. corporate tax returns, the U.S. Internal Revenue Service provides estimates of population and subpopulation totals for several hundred financial items. The basic sample design is highly stratified and fairly complex. Starting with the 1981 and 1982 samples, the design was altered to include a double sampling procedure. This was motivated by the need for better allocation of resources, in an environment of shrinking budgets. Items not observed in the subsample are predicted, using a modified hot deck imputation procedure. The present paper describes the design, estimation, and evaluation of the effects of the new procedure.

Description:

The Canadian Census of Construction (COC) uses a complex plan for sampling small businesses (those having a gross income of less than $750,000). Stratified samples are drawn from overlapping frames. Two subsamples are selected independently from one of the samples, and more detailed information is collected on the businesses in the subsamples. There are two possible methods of estimating totals for the variables collected in the subsamples. The first approach is to determine weights based on sampling rates. A number of different weights must be used. The second approach is to impute values to the businesses included in the sample but not in the subsamples. This approach creates a complete “rectangular” sample file, and a single weight may then be used to produce estimates for the population. This “large-scale imputation” technique is presently applied for the Census of Construction. The purpose of the study is to compare the figures obtained using various estimation techniques with the estimates produced by means of large-scale imputation.

Description:

In the presence of unit nonresponse, two types of variables can sometimes be observed for units in the “intended” sample s, namely, (a) variables used to estimate the response mechanism (the response probabilities), (b) variables (here called co-variates) that explain the variable of interest, in the usual regression theory sense. This paper, based on Särndal and Swensson (1985 a, b), discusses nonresponse adjusted estimators with and without explicit involvement of co-variates. We conclude that the presence of strong co-variates in an estimator induces several favourable properties. Among other things, estimators making use of co-variates are considerably more resistant to nonresponse bias. We discuss the calculation of standard error and valid confidence intervals for estimators involving co-variates. The structure of the standard error is examined and discussed.

Description:

The procedure of subsampling the nonrespondents suggested by Hansen and Hurwitz (1946) is considered. Post-stratification prior to the subsampling is examined. For the mean of a characteristic of interest, ratio estimators suitable for different practical situations are proposed and their merits are examined. Suitable ratio estimators are also suggested for the situations in which the Hard-Core are present.

Description:

Missing survey data occur because of total nonresponse and item nonresponse. The standard way to attempt to compensate for total nonresponse is by some form of weighting adjustment, whereas item nonresponses are handled by some form of imputation. This paper reviews methods of weighting adjustment and imputation and discusses their properties.

Description:

In this paper, different types of response/nonresponse and associated measures such as rates are provided and discussed together with their implications on both estimation and administrative procedures. The missing data problems lead to inconsistent terminology related to nonresponse such as completion rates, eligibility rates, contact rates, and refusal rates, many of which can be defined in different ways. In addition, there are item nonresponse rates as well as characteristic response rates. Depending on the uses, the rates may be weighted or unweighted.

Description:

Using the optimal estimating functions for survey sampling estimation (Godambe and Thompson 1986), we obtain some optimality results for nonresponse situations in survey sampling.

Description:

Canada’s diversity and rich cultural heritage have been shaped by the people who have come from all over the world to call it home. But even in our multicultural society, eliminating all forms of discrimination remains a challenge. In this episode, we turn a critical eye to the ways that cognitive bias risks perpetuating systemic racism. Statistics are supposed to accurately reflect the world around us, but are all data created equal? Join our guests, Sarah Messou-Ghelazzi, Communications Officer, Filsan Hujaleh, Analyst with the Centre for Social Data Insights and Innovation, and Jeff Latimer, Director General - Accountable for Health, Justice, Diversity and Populations at Statistics Canada as we explore the role data can play to make Canada a more equal society for all.

Description:

This infographic explains the steps involved in collecting data for all Statistics Canada household and business surveys. The responses are compiled, analyzed and used to make important decisions and are kept strictly confidential.

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

Description:

This infographic provides a high-level overview of Statistics Canada’s Disaggregated Data Action Plan, which will produce detailed statistical information on specific population groups. This plan is essential to highlight the lived experiences of diverse groups of people in Canada, such as women, Indigenous peoples, racialized populations and people living with disabilities.

Description:

This video is intended to teach viewers the differences between three fundamental statistical concepts. First, the mean, then the median and finally, the mode.

Description:

In this module, we will explore the concept of dispersion, also called variability. This concept includes: the range, the interquartile range, the standard deviation and the normal distribution.

Description:

As Canada's national statistical organization, Statistics Canada is committed to sharing our knowledge and expertise to help all Canadians develop their data literacy skills. The goal is to provide learners with information on the basic concepts and skills with regard to a range of data literacy topics.

The training is aimed at those who are new to data or those who have some experience with data but may need a refresher or want to expand their knowledge. We invite you to check out our Learning catalogue to learn more about our offerings including a great collection of short videos. Be sure to check back regularly as we will be continuing to release new training.

Description:

This video is intended for viewers who wish to gain a basic understanding of correlation and causality. As a prerequisite, before beginning this video, we highly recommend having already completed our videos titled “What is Data? An Introduction to Data Terminology and Concepts” and “Types of Data: Understanding and Exploring Data”.

Description:

In this video, viewers will learn the differences between three types of measure: proportions, ratios, and rates. In addition, viewers by the end of this video will be able to determine how each measure is calculated and when it is best to use one measure rather than the other.

Description:

One important distinction we will make in this video is the differences between Data Science, Artificial Intelligence and Machine Learning. You'll learn what machine learning can be used for, how it works, and some different methods for doing it. And you'll also learn how to build and use machine learning processes responsibly.

This video is recommended for those who already have some familiarity with the concepts and techniques associated with computer programming and using algorithms to analyze data.

Description: This article provides information about population totals in the Labour Force Survey (LFS), including details on who is included in the survey target population, and a description of the methodology used to produce monthly population totals in the LFS. The note also provides guidance on how to interpret population statistics in the LFS, and discusses the extent to which the LFS can be used to examine disaggregated labour market indicators for new immigrants and non-permanent residents.

Description: This document briefly describes the small area estimation methodology developed to produce monthly estimates of employment and unemployment rate for census metropolitan areas, census agglomerations, and self-contained labour areas using data from the Labour Force Survey, Employment Insurance statistics and population projections.

Description: This study uses data from multiple waves of the Canadian Social Survey (CSS) to examine trends in three key Quality of Life indicators, namely life satisfaction, experiences of financial hardship, and future outlook. Monitoring these well-being indicators following periods of considerable social and economic change is particularly important. Beginning in the summer of 2021, the CSS, a new quarterly survey, captured the latter part of the COVID-19 pandemic as well as the rising cost of living in Canada, allowing for an understanding of how Canadians are coping with these challenges.

Description: In this paper, we look for presence of heterogeneity in conducting impact evaluations of the Skills Development intervention delivered under the Labour Market Development Agreements. We use linked longitudinal administrative data covering a sample of Skills Development participants from 2010 to 2017. We apply a causal machine-learning estimator as in Lechner (2019) to estimate the individualized program impacts at the finest aggregation level. These granular impacts reveal the distribution of net impacts facilitating further investigation as to what works for whom. The findings suggest statistically significant improvements in labour market outcomes for participants overall and for subgroups of policy interest.

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:

This study documents the methodological and technical challenges that are involved in performing analysis on small groups using a sample survey, oversampling, response rate, non-response rate due to language, release feasibility and sampling variability. It is based on the 1999 General Social Survey (GSS) on victimization.

Description:

Low income cut-offs (LICOs) are intended to convey the income level at which a family may be in straitened circumstances because it has to spend a greater portion of its income on the basics (food, clothing and shelter) than does the average family of similar size. The LICOs vary by family size and by size of community.

This publication provides a brief explanation of how the LICOs are derived and updated annually. In addition, it provides on a historical basis, LICOs for different family sizes by size of area of residence. LICOs are calculated based on the spending patterns of families on basic 'necessities' - food, shelter and clothing - as collected from the Survey of Household Spending (formerly referred to as the Family Expenditure Survey (FAMEX)).

Description:

This study was initiated to test the validity of probabilistic linkage methods used at Statistics Canada. It compared the results of data linkages on infant deaths in Canada with infant death data from Nova Scotia and Alberta. It also compared the availability of fetal deaths on the national and provincial files.

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).

Description:

The framework described here is intended as a basic operational instrument for systematic development of statistical information respecting the evolution of science and technology and its interactions with the society, the economy and the political system of which it is a part.