The hierarchy of the public sector along with its subcomponents.

Public sector:

• General governments
  • Federal general government
    • Government
      • Ministries and departments, non-autonomous funds and organizations
      • Autonomous funds and organizations
    • Federal non-autonomous pension plans
  • Social Security Funds^{Footnote 1}
    • Canada Pension Plan
    • Quebec Pension Plan
  • Provincial and territorial general government
    • Government
      • Ministries and departments, non-autonomous funds and organizations
      • Autonomous funds and organizations
    • Provincial non-autonomous pension plans
    • Universities and colleges
      • Universities^{Footnote 2}
      • Colleges, vocational and trade institutions^{Footnote 2}
    • Health and social service institutions
      • Health boards^{Footnote 2}
      • Social service organizations and community boards^{Footnote 2}
      • Other health and social service organizations^{Footnote 2}
  • Local general government
    • Government
      • Municipalities and quasi-municipalities, non-autonomous funds and organizations
      • Autonomous funds and organizations
    • School boards^{Footnote 2,Footnote 3}
  • Aboriginal general government
    • Government
      • Aboriginal governments
• Government business enterprises
  • Federal government business enterprises
  • Provincial and territorial government business enterprises
  • Local government business enterprises

Footnotes

The work of a Mathematical Statistician

At Statistics Canada, we produce and interpret a high volume of statistical information. We sample, collect, acquire, clean, correct, combine and analyze data to explain statistical information related to many aspects of Canada's economy and society. We produce statistics by conducting censuses every five years and by conducting numerous surveys, but also by exploiting data coming from a very broad range of data sources. We develop and use innovative solutions including machine learning and big data, state-of-the-art statistical theories and leading-edge statistical methods.

Statistics Canada is currently undertaking a significant transformation. Outcomes of this transformation will be an agency that is responsive to emerging data needs, increases the statistical literacy of Canadians and facilitates the responsible use of data for decision making. Innovative statistical methods are now more than ever essential to our success. A very knowledgeable, talented and diversified workforce is at the core of this transformation and Mathematical Statisticians play a key role.

Mathematical Statisticians apply, adapt and develop mathematical, statistical or survey methods to practical problems. They explore and adopt sophisticated methods to integrate and transform alternate data sources into statistical information. Their work is crucial to Statistics Canada. The quality of data outputs and the costs of operations are heavily dependent on the methodology used.

As a mathematical statistician, your main duties will consist of designing, implementing and evaluating statistical methods related to the production of official statistics. This could include work on surveys, work on research projects in various areas related to statistical methods, or work on new methods such as integrating data from a variety of existing sources or adopting new methods to analyze data. Mathematical Statisticians can also be involved in projects related to the combination of classic and leading edge statistical methods, including experimentation with machine learning, artificial intelligence techniques, non-probabilistic sampling, micro simulation and modeled/synthetic data. Mathematical Statisticians face a wide range of theoretical and practical statistical challenges!

Statistics Canada projects are normally developed through multidisciplinary project teams. Such teams can include experts from various area: subject-matter (e.g., economists, sociologists, geographers), survey operations, systems development and methodology (mathematical statisticians). This structure requires mathematical statisticians to acquire some knowledge of the client area in order to determine and meet its methodological needs.

Within a team, the Mathematical Statistician brings his or her expertise, experience and a critical, analytical mind to the area of statistical and survey methods. In the multidisciplinary project structure, he or she is primarily a service provider. The work of a Mathematical Statistician is highly diversified and requires creativity and adaptability. Individual Mathematical Statisticians usually work on several projects or activities at the same time. Each project is a new challenge; ready-made solutions in the literature can rarely be directly applied. To design and implement effective, scientifically sound methodology, a Mathematical Statistician must always maintain a good balance of skills in analytical and empirical research and operational work. The majority of Mathematical Statisticians provide methodological support services while some of them are also involved in research.

Research

Like any organization striving to be the best in its field, Statistics Canada places great emphasis on research. The organization has a long and rich tradition of research in the area of statistical methods. In particular, methodological research focuses on cutting-edge ways to produce reliable statistics at a lower cost.

Statistics Canada provides the environment and support that enable Mathematical Statisticians to deal with all types of research problems, whether they are associated with a specific project, or are more general in nature.

Mathematical Statisticians regularly conduct theoretical studies and empirical simulations to support the methodological services they provide to project teams. They also carry out research on a variety of subjects related to statistical methods, such as spatial and temporal estimation, non-sampling variance, outlier detection, benchmarking, interpolation and calendarization, longitudinal data analysis, and time series. Initially, research could make up only a small part of the duties of a mathematical statistician. However, it could become a major part of his/her duties depending on his/her experience and interests.

Results of mathematical statisticians' research projects may be presented at relevant conferences and published in technical journals. One of these is Statistics Canada's own internationally renowned journal, Survey Methodology.

To foster and promote research, Statistics Canada has established an external fellowship program. In addition, Statistics Canada is actively involved in joint research projects with universities and with statistical agencies in other countries.

Work environment

As a new employee, you will work closely with a more experienced Mathematical Statistician which will allow you to gain valuable experience that will enhance your professional skills.

Statistics Canada is committed to offering its employees a modern and flexible workplace. A great importance is placed on the well-being of employees. We have numerous programs and facilities designed for the benefit of employees. Health and safety, respect and fairness, flexible work arrangements, a sense of belonging and recognition and workplace wellness are at the heart of our organizational culture.

Training and development

Statistics Canada gives high priority to human resource training and development. Employees are encouraged to develop their interests and are supported throughout their career. Statistics Canada offers a complete, well-organized development program in both official languages.

Our statistical training program is large, varied and includes courses or other learning activities of high quality. In the current modernization context at Statistics Canada, mathematical-statisticians must maintain and develop their capacities related to traditional survey methods, while making room for leading-edge methods, data integration and data science.

One of the goals of our training and development program is to build a culture of productive learning. The courses in the classic classroom format are only one element among many of our training tools, that also include self-directed, informal, and hands on training.

In-house courses

A number of courses on statistics and survey methodology are offered on a regular basis by guest instructors or experienced Statistics Canada employees. The courses cover both classical theory and the results of recent research. To provide technical and professional support, a complete range of courses is also offered on other subjects as varied as informatics, project management, employee supervision and presentation skills.

All new employees also participate in a two-week, full-time course called Survey Skills Exploration Course. Participants work in teams to design a sample survey on a predetermined socio-economic topic thereby increasing their awareness of the policies, principles, complexities, and interrelationships inherent in the design of a statistical survey. This practical training is complemented by classroom sessions that provide additional knowledge on survey methods and procedures.

Seminars, Conferences, and Publications

Mathematical statisticians are encouraged to present the results of their work at seminars and at relevant conferences, and to submit articles to technical journals. In addition to publishing the journal Survey Methodology, Statistics Canada holds an annual symposium on a topical theme related to statistical methods.

University education

Statistics Canada encourages employees to continue their professional development by taking academic courses relevant to their job. Three universities in the Ottawa-Gatineau area allow employees to improve their knowledge. As well as regular courses offered by local universities, there are programs customized for Statistics Canada personnel. Furthermore, on occasion, Statistics Canada grants education leave to employees. These employees have the possibility of full-time education leave to pursue an additional university degree in statistics or a related field.

Pay rates

Generally speaking, all candidates are hired at the MA -2 level. The starting salary of a mathematical statistician is $67,476^{Footnote *}. After 16 to 24 months experience at Statistics Canada, the salary reaches the first step of the MA-3 level. Annual pay increments then take place within the MA-3 level until the maximum salary is reached.

A registered pension plan, a dental care plan, a health care plan, a disability insurance plan, and life insurance are included in the benefits of the employees of the federal public service. As a new employee, you are entitled every year to 20 days of vacation leave, 15 days of sick leave, 5 days of leave for family-related responsibilities and 2 days of leave for a personal reason. Maternity/parental leave and up to 5 years of leave without pay for childcare and eldercare are also available.

Who can apply

Persons residing in Canada and Canadian citizens residing abroad. Preference will be given to veterans, Canadian citizens and permanent residents.

Application process

Step 1: Applications are online through the Public Service Commission website (Government of Canada jobs).

• Provide the following information:
  • your résumé;
  • your grades for courses already taken at a recognized post-secondary institution (with complete codes and titles);
  • a list of courses that you are taking or will be taking at a recognized post-secondary institution during this academic year (with complete codes and titles).

Step 2: Write the test.

Step 3: Successful candidates will be invited to an interview.

Upon request, you must be able to provide the following documents:

• a copy of your official transcripts from recognized post-secondary institutions;
• proof of Canadian equivalency if you have a foreign degree or degrees.

Qualifications and other requirements

Candidates must be able to demonstrate the following:

• A degree from a recognized post-secondary institution with specialization in:
  1. mathematics, statistics or operational research or
  2. one of the physical, life or social sciences, combined with an acceptable number of courses (normally 15 one-term courses/ approximately 45 credits) in mathematics, statistics or operational research at the level of a recognized post-secondary institution.
• Application of mathematical or statistical theories and techniques (including but not limited to probability theory and the distribution of random variables, hypothesis testing, analysis of variance, regression analysis, data analysis).
• Application of mathematical, statistical or survey methods and concepts (including but not limited to questionnaire design, sample design, estimation).
• Demonstrating integrity and respect (acting with transparency and fairness).
• Thinking things through (exercising sound judgment and obtaining relevant facts before making decisions).
• Working effectively with others (understanding their colleagues' roles, responsibilities and workloads, and balancing their own needs with those of other team members).
• Showing initiative and being action-oriented (accepting responsibilities and putting forward ideas and opinions).
• Ability to communicate effectively in writing in English or French.

Frequently asked questions

Visit our Frequently asked questions.

Suggested readings

In English

• Cochran, W.G. (1977), Sampling Techniques, John Wiley & Sons
• Govindarajulu, Z. (1999), Elements of Sampling Theory and Methods, Prentice Hall
• Hansen, M., Hurwitz, W. and Madow, W. (1953), Sample Survey Methods and Theory, John Wiley and Sons
• Kish, L. (1965), Survey Sampling, John Wiley & Sons
• Levy, P.S. and Lemeshow, S. (1999), Sampling of Populations: Methods and Applications, John Wiley & Sons
• Lohr, S.L. (1999), Sampling : Design and Analysis, Duxbury Press
• Raj, D. and Chandhok, P. (1998), Sample Survey Theory, Narosa Publishing House
• Rao, P.S.R.S. (2000), Sampling Methodologies With Applications, Chapman and Hall
• Sarndal, C.E., Swensson, B. and Wretman, J. (1992), Model-Assisted Survey Sampling, Springer-Verlag
• Satin, A. & Shastry, W. (1993), Survey Sampling: A Non-mathematical guide, 2nd edition, Statistics Canada, catalogue no . 12-602E
• Statistics Canada (2003), Survey methods and practices, Statistics Canada, catalogue no . 12-587-XPE
• Thompson, M.E. (1997), Theory of Sample Surveys, Chapman and Hall
• Thompson, S.K. (1992), Sampling, John Wiley & Sons

In French

• Ardilly, P. (1994), Les techniques de Sondage, Technip
• Brossier, G. et Dussaix, A.-M. éd . (1999), Enquêtes et sondages, Méthodes, modèles, applications, nouvelles approches, Dunod
• Morin, H. (1992) Théorie de l'échantillonnage, Les Presses de l'Université Laval
• Satin, A. & Shastry, W. (1993), L'échantillonnage - Un guide non mathématique, 2ième édition, Statistique Canada, 12-602F au catalogue.
• Statistique Canada (2003), Méthodes et pratiques d'enquête, Statistique Canada, 12-587-XPF au catalogue.
• Tillé, Y. (2001), Théorie des sondages, Échantillonnage et estimation en populations finies, Dunod

Examples of questions for the written test for Mathematical Statisticians

The written test is evaluating knowledge AND ability to communicate in writing. It consists of two parts. Part A contains one question to test writing ability. Part B tests knowledge and contains multiple choice questions, fill-in-the-blank questions and an open question. There is no break period between the two parts of the test.

Examples of questions similar to those found on the test are given below.

Please note that tests from previous years are not available.

Part A - Writing Ability

Example 1
Prepare a letter of approximately 200 to 300 words to the director of recruitment for Statistics Canada in which you explain how your training, work experience and interpersonal skills make you a strong candidate for a position as a mathematical statistician.

Example 2
In 2002 and 2007, public health officials conducted a survey on the lifestyle choices of members of your community. The following table shows an extract of the official results of that survey:

As a journalist involved in community affairs, you have followed this story closely from the beginning. Therefore, your editor-in-chief has asked you to write an article for your newspaper which explains the survey results to your readers.

Please write this article in 200 to 300 words.

Part B - Knowledge

Probability and Statistics

1. In a batch of 10 items, we wish to extract a sample of 3 without replacement. How many different samples can we extract?

Answer: 10! / (7!*3!) = 10*9*8 / (3*2*1) = 120

2. The difference between the parameter we wish to estimate and the expected value of its estimator is __________.

Answer: the bias

3. Let X and Y be independent random variables. Suppose the respective expected values are E(X) = 8 and E(Y) = 3 and the respective variances are V(X) = 9 and V(Y) = 6. Let Z be defined as Z = 2X – 3Y +5. Based on these data, the value of E(Z) is _____ and the value of V(Z) is _____.

Answer: 12 and 90

4. Which of the following statements about the X² (Chi-square) distribution is always false?

1. The X² distribution is asymmetrical.
2. The variance of a random variable having a X² distribution is twice its mean.
3. If X₁ and X₂ are two independent random variables with a X² distribution with n₁ and n₂ degrees of freedom respectively, then the variable Y = X₁ + X₂ has an F (Fisher) distribution with n₁ and n₂ degrees of freedom.
4. If X₁ , …, X_n are independent random variables having a normal distribution N(0,1), then X₁² +…+ X_n² has a X² distribution with n degrees of freedom.
5. The X² distribution is dependent only on a single parameter.

Answer: C

Sampling

5. Single stage cluster sampling is more precise than simple random sampling when the ___________ is negative.

Answer: intra-cluster correlation

6. In order to estimate the total for a variable of interest, a simple random sample without replacement of size N/4 from a population of size N is sought. After some thought, it is decided that a simple random sample without replacement of size N/2, instead, will be drawn from the same population. By what factor is the variance of this estimate reduced with this increased sample size?

Answer: 3

Mathematics

7. The inverse of the matrix $X=5\left[\begin{array}{cc}2& 5\\ 4& -1\end{array}\right]$ is ___________.

Answer: $X^{-1}=\frac{1}{5}\left[\begin{array}{cc}\frac{1}{22}& \frac{5}{22}\\ \frac{2}{11}& \frac{-1}{11}\end{array}\right]$or $X^{-1}=\left[\begin{array}{cc}\frac{1}{110}& \frac{1}{22}\\ \frac{2}{55}& \frac{-1}{55}\end{array}\right]$

Data Analysis

8. The primary goal of principal component analysis is to:

1. Divide a set of multivariate observations into classes.
2. Assign a particular multivariate observation to one of several classes.
3. Characterize the correlation structure between two sets of variables by replacing them by two smaller sets of variables which are highly correlated.
4. Find the variables among a set of predictor variables that are the best predictors of a set of variables of interest.
5. Explain the variability in a large set of variables by replacing it by a smaller set of transformed variables that explains a large portion of the total variability.

Answer: E

Open Question

9. A basic question in planning a sample survey is the size of the sample that is required. In your opinion, what factors should be considered when determining the size of the sample and how does each one affect the sample size?

Testimonials

"Statistics Canada is a warm, supportive workplace where you can learn and grow as a data science professional. Through the wide range of projects and available training, there are many opportunities to develop and apply data science and machine learning methods."

"Statistics Canada has a wonderful workplace culture that has allowed me to develop my skills as a methodologist in a dynamic and welcoming atmosphere. The people at Statistics Canada challenge and support each other as producers of quality information, lifelong learners and dedicated professionals."

"At Statistics Canada, my projects allow me to work on many steps of the survey process using state-of-the-art statistical methods. Furthermore, it's easy to achieve a balance between my work and my personal life. I have access to flexible hours which gives me the opportunity to participate in various activities outside of work."

"I've always had varied interests and skills: should I become an author, teacher or mathematician? I discovered that I could do all of that at StatCan, and even more! Not only have I become an expert in implementing the Bootstrap in surveys, but I also provide training on related technical subjects both at the Agency and externally."

"I love my job at Statistics Canada! I have the opportunity to work with really knowledgeable peers on a variety of interesting and innovative projects. And all this while continuing my training in statistics and enjoying a great work life balance!"

"Working at Statistics Canada meets all my needs: I use what I have studied to work directly for the interest of Canadians and society, in a pleasant and healthy work environment. In addition, I can pursue research and international collaboration initiatives, which has allowed me to participate in numerous conferences and to win the International Association for Official Statistics prize for young statisticians in 2020."

"I was glad to find a job that allows me to use all my skills acquired through my years in university. Innovative projects, excellent working conditions, plenty of opportunities for advancement… All this and I get to work with a dynamic group of people! I could not ask for better."

"I enjoy very much the research and development aspects of my daily work that allow me to apply skills learned in university to prominent and innovative projects. Statistics Canada is an employer that also promotes wellness and active living at the workplace. I just love to come to work every day!"

"As a mathematical statistician, I have daily opportunities to work on diverse statistical challenges, both theoretical and applied, alongside many talented individuals. As a working mother, Statistics Canada allows me the flexibility to raise my family while continuing to research new and exciting areas of statistics, all while connecting with statistical colleagues around the world."

"The training offered at Statistics Canada has allowed me to keep learning since my first day on the job — in a wide range of areas including my second language and supervising skills as well as statistics and computer programming."

"The MA stream at Statistics Canada has given me not just a job, but a career. From junior to senior, I have been able to choose my path and work on projects that both interest and challenge me. I feel Statistics Canada has really invested in my development, even while starting a family."

Contact our recruitment team

Note that if you require help with the on-line application process, you must contact the Public Service Commission of Canada at 1-888-780-4444.

Contact us at statcan.marecruitment-marecrutement.statcan@statcan.gc.ca.