Statistics MSc
School of Mathematical and Physical Sciences ,
Faculty of Science
-
Start date
September 2025 -
Duration
1 year 2 years 3 years -
Attendance
Full-time Part-time Distance learning
Explore this course:
Apply now for 2025 entry or register your interest to find out about postgraduate study and events at the University of Sheffield.

Course description
Our Statistics MSc will teach you the theories behind a variety of statistical techniques, and how to apply them in scenarios that professional statisticians face every day.
You’ll develop a detailed working knowledge of important statistical techniques and concepts, including linear and generalised linear modelling, Bayesian statistics, time series and machine learning.
Our Statistics MSc includes modules on how to collect data and design experiments, and the role of statistics in clinical trials. You’ll learn how to analyse and draw meaningful conclusions from data, and develop your programming skills using the statistical computing software R.
Around one-third of the course is devoted to your dissertation. This may focus on investigating a data set, or a more theoretical or methodological topic. You’ll gain skills to help you stand out in the graduate job market, such as planning and researching a project, data acquisition, problem specification, analysis and reporting your findings.
External clients, such as pharmaceutical companies or sports modelling organisations, often provide dissertation topics. Distance learning students often come with projects designed by their employer.
Recent examples of dissertation topics include:
- Probabilistic Topic Modelling
- Spatio-temporal Modelling of Social Phenomena
- Feature selection for high dimensional data
- Modelling Football Results
Accreditation
This course is accredited by the Royal Statistical Society
Modules
Core modules:
- The Statistician's Toolkit
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This is the first of two 'core' modules students studying on statistics MScs. The aim of this module is to prepare statisticians for the workplace, equipping them with essential statistical modelling, computing and professional skills. The module includes the study of linear and generalised linear modelling, and data analysis using the programming language R.
30 credits - Bayesian Statistics and Computational Methods
-
This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python. Advanced computational techniques will be explored, in the second semester, using STAN.
30 credits - Machine Learning
-
Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of 'Big Data', statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.
15 credits - Sampling Theory and Design of Experiments
-
Whereas most statistics modules are concerned with the analysis of data, this module is focussed on the collection of data. In particular, this module considers how to collect data efficiently: how to ensure the quantities of interest can be estimated sufficiently accurately, using the smallest possible sample size. Three settings are considered: sample surveys (for example when conducting an opinion poll), physical experiments, as may be used in industry, and experiments involving predictions from computer models, where there is uncertainty in the computer model prediction.
15 credits - Time Series
-
This module considers the analysis of data in which the same quantity is observed repeatedly over time (e.g., recordings of the daily maximum temperature in a particular city, measured over months or years). Analysis of such data typically requires specialised methods, which account for the fact that successive observations are likely to be related. Various statistical models for analysing such data will be presented, as well as how to implement them using the programming language R.
15 credits - Medical Statistics
-
This module introduces an important application of statistics: medical research, specifically, the design and analysis of clinical trials. For any new drug to be approved by a regulator (such as the Medicines and Healthcare products Regulatory Agency in the UK) for use on patients, the effectiveness of the drug has to be demonstrated in a clinical trial. This module explains how clinical trials are designed and how statistical methods are used to analyse the results, with a particular focus on 'survival' or 'time-to-event' analysis.
15 credits - Dissertation
-
The dissertation is an extensive study giving the student the opportunity to synthesise theoretical knowledge with practical skills and giving experience of the phases of a relatively large piece of work: planning to a deadline; researching background information; acquisition and validation of data; problem specification; the carrying through of relevant analyses; and reporting, both at length through the dissertation and in summary, through, for example, a poster display. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.
60 credits
Optional modules:
With the approval of the MSc Course Director and School up to 30 credits of modules can be replaced with up to two modules from this group.
- Machine Learning and Adaptive Intelligence
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The module is about core technologies underpinning modern artificial intelligence. The module will introduce statistical machine learning and probabilistic modelling and their application to describing real-world phenomena. The module will give students a grounding in modern state-of-the-art algorithms that allow modern computer systems to learn from data. It has a considerable focus on the mathematical underpinnings of key ML approaches, requiring some knowledge of linear algebra, differentiation and probability.
15 credits - Data Modelling and Machine Intelligence
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All of our lives are affected by machine intelligence and data models - Google is a very visible example. But if you are a victim of identity theft, if you want a loan to buy a house or if you want to pass through immigration at an airport, a model derived from data using some form of machine learning technique will be involved.
15 credits
Engineers increasingly look to machine intelligence techniques such as neural networks and other machine learning methods to solve problems that are not amenable to conventional analysis e.g. by application of Newton's and Kirchhoff's laws, and other physical principles. Instead they use measurements of system variables to compute a model of the process that can then be used in design, analysis and forecasting. System identification is a specific example of data modelling.
We will look at the underlying principles of machine learning, the advantages and limitations of the various approaches and effective ways of applying them with the aim of making you a competent practitioner. - Optimisation: Theory, algorithms and applications
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This unit provides detailed presentations on the use of numerical optimisation and search methods for a wide range of engineering problems. Traditional approaches drawn from Operations Research will be enhanced by topics based on recent developments in heuristic methods, such as evolutionary computing, e.g. genetic algorithms and swarm intelligence.
15 credits - Economic Evaluation
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This module introduces the basic principles of economic evaluation as applied to healthcare interventions. The course introduces the concept of economic evaluation, the different types that are available and the various stages and techniques that need to be applied to generate results. Current practice guidelines will be described so that students can understand the current policy context of the methods. Also, as alternative techniques are described, their strengths and weaknesses will be highlighted, with the students being encouraged to critically appraise their appropriateness to different contexts.
15 credits - Epidemiology
-
Epidemiology is the discipline underpinning both effective public health practice and research into the causes, control and prevention of disease. Knowledge and understanding of epidemiological concepts and methods is a basic requirement for effective public health practice.
15 credits
This module will provide an introduction to epidemiology covering key epidemiological concepts; measures of disease; association and causation; confounding and bias. It will also introduce research designs including cross-sectional, ecological, cohort, case-control and intervention studies and introduce population health measures such as screening. - Qualitative Research Design and Analysis
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On completing the module students will be expected to be able to: understand a range of qualitative research approaches, data collection methods and forms of analysis; plan and undertake a simple analysis of student-generated qualitative data; critically appraise the methods and results of qualitative research.
15 credits - Systematic Reviews and Critical Appraisal Techniques
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To familiarise students with principles of systematic reviews and critical appraisal and the acquisition of skills necessary to undertake such work. The unit includes an introduction to information systems; principles of systematic literature reviews and critical appraisal; search strategies; computer-assisted search methods; practicalities of writing up the results of a systematic review; introduction to Meta- analysis; and dissemination of findings.
15 credits
Year one:
- Machine Learning
-
Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of 'Big Data', statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.
15 credits - Time Series
-
This module considers the analysis of data in which the same quantity is observed repeatedly over time (e.g., recordings of the daily maximum temperature in a particular city, measured over months or years). Analysis of such data typically requires specialised methods, which account for the fact that successive observations are likely to be related. Various statistical models for analysing such data will be presented, as well as how to implement them using the programming language R.
15 credits - The Statistician's Toolkit
-
This is the first of two 'core' modules students studying on statistics MScs. The aim of this module is to prepare statisticians for the workplace, equipping them with essential statistical modelling, computing and professional skills. The module includes the study of linear and generalised linear modelling, and data analysis using the programming language R.
30 credits
With the approval of the MSc Course Director and School up to 15 credits may be replaced with up to one module from this group.
- Systematic Approaches to Evidence Assessment Online
-
This module , which is delivered online, provides the skills and knowledge required to conduct rapid assessments of the evidence base and then to apply these assessments to health management and/or clinical practice. It introduces and explains rapid review methodologies that seek to optimise the balance between rigour and relevance, ensuring the timely and judicious use of evidence that is both user sensitive and context dependent. This module will also address the growing demand for knowledge translation of research findings, specifically within the context of developing countries. A key feature is production of a culturally-sensitive action plan that takes into account local feasibility and implementation issues.
15 credits - Epidemiology Online
-
As one of the core disciplines of Public Health, epidemiology is concerned with the methods of studying health related states and events to control health problems. The module, which is delivered online, covers epidemiological measures, main study designs, screening and surveillance. The primary objective is to introduce students to the principles, tools and applications of epidemiology and to help develop their practical skills through a range of activities.
15 credits
Year two:
- Sampling Theory and Design of Experiments
-
Whereas most statistics modules are concerned with the analysis of data, this module is focussed on the collection of data. In particular, this module considers how to collect data efficiently: how to ensure the quantities of interest can be estimated sufficiently accurately, using the smallest possible sample size. Three settings are considered: sample surveys (for example when conducting an opinion poll), physical experiments, as may be used in industry, and experiments involving predictions from computer models, where there is uncertainty in the computer model prediction.
15 credits - Bayesian Statistics and Computational Methods
-
This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python. Advanced computational techniques will be explored, in the second semester, using STAN.
30 credits - Medical Statistics
-
This module introduces an important application of statistics: medical research, specifically, the design and analysis of clinical trials. For any new drug to be approved by a regulator (such as the Medicines and Healthcare products Regulatory Agency in the UK) for use on patients, the effectiveness of the drug has to be demonstrated in a clinical trial. This module explains how clinical trials are designed and how statistical methods are used to analyse the results, with a particular focus on 'survival' or 'time-to-event' analysis.
15 credits - Dissertation
-
The dissertation is an extensive study giving the student the opportunity to synthesise theoretical knowledge with practical skills and giving experience of the phases of a relatively large piece of work: planning to a deadline; researching background information; acquisition and validation of data; problem specification; the carrying through of relevant analyses; and reporting, both at length through the dissertation and in summary, through, for example, a poster display. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.
60 credits
Year one:
- The Statistician's Toolkit
-
This is the first of two 'core' modules students studying on statistics MScs. The aim of this module is to prepare statisticians for the workplace, equipping them with essential statistical modelling, computing and professional skills. The module includes the study of linear and generalised linear modelling, and data analysis using the programming language R.
30 credits - Medical Statistics
-
This module introduces an important application of statistics: medical research, specifically, the design and analysis of clinical trials. For any new drug to be approved by a regulator (such as the Medicines and Healthcare products Regulatory Agency in the UK) for use on patients, the effectiveness of the drug has to be demonstrated in a clinical trial. This module explains how clinical trials are designed and how statistical methods are used to analyse the results, with a particular focus on 'survival' or 'time-to-event' analysis.
15 credits
Year two:
- Sampling Theory and Design of Experiments
-
Whereas most statistics modules are concerned with the analysis of data, this module is focussed on the collection of data. In particular, this module considers how to collect data efficiently: how to ensure the quantities of interest can be estimated sufficiently accurately, using the smallest possible sample size. Three settings are considered: sample surveys (for example when conducting an opinion poll), physical experiments, as may be used in industry, and experiments involving predictions from computer models, where there is uncertainty in the computer model prediction.
15 credits - Bayesian Statistics and Computational Methods
-
This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python. Advanced computational techniques will be explored, in the second semester, using STAN.
30 credits
Year three:
- Machine Learning
-
Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of 'Big Data', statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.
15 credits - Time Series
-
This module considers the analysis of data in which the same quantity is observed repeatedly over time (e.g., recordings of the daily maximum temperature in a particular city, measured over months or years). Analysis of such data typically requires specialised methods, which account for the fact that successive observations are likely to be related. Various statistical models for analysing such data will be presented, as well as how to implement them using the programming language R.
15 credits - Dissertation
-
The dissertation is an extensive study giving the student the opportunity to synthesise theoretical knowledge with practical skills and giving experience of the phases of a relatively large piece of work: planning to a deadline; researching background information; acquisition and validation of data; problem specification; the carrying through of relevant analyses; and reporting, both at length through the dissertation and in summary, through, for example, a poster display. Most dissertations involve the investigation of a data set, entailing both a description of the relevant background and a report on the data analysis.
60 credits
The content of our courses is reviewed annually to make sure it's up-to-date and relevant. Individual modules are occasionally updated or withdrawn. This is in response to discoveries through our world-leading research; funding changes; professional accreditation requirements; student or employer feedback; outcomes of reviews; and variations in staff or student numbers. In the event of any change we will inform students and take reasonable steps to minimise disruption.
Open days
Interested in postgraduate taught study? Register your interest in studying at Sheffield or attend an event throughout the year to find out what makes studying at here special.
Duration
- 1 year full-time
- 2-3 years part-time by distance learning
Teaching
You’ll be taught through lectures, tutorials, computing sessions and group work. Most statistics lectures are recorded so you can watch them again later.
You’ll be expected to spend around 35 hours each week on your studies, with 8-12 hours in lectures or computing classes, and the remainder consisting of independent study.
Distance learning option
Our distance learning option is taught online with support via email and an online forum. Distance learners also come to the University for residential weeks. You'll need to be in Sheffield for a few days between late May and early June each year for your exams.
You're expected to spend around 20 hours each week on your studies if you're doing the two-year version of the course, and around 12 to 15 hours each week if you're doing the three-year version.
Assessment
Our assessment methods are designed to support the achievement of learning outcomes and develop your professional skills. This includes ongoing project work for some modules, examinations, coursework and a dissertation.
Regular feedback is also provided, so you can understand your own development throughout the course.
Your career
Our graduates have the specialist modelling and analysis skills employers need to interpret the complex datasets that underpin a variety of professions, from business, manufacturing and marketing to policy making, science and healthcare. Our graduates have been hired by employers such as Amazon, Barclays, Dell, Goldman Sachs, IBM, PwC, Sky, the NHS and the Civil Service.
You’ll cover advanced topics and gain extensive research training, which is also great preparation for a PhD. Sheffield mathematics graduates have secured postgraduate research positions at many of the world's top 100 universities.
Our Statistics MSc satisfies the eligibility criteria for the Royal Statistical Society’s Graduate Statistician award – a stepping-stone to full professional membership of the RSS and Chartered Statistician status.
School
School of Mathematical and Physical Sciences
The School of Mathematical and Physical Sciences is leading the way with groundbreaking research and innovative teaching.
Our mathematicians and statisticians have expertise across pure mathematics, applied mathematics, probability and statistics. We focus on a variety of topics, from the most abstract questions in algebraic geometry and number theory, to the calculations behind infectious disease, black holes and climate change.
In the Research Excellence Framework 2021, 96 per cent of our mathematical sciences research was rated in the highest two categories as world-leading or internationally excellent.
We have strong links with the Society for Industrial and Applied Mathematics, the Institute of Mathematics and its Applications, the European Physical Society, and the International Society on General Relativity and Gravitation. With the support of the London Mathematical Society, we are also an organiser of the Transpennine Topology Triangle, a key focal point for topology research in the UK.
Mathematics and statistics staff have received honours from the Royal Society, the Society for Mathematical Biology and the Royal Statistical Society, who also provide professional accreditation for our statistics courses.
Entry requirements
Minimum 2:1 undergraduate honours degree in a relevant subject with relevant modules.
We look for applications that demonstrate background within mathematics (particularly calculus and linear algebra), probability (and/or stochastic processes) and statistics (eg Linear modelling, multivariate methods, machine learning, time series etc). Typically we require a selection of modules from each of the three areas to cover each year of undergraduate study and at least 50% of the degree to be in a mathematical subject.
Applications with employment history in statistical or data science fields are also welcomed, including for distance learning courses. In such cases we consider the balance of both relevant parts of the employment history and academic qualifications.
English language requirements
IELTS 6.5 (with 6 in each component) or University equivalent.
If you have any questions about entry requirements, please contact the school/department.
Fees and funding
Alumni discount
Save up to £2,500 on your course fees
Are you a Sheffield graduate? You could save up to £2,500 on your postgraduate taught course fees, subject to eligibility.
Apply
You can apply now using our Postgraduate Online Application Form. It's a quick and easy process.
Contact
Any supervisors and research areas listed are indicative and may change before the start of the course.
Recognition of professional qualifications: from 1 January 2021, in order to have any UK professional qualifications recognised for work in an EU country across a number of regulated and other professions you need to apply to the host country for recognition. Read information from the UK government and the EU Regulated Professions Database.