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Statistics
School of Mathematics and Statistics,
Faculty of Science
Course description
This course 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. You’ll learn how to analyse and draw meaningful conclusions from data, and develop your programming skills using the statistical computing software R.
This course also includes modules on how to collect data and design experiments, and the role of statistics in clinical trials.
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. The aim is to give you skills to include on your CV, such as planning and researching a project, data acquisition, problem specification, analysis and reporting your findings.
Dissertation topics are often provided by external clients – for example, pharmaceutical companies or sports modelling organisations. Distance learning students often come with projects designed by their employer.
Accreditation
This course is accredited by the Royal Statistical Society
Modules
Core modules:
- 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 - Bayesian Statistics and Computational Methods
-
This module introduces the Bayesian approach to statistical inference. The Bayesian method is fundamentally different in philosophy from conventional frequentist/classical inference, and has been the subject of some controversy in the past, but is now widely used. The module also presents various computational methods for implementing both Bayesian and frequentist inference, in situations where obtaining results 'analytically' would be impossible. The methods will be implemented using the programming languages R and Stan, and some programming is taught alongside the theory lectures.
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
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
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 - 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 - Bayesian Statistics and Computational Methods
-
This module introduces the Bayesian approach to statistical inference. The Bayesian method is fundamentally different in philosophy from conventional frequentist/classical inference, and has been the subject of some controversy in the past, but is now widely used. The module also presents various computational methods for implementing both Bayesian and frequentist inference, in situations where obtaining results 'analytically' would be impossible. The methods will be implemented using the programming languages R and Stan, and some programming is taught alongside the theory lectures.
30 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:
- Bayesian Statistics and Computational Methods
-
This module introduces the Bayesian approach to statistical inference. The Bayesian method is fundamentally different in philosophy from conventional frequentist/classical inference, and has been the subject of some controversy in the past, but is now widely used. The module also presents various computational methods for implementing both Bayesian and frequentist inference, in situations where obtaining results 'analytically' would be impossible. The methods will be implemented using the programming languages R and Stan, and some programming is taught alongside the theory lectures.
30 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
Year three:
- 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 - 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 - 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'll consult and inform students in good time and take reasonable steps to minimise disruption.
Open days
An open day gives you the best opportunity to hear first-hand from our current students and staff about our courses.
You may also be able to pre-book a department visit as part of a campus tour.Open days and campus tours
Duration
- 1 year full-time
- 2-3 years part-time by distance learning
Teaching
There are 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
This 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
Some modules may be continuously assessed through ongoing project work with no examination but most taught modules are assessed by a mixture of examinations and coursework. The assessment of the dissertation module is based entirely on your submitted dissertation.
Your career
You'll graduate with the specialist modelling and analysis skills employers need to interpret the complex datasets that underpin many 21st century professions – from business, manufacturing and marketing to policymaking, science and healthcare.
Employers that have hired graduates from our School of Mathematics and Statistics include Amazon, Barclays, Dell, Goldman Sachs, IBM, PwC, Sky, the NHS and the Civil Service.
This degree 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.
Department
School of Mathematics and Statistics
The School of Mathematics and Statistics is one of the biggest departments at the University of Sheffield. It’s home to more than 50 academic staff with expertise across many areas of pure mathematics, applied mathematics, probability and statistics. We aspire to be an inclusive and welcoming environment for all who enjoy mathematics.
Our mathematics and statistics researchers work on a wide 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 research was rated in the highest two categories as world-leading or internationally excellent.
Staff in the School of Mathematics and Statistics 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.
With the support of the London Mathematical Society, we are an organiser of the Transpennine Topology Triangle – a key focal point for topology research in the UK.
We also 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.
Entry requirements
Minimum 2:1 undergraduate honours degree, with substantial mathematical and statistical components. In particular, you should have studied the following topics and performed well in assessments on them (for example, a score of at least 60 per cent).
- Mathematical Methods for Statistics: ideas and techniques from linear algebra, including multiple integration, differentiation, matrix algebra, the theory of quadratic forms.
- Probability and Probability Distributions: the laws of probability and of conditional probability, the concepts of random variables and random vectors and their distributions, the methodology for calculating with them; laws of large numbers and central limit phenomena.
- Basic Statistics: hypothesis testing; point estimation and confidence intervals; likelihood methods; linear modelling; use of statistical software, for example, R.
Before you start your MSc course, you should also read through the introductory material:
Preparing for your MSc course in Statistics
Overall IELTS score of 6.5 with a minimum of 6.0 in each component, or equivalent.
If you have any questions about entry requirements, please contact the department.
Fees and funding
Apply
You can apply now using our Postgraduate Online Application Form. It's a quick and easy process.
Contact
postgradmaths-enquiry@shef.ac.uk
+44 114 222 3789
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.