100% of our research impact is ranked outstanding (1st in the UK) (Research Excellence Framework 2021)
RSS Graduate Statistician status awarded upon graduation
Contemporary statistics brought to life by our enthusiastic subject experts
Taught by world-leading experts in this field, the MSc Statistics programme is the perfect blend of mathematical theory with real-world applications. Develop an advanced understanding of the application of statistical models to find solutions to scientific, industrial and social challenges. You will become proficient in analysis, understanding the performance of algorithms via coding and the machine learning approaches applied in both synthetic and real-world studies.
Who is This Programme For?
Statistics, alongside its close cousins data science and AI, is core to operational, research and development, and strategic activities of many industrial sectors, from, psychology to neuroscience, from risk management to climate science, from energy production to engineering, and from quality control to finance and economics. A career as a statistician is never dull. Completion of this Master’s will prepare you for roles in industry, or to progress to a PhD programme, confident in your mathematical understanding and in the analytical, computing and critical-thinking skills required.
This programme is suited to those with an undergraduate degree in mathematics, statistics, physics or econometrics.
Looking ahead to employability
Graduates with a strong grasp of the implementation of contemporary statistical methods are widely sought after to work in operational, research and development, and decision making roles. To prepare you for your career, our teaching and learning strategy involves a variety of techniques that cascade from the lecture theatre and include practical sessions with hands-on problem-solving, online quizzes and computing lab sessions. These develop:
Your technical and mathematical aptitude
Confidence in your computing expertise through application to data analysis and manipulation, problem-solving and quantitative reasoning
Critical thinking and statistical modelling skills through individual and group project work
Communication and collaboration skills through oral and written exercises
What to expect
There are three phases to your learning. You will begin by developing and strengthening your core knowledge and skills in classical and modern statistical methods and inference. Topics covered include frequentist and Bayesian inference, generalised linear models, statistical programming and communication. In phase two you will choose your specialist optional modules to suit your interests. These modules, which vary in their balance between theory, methods and application, cover a wide variety of statistical topics. The final phase is your dissertation project where you work under the guidance of an experienced statistical researcher. These projects are tailored to your interests – you might wish to progress your understanding of a topic covered in a taught module, or you may opt to investigate a methodological topic not covered by one of the taught modules.
Three things we would like you to know
We make sure you have a strong understanding of the challenges facing the modern statistician: from ethical issues to big data to working as part of a multi-disciplinary team
You will become proficient in coding in R and Python
Many of our graduates are now leaders in their fields
You might also be interested in..
Our other statistics based Master’s degrees. We offer an MSc Medical Statistics for those interested in medical research and the development of new treatments. You will be taught by renowned experts in this particular field and receive specialist training in areas such as clinical trials, and the cause and risk factor of diseases. We also offer an MSc Statistics and Artificial Intelligence for those wishing to gain an understanding of the statistical foundations behind AI models and machine learning.
Our MSc Statistics graduates are highly employable and are valued by employers for their in-depth specialist knowledge and wealth of technical and transferable skills. You will graduate from this degree with a comprehensive skill set, including data analysis and manipulation, logical thinking, problem-solving and quantitative reasoning, as well as advanced knowledge of the discipline. The starting salary for many graduate statistical roles is highly competitive, and popular career options include:
Statistician
Medical Statistician
Biostatistician
Epidemiologist
Data Scientist
Actuary
Financial Analyst
Statistical Consultant
University lecturer (contingent on first successfully completing a PhD)
Our graduates are also well-placed to enrol in a PhD programme, either in Statistics or a related discipline. A PhD programme provides training in independent research and can be undertaken either as a route into an academic research career, or as an advanced qualification for a specialist technical role in either the private or public sector.
PhD Statistics at KAUST "The academics' inspiring instructions and the well-designed courses of Lancaster University introduced me to a research culture of critical enquiry and bold exploration, which includes issues around fundamental inquiries and practical problems. Aside from the fascinating statistical content and the enthusiastic course instructors, the teaching at Lancaster was also oriented towards assisting students express themselves academically"
Joseph Price
Research Assistant at Lancaster "The MSc Statistics programme at Lancaster has not only given me a strong foundation in the fundamentals of statistics, it has also given me the opportunity to explore and specialise in areas that interest me the most. My specific interest is in medical statistics and I’ve been able to study different aspects of this field in great depth. Since taking modules in clinical trials and epidemiology, I have understood much better both the academic and media-reported use of statistics in this field."
Tara McClaughlin
Property Consultant at Ridge and Partners "Undertaking the MSc Statistics course at Lancaster University has provided me with a diverse range of cutting-edge skills that have opened doors to numerous working disciplines, such as medical statistics, research, and data analytics. By exploring niche areas, I quickly learnt to rely on my own abilities to complete work – a skill that has helped me to succeed in a professional environment. The course required plenty of coding, which I have found is fundamental to a career in data analytics."
Entry requirements
Academic Requirements
2:1 Hons degree (UK or equivalent) in Mathematics or Statistics.
We may also consider non-standard applications where you have studied a degree in other quantitative subjects that include courses in probability, statistics, linear algebra, and calculus, or you have a 2:2 honours degree equivalent result combined with extensive relevant experience.
You should clearly be able to demonstrate how your skills have prepared you for relevant discussions and assessments during postgraduate study.
If you have studied outside of the UK, we would advise you to check our list of international qualifications before submitting your application.
English Language Requirements
We may ask you to provide a recognised English language qualification, dependent upon your nationality and where you have studied previously.
We normally require an IELTS (Academic) Test with an overall score of at least 6.5, and a minimum of 6.0 in each element of the test. We also consider other English language qualifications.
Delivered in partnership with INTO Lancaster University, our one-year tailored pre-master’s pathways are designed to improve your subject knowledge and English language skills to the level required by a range of Lancaster University master’s degrees. Visit the INTO Lancaster University website for more details and a list of eligible degrees you can progress onto.
Course structure
You will study a range of modules as part of your course, some examples of which are listed below.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research. Not all optional modules are available every year.
Core
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The three month dissertation period (mid-June to mid-September) will involve the application of statistical methodology to a substantive problem. This dissertation is written by the student under the direction of a supervisor. Some projects are collaborative: examples include GlaxoSmithKline; AstraZeneca; Wrightington Hospital; Royal Lancaster Infirmary; Leahurst Veterinary Centre; and the Department of the Environment.
Students will gain a thorough understanding of advanced statistical methods which go beyond the scope of MSc taught components, and will learn about the development of original statistical methodology which will contribute to a fuller understanding of existing methodology. Students are required to make innovative use of the statistical method, leading to substantive findings which would not readily be obtainable by routine application of standard techniques.
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This module is only core for those with the required mathematical background to complete it. Some students may require an introduction to the area, at the graduate level, and they will study the core module titled ‘Statistical Fundamentals I’. If you complete this module, you will not be required to take Statistical Fundamentals I.
The areas that will be covered are statistical inference using maximum likelihood and generalised linear models (GLMs). Building on an undergraduate-level understanding of mathematics, statistics (hypothesis testing and linear regression) and probability (univariate discrete and continuous distributions; expectations, variances and covariances; the multivariate normal distribution), this module will motivate the need for a generic method for model fitting and then demonstrate how maximum likelihood provides a solution to this. Following on from this, GLMs, a widely and routinely used family of statistical models, will be introduced as an extension of the linear regression model.
This module will develop the core topic of maximum likelihood inference previously introduced in MATH501 Statistical Fundamentals I by expanding on numerical and theoretical aspects. Numerical aspects will include obtaining the maximum likelihood estimate using numerical optimisation functions in R, and using the profile likelihood function to obtain both the maximum likelihood estimate and confidence intervals. Theoretical elements covered will include derivation of asymptotic distributions for the maximum likelihood estimator, deviance and profile deviance.
The second half of the module will introduce Bayesian inference as an alternative to maximum likelihood inference. Building on existing knowledge of the likelihood function, the prior and posterior distributions will be introduced. For simple models, analytical forms for the posterior distribution will be introduced and point estimates for the parameter obtained. For more complex models, numerical methods of sampling from the posterior distribution will be demonstrated.
This module provides an introduction to statistical learning. General topics covered include big data, missing data, biased samples and recency. Likelihood and cross-validation will be introduced as generic methods to fit and select statistical learning models. Cross-validation will require an understanding of sample splitting into calibration, training and validation samples. The focus will then move to handling regression problems for large data sets via variable reduction methods such as the Lasso and Elastic Net. A variety of classification methods will be covered including logistic and multinomial logistic models, regression trees, random forests and bagging and boosting. Examination of classification methods will culminate in neural networks which will be presented as generalised linear modelling extensions. Unsupervised learning for big data is then covered including K-means, PAM and CLARA, followed by mixture models and latent class analysis.
The aim of this module is to provide students with a range of skills that are necessary for applied statistical work including team-working, oral presentation, statistical computing, and the preparation of written reports including statistical analyses. All students will obtain a thorough grasp of R (including R objects and functions, graphs, basic simulations and programming) and be given an introduction to a second statistical computing package.
Students will also learn how to utilise LaTex for writing a complex and structured scientific report that may include mathematical formulae, tables and figures, as well as learn the intricacies of effective scientific writing style such as grammar, referencing, and the presentation of results in appropriate tables and graphs. They will enhance their oral presentation technique using LaTex Beamer to create slides that include complex mathematical formulae, as well as embark on an in-depth team project using Git, R Markdown or iPython notebooks.
Optional
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Clinical trials are planned experiments on human beings designed to assess the relative benefits of one or more forms of treatment. For instance, we might be interested in studying whether aspirin reduces the incidence of pregnancy-induced hypertension, or we may wish to assess whether a new immunosuppressive drug improves the survival rate of transplant recipients.
This module combines the study of technical methodology with discussion of more general research issues, beginning with a discussion of the relative advantages and disadvantages of different types of medical studies. The module will provide a definition and estimation of treatment effects. Furthermore, cross-over trials, issues of sample size determination, and equivalence trials are covered. There is an introduction to flexible trial designs that allow a sample size re-estimation during the ongoing trial. Finally, other relevant topics such as meta-analysis and accommodating confounding at the design stage are briefly discussed.
Students will gain knowledge of the basic elements of clinical trials. They will develop the ability to recognise and use principles of good study design, and will also be able to analyse and interpret study results to make correct scientific inferences.
This module introduces the expectation-maximisation algorithm, an iterative algorithm for obtaining the maximum likelihood estimate of parameters in problems with intractable likelihoods. Students will explore the use of Markov chain Monte Carlo (MCMC) methods, and will discover the features of the Metro-Hastings algorithm, with emphasis on the Gibbs sampler, independence sampler and random walk Metropolis. Whilst relating to this, students will consider how such methods are closely integrated with Bayesian modelling techniques such as hierarchal modelling, random effects and mixture modelling.
Data augmentation will receive recurring coverage over the course of the module. Students will also gain transferrable knowledge of the usefulness of computers in assisting statistical analysis of complex methods, in addition to experience with the computer statistical package R.
This module provides a comprehensive introduction to deep neural networks, covering key mathematical concepts, network architecture, and optimization techniques. You'll gain hands-on experience by building models from scratch and advancing to industry-standard software tools for tasks like image classification and natural language processing.
Through real-world applications, you’ll tackle modern machine learning challenges, develop coding expertise, and enhance your ability to analyse and present data. Coursework will refine your technical communication skills, preparing you to excel in both individual and collaborative settings.
This module offers an in-depth exploration of the mathematical and algorithmic foundations of artificial intelligence, with a specific focus on machine learning. You will learn how to analyse real-world challenges, design appropriate AI models, and apply machine learning algorithms to complex datasets. Key algorithms will be discussed in detail, including their motivation, underlying theory, implementation, and practical applications using programming and statistical software.
By the end of the module, you will have the skills to model real-world phenomena, assess the effectiveness of various machine learning algorithms, and make evidence-based decisions grounded in statistical learning theory.
Hierarchical data arise in a multitude of settings, specifically whenever a sample is grouped (or clustered) according to one or more factors with each factor having many levels. For instance, school pupils may be grouped by teacher, school and local education authority. There is a hierarchical structure to this grouping since schools are grouped within local education authority and teachers are grouped within schools. If multiple measurements of a response variable, say test score, are made for each pupil across multiple measurement times, the data are also longitudinal.
This module motivates the need for statistical methodology to account for these kinds of hierarchical structure. The differences between marginal and conditional models, and the advantages and disadvantages of each, will be discussed. Linear mixed effects models (LMMs) for general multi-level data will be introduced as an extension to the linear regression model. Longitudinal data will be introduced as a special case of hierarchical data motivating the need for temporal dependence structures to be incorporated within LMMs. Finally, the drawbacks of LMMs will be used to motivate generalised linear mixed effects models (GLMMs), with the former a special case of the latter. GLMMs broaden the scope of data sets which can be analysed using mixed-effects models to incorporate all common types of response variable.
All modelling will be carried out using the statistical software package R.
Introducing epidemiology, the study of the distribution and determents of disease in human population, this module presents its main principles and statistical methods. The module addresses the fundamental measures of disease, such as incidence, prevalence, risk and rates, including indices of morbidity and mortality.
Students will also develop awareness in epidemiologic study design, such as ecological studies, surveys, and cohort and case-control studies, in addition to diagnostic test studies. Epidemiological concepts will be addressed, such as bias and confounding, matching and stratification, and the module will also address calculation of rates, standardisation and adjustment, as well as issues in screening.
This module provides students with a historical and general overview of epidemiology and related strategies for study design, and should enable students to conduct appropriate methods of analysis for rates and risk of disease. Students will develop skills in critical appraisal of the literature and, in completing this module, will have developed an appreciation for epidemiology and an ability to describe the key statistical issues in the design of ecological studies, surveys, case-control studies, cohort studies and RCT, whilst recognising their advantages and disadvantages.
This module addresses a range of topics relating to survival data; censoring, hazard functions, Kaplan-Meier plots, parametric models and likelihood construction will be discussed in detail. Students will engage with the Cox proportional hazard model, partial likelihood, Nelson-Aalen estimation and survival time prediction and will also focus on counting processes, diagnostic methods, and frailty models and effects.
The module provides an understanding of the unique features and statistical challenges surrounding the analysis of survival avant history data, in addition to an understanding of how non-parametric methods can aid in the identification of modelling strategies for time-to-event data, and recognition of the range and scope of survival techniques that can be implemented within standard statistical software.
General skills will be developed, including the ability to express scientific problems in a mathematical language, improvement of scientific writing skills, and an enhanced range of computing skills related to the manipulation on analysis of data.
On successful completion of this module, students will be able to apply a range of appropriate statistical techniques to survival and event history data using statistical software, to accurately interpret the output of statistical analyses using survival models, fitted using standard software, and the ability to construct and manipulate likelihood functions from parametric models for censored data. Students will also gain observation skills, such as the ability to identify when particular models are appropriate, through the application of diagnostic checks and model building strategies.
This module introduces key statistical techniques for analysing high-dimensional data, starting with the multivariate normal distribution and its properties. You'll explore matrix decompositions, low-rank approximations, and their roles in dimension reduction and matrix completion. Unsupervised learning methods such as Principal Component Analysis (PCA), Factor Analysis (FA), and clustering algorithms like K-means and Gaussian Mixture Models will be covered. The module also introduces graphical models to represent conditional dependencies in data and methods like the graphical Lasso for graph selection.
Throughout the course, both theoretical concepts and practical applications will be emphasized. You’ll use R to implement these methods, giving you hands-on experience analysing real-world data.
There may be extra costs related to your course for items such as books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation, you may need to pay a subscription to a professional body for some chosen careers.
Specific additional costs for studying at Lancaster are listed below.
College fees
Lancaster is proud to be one of only a handful of UK universities to have a collegiate system. Every student belongs to a college, and all students pay a small College Membership Fee which supports the running of college events and activities. Students on some distance-learning courses are not liable to pay a college fee.
For students starting in 2025, the fee is £40 for undergraduates and research students and £15 for students on one-year courses.
Computer equipment and internet access
To support your studies, you will also require access to a computer, along with reliable internet access. You will be able to access a range of software and services from a Windows, Mac, Chromebook or Linux device. For certain degree programmes, you may need a specific device, or we may provide you with a laptop and appropriate software - details of which will be available on relevant programme pages. A dedicated IT support helpdesk is available in the event of any problems.
The University provides limited financial support to assist students who do not have the required IT equipment or broadband support in place.
For most taught postgraduate applications there is a non-refundable application fee of £40. We cannot consider applications until this fee has been paid, as advised on our online secure payment system. There is no application fee for postgraduate research applications.
For some of our courses you will need to pay a deposit to accept your offer and secure your place. We will let you know in your offer letter if a deposit is required and you will be given a deadline date when this is due to be paid.
The fee that you pay will depend on whether you are considered to be a home or international student. Read more about how we assign your fee status.
If you are studying on a programme of more than one year’s duration, tuition fees are reviewed annually and are not fixed for the duration of your studies. Read more about fees in subsequent years.
Scholarships and bursaries
You may be eligible for the following funding opportunities, depending on your fee status and course. You will be automatically considered for our main scholarships and bursaries when you apply, so there's nothing extra that you need to do.
The programme is amongst those recommended by the National Institute for Health and Care Research for applications to their Pre-doctoral Fellowship in Medical Statistics. The fellowship offers an exciting opportunity to be employed by a university or research institute for two years, involving completing a fully-funded MSc in the first year and working on research projects in the second. It may be possible to find Lancaster-based statisticians able to support fellowship applications as supervisors or to find supervisors at other regional institutions.
Teaching in our School is delivered through a range of methods to create the best possible learning experience. Alongside traditional lectures, you can expect to benefit from small workshop groups. These groups are guided by tutors who are active researchers and offer you an opportunity to put what you have learnt in lectures into practice. We also run computer lab sessions focused on developing your programming and analytical skills through the use of specialist statistical software.
We utilise a range of assessment methods to support and encourage you to demonstrate your knowledge and ability fully. Most of our modules include end of year exams, and you will also undertake research projects, group work and presentations.
Community
Studying in the School of Mathematical Sciences, you will become part of a friendly and encouraging community. Our students and staff are passionate about the subject area, creating a supportive learning environment. The wealth of knowledge, experience and expertise within the School enables us to understand what is required by and from our students. We use this experience to ensure you are in the strongest possible position to realise your aspirations and succeed in your chosen career. Our dedicated team of support staff provide an excellent first line support service to ensure you have a positive experience of studying with us. We believe it is vital to foster a relaxed, supportive and friendly working environment to ensure you can excel during your time with us.
Important Information
The information on this site relates primarily to 2025/2026 entry to the University and every effort has been taken to ensure the information is correct at the time of publication.
The University will use all reasonable effort to deliver the courses as described, but the University reserves the right to make changes to advertised courses. In exceptional circumstances that are beyond the University’s reasonable control (Force Majeure Events), we may need to amend the programmes and provision advertised. In this event, the University will take reasonable steps to minimise the disruption to your studies. If a course is withdrawn or if there are any fundamental changes to your course, we will give you reasonable notice and you will be entitled to request that you are considered for an alternative course or withdraw your application. You are advised to revisit our website for up-to-date course information before you submit your application.
More information on limits to the University’s liability can be found in our legal information.
Our Students’ Charter
We believe in the importance of a strong and productive partnership between our students and staff. In order to ensure your time at Lancaster is a positive experience we have worked with the Students’ Union to articulate this relationship and the standards to which the University and its students aspire. View our Charter and other policies.