Data analysis and statistical models support many aspects of the modern world, from science and technology to finance and business. They allow us to overcome scientific, industrial and social problems and a Masters-level understanding of them is beneficial in many careers.
Our Royal Statistical Society (RSS) accredited Masters programme combines a blend of theoretical study with real-world application. Over the year, you will develop advanced statistical skills and knowledge, while having the opportunity to put what you learn into practice and gain valuable, real-world experience. In addition to acquiring advanced technical knowledge, you will also develop project management and communication skills. Upon graduating, you will be ideally placed to pursue a career as a statistician, confident that you can apply your analytical and programming skills in a diverse range of applications.
A carefully structured approach will enable you to develop and strengthen your essential core skills in both classical and modern statistical methods and inference before progressing to the more advanced and specialist modules. The specialist modules cover a diverse range of statistical topics reflecting both areas of Departmental research expertise and the requirements of leading employers of statisticians. You will be supported in selecting those specialist modules that best reflect your own interests and career aspirations.
Alongside the technical modules, you will undertake a module to advance key transferable skills in programming and communications. Programming, and the confident use of statistical software, enables the analysis of large and complex data sets, whilst communication is an essential skill for all statisticians, who must be able to engage in dialogue with members of the project team, stakeholders and end-users. You will be based within the Department of Mathematics and Statistics where you will have access to specialist software and equipment. You will have the opportunity to engage with academic staff members, all of whom are active statistical researchers, and to participate in departmental research colloquia and seminars should you choose to do so.
Finally, over the course of three months, you will complete a Masters-level dissertation. A statistical researcher, who will guide and support you throughout the period, will supervise this independent project. They will advise on the direction of the project, as well as contributing guidance on technical aspects of modelling, interpretation of analysis and presentation of the final report. Undertaking this dissertation will allow you to bring together and put into practice the discipline specific skills, knowledge and experience you have gained throughout the year. This will take your understanding of advanced statistics beyond classroom learning allow you to develop a working understanding of statistical methodology and build your confidence in working independently and leading the statistical direction of a project. This experience will be invaluable as you progress into a career.
Graduate Statistician status is awarded by the Royal Statistical Society to successful graduates of accredited degrees.Learn more about the Royal Statistical Society accreditation
2:1 Hons degree (UK or equivalent) in a subject with a strong mathematics or statistics component.
We may also consider non-standard applicants, please contact us for information.
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.
If your score is below our requirements, you may be eligible for one of our pre-sessional English language programmes.
Contact: Admissions Team +44 (0) 1524 592032 or email firstname.lastname@example.org
You will study a range of modules as part of your course, some examples of which are listed below.
MSc Statistics Dissertation
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. Many projects are collaborative: recent collaborations 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.
Statistical Fundamentals I
This module provides an introduction, at graduate level, to two core areas which are essential building blocks to further advanced study of statistical modelling, methodology and theory. 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.
Statistical Fundamentals II
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.
Statistics in Practice
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.
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.
Computationally Intensive Methods
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.
Extreme Value Theory
Extreme Value Theory is an area of probability theory which describes the stochastic behaviour of events occurring in the tail of a distribution (eg. block maxima). This course will cover both an overview of key theoretical results and the statistical modelling approaches which are motivated by these results. Theoretical results covered will include limiting distributions for block maxima and Peaks Over Threshold events in the case of both independent and time-series data. Modelling will involve the development of extreme value statistical models and their application to data sets taken from financial and environmental applications. The concepts of risk will be explored, leading to an understanding of return levels and Value At Risk measures. The concept of extremal dependence will be introduced.
Methods for Missing Data
Almost every set of data, whether it consists of field observations, data from laboratory experiments, clinical trial outcomes, or information from population surveys or longitudinal studies, has an element of missing data. For example, participants in a survey or clinical trial may drop-out of the study, measurement instruments may fail, or human error invalidate instrumental readings. Missingness may or may not be related to the information being collected; for instance, drop out may occur because a patient dislikes the side-effects of an experimental treatment or because they move out of the area or because they find that they no longer have the time to attend follow up appointments. In this module you will learn about the different ways in which missing data can arise, and how these can be handled to mitigate the impact of the missingness on the data analysis. Topics covered include single imputation methods, Bayesian imputation, multiple imputation (Rubin's rules, chained equations and multivariate methods, as well as suitable diagnostics) and modelling dropout in longitudinal modelling.
Modelling Multilevel and Longitudinal Data
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.
Principles of Epidemiology
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.
Survival and Event History Analysis
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.
The course is designed to provide foundational knowledge in linear and non-linear time-series analysis through building awareness of various well used time-series models. While the module focuses on univariate analysis, students will have time to read around lecture notes and materials to extend their understanding of these methods. By the end of the course, the student should understand both the theoretical and practical foundations of time-series analysis, how to fit, and choose from a range of models. They will understand different methods of evaluating time-series model performance and how these models can be used to provide forecasts.
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.
Fees and Funding
We set our fees on an annual basis and the 2023/24 entry fees have not yet been set.
Scholarships and bursaries
At Lancaster, we believe that funding concerns should not stop any student with the talent to thrive.
We offer a range of scholarships and bursaries to help cover the cost of tuition fees and/or living expenses.
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.
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.
For students starting in 2022, the fee is £40 for undergraduates and research students and £15 for students on one-year courses. Fees for students starting in 2023 have not yet been set.
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.
Fees in subsequent years
The University will not increase the Tuition Fee you are charged during the course of an academic year.
If you are studying on a programme of more than one year's duration, the tuition fees for subsequent years of your programme are likely to increase each year. The way in which continuing students' fee rates are determined varies according to an individual's 'fee status' as set out on our fees webpages.
Mathematics and Statistics
- Data Science MSc
- Data Science PgCert
- Data Science PgDip
- Mathematics PhD
- Natural Sciences MSc by Research
- Natural Sciences PhD
- Social Statistics PhD
- Statistics PgDip
- Statistics PhD
- Statistics PhD (Integrated)
- Statistics and Epidemiology PhD
- Statistics and Operational Research MRes
- Statistics and Operational Research (STOR-i) PhD
The information on this site relates primarily to 2022/2023 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.