MSc Statistics

For entry in the academic year beginning September 2027, the tuition fees are as follows:

• MSc (full-time)
  UK students (per annum): £17,600
  International, including EU, students (per annum): £39,200
• MSc (part-time)
  UK students (per annum): £8,800
  International, including EU, students (per annum): £19,600

The fees quoted above are fully inclusive of tuition, administration and computational costs.

Fees for entry are subject to yearly review. The University reserves the right to increase your tuition fee by up to 7% each year for courses lasting more than one year, including to reflect rising costs associated with delivering our educational and wider student experience. Postgraduate fees information .

Always contact the admissions team if you are unsure which fee applies to your qualification award and method of attendance.

International student CAS deposit

Self-funded international applicants are required to pay a deposit of £2500 towards their tuition fees before a confirmation of acceptance for studies (CAS) is issued. Some applicants will be required to pay a higher deposit. More information on tuition fee deposits .

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

We offer a number of postgraduate taught scholarships and awards to outstanding UK and international students each year.

The University of Manchester is committed to widening participation in master's study, and allocates £300,000 in funding each year. Our Manchester Master's Bursaries are aimed at widening access to master's courses by removing barriers to postgraduate education for students from underrepresented groups.

We also welcome the best and brightest international students each year and reward excellence with a number of merit-based scholarships. See our range of master’s scholarships for international students .

And, if you have completed an undergraduate degree at The University of Manchester, or are currently in your final year of an undergraduate degree with us, you may be eligible for a discount of 10% on tuition fees if you choose to study on a taught postgraduate course here. Find out if you're eligible and how to apply .

For more information on master's tuition fees and studying costs, visit the University of Manchester funding for master's courses website to help you plan your finances.

Longitudinal and spatial data analysis are essential tools in modern research, particularly in fields such as public health, epidemiology, environmental science, and the social sciences. As the availability of such data rapidly increases, statisticians play a vital role in developing sophisticated models to address complex scientific questions and provide meaningful insights.

 

The primary objective of longitudinal data analysis is to investigate how a response variable changes over time in relation to explanatory variables while accounting for within-subject correlations. This involves identifying and quantifying random variations from different sources and characterising the within-subject correlation structure. Longitudinal data is essential for studying individual trajectories, temporal trends, and treatment effects over time, making it highly relevant in clinical trials and behavioural research.

 

Spatial data analysis, on the other hand, focuses on data observed across different geographical locations. The goal is to model and understand spatial dependence, identify spatial patterns, estimate the effects of exposures or interventions across regions, and make predictions for unobserved locations. This is essential in fields like environmental monitoring, disease mapping, and urban planning, where spatial variability plays a key role in decision-making.

 

Both longitudinal and spatial data analysis deal with correlated data, where observations are not independent, which distinguishes these methods from standard statistical techniques. This course provides students with the necessary skills to analyse and model such data, enabling them to apply these techniques to real-world problems. 

Students are not permitted to take, for credit, MATH48132 in an undergraduate programme and then MATH68132 in a postgraduate programme at the University of Manchester, as the courses are identical.

This unit aims to:

Introduce students to advanced statistical methods for analysing correlated data, with a particular focus on models for both longitudinal and spatial datasets. The course will cover key theoretical concepts and practical applications, equipping students with the skills to handle complex data structures that arise when observations are collected over time (longitudinal) or across geographical or spatial locations.  

On successful completion of this course unit students will have a good understanding of: 

• apply advanced statistical models, including general linear models with correlated random errors, linear mixed models, generalise linear mixed models and generalised estimating equations, to analyse longitudinal data;
• describe the theory behind the parameter estimation and model selection criteria for these models;
• distinguish between various types of spatial data and choose appropriate statistical methods for their analysis;
• identify and model spatial autocorrelation in spatial data to capture spatial dependence;  
• implement the statistical methods in statistical software R for real-data analysis.

1. Introduction to Longitudinal data

2. Linear mixed models: Fixed effects, random effects,  various covariance models variance components,  restricted maximum likelihood estimation, prediction of random effects

3. Non-normal longitudinal data models

4. Introduction to spatial data: types of spatial data, motivating examples from environmental epidemiology and social sciences. Geostatistical theory and modelling: stationarity and isotropy, Gaussian processes, covariance function, Variograms, Model adequacy and spatial prediction.  

5. Area-level data

6. Point process data 

Teaching is composed of two hours of lectures and one tutorial class per week. One week is reserved for coursework. Teaching materials will be made available online for reference and review. 

• Coursework 30%.
• End of semester examination: weighting 70%

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

• Davis, C. S. (2002). Statistical methods for the analysis of repeated measurements. Springer, New York
• Diggle, P. J., Heagerty, P., Liang, K Y. and Zeger, S. L. (1994). Analysis of longitudinal data. 2nd Edition. Oxford University Press
• Fitzmaurice, G. M., Laird, N. M., and Ware, J. H. (2004). Applied longitudinal analysis. New York, Wiley.
• Gelfand, A. E., Diggle, P., Guttorp, P., & Fuentes, M. (2010). Handbook of spatial statistics. CRC press.
• Moraga, P. (2019). Geospatial health data: Modeling and visualization with R-INLA and shiny. Chapman and Hall/CRC.
• Diggle, P. J., & Ribeiro, P. J. (2007). An overview of model-based geostatistics. Model-based Geostatistics, 27-45.
• Baddeley, A., Rubak, E., & Turner, R. (2015). Spatial point patterns: methodology and applications with R. CRC press.