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.

In practice, most data sets are multivariate, consisting of observations on several variables for each individual or object. Such data sets arise in many fields, including science, social sciences, and medicine, making techniques for their analysis an important area of statistics. This course introduces a variety of techniques, some of which generalise univariate methods, while others introduce new approaches (e.g. principal component analysis). The course focuses on continuous multivariate data, providing students with the theoretical tools and foundational knowledge necessary for advanced machine learning studies. Students will gain practical experience using R for data analysis throughout the course.  

Students are not permitted to take more than one of MATH38061 or MATH48061 for credit in the same or different undergraduate year.

 

Students are not permitted to take MATH48061 and MATH68061 for credit in an undergraduate programme and then a postgraduate programme.

 

Note that MATH68061 is an example of an enhanced level 3 module as it includes all the material from MATH38061.

 

When a student has taken level 3 modules which are enhanced to produce level 6 modules on an MSc programme taken within the School of Mathematics, then they are limited to a maximum of two such modules (with no alternative arrangements available otherwise)

The unit aims to:

Familiarise students with the ideas and methodology of foundational multivariate statistics, preparing them for advanced machine learning concepts. This includes their application in data analysis using the R statistical computing package. 

On successful completion of the course students will be able to:

• Explain the properties of random vectors and matrices, and calculate sample statistics (mean vectors, covariance matrices, correlation matrices) with transformations to simplify analysis.
• Apply the multivariate normal distribution and related distributions (e.g. Wishart, Hotelling’s T-squared) to analyse and model multivariate data.
• Estimate parameters (mean vector, covariance matrix) from multivariate data using maximum likelihood and Bayesian methods.
• Formulate and test hypotheses about mean structures and covariance matrices, and interpret confidence intervals in multivariate contexts.
• Apply dimension reduction techniques such as PCA, CCA and corresponding analysis to summarise and simplify multivariate data.
• Classify multivariate data using clustering and discriminant analysis.
• Apply popular computing software such as R or Python to visualise, analyse, and interpret multivariate data.

Part A – Core concepts and inferential techniques in multivariate analysis

• Random vectors and matrices – introductory ideas and basic concepts, linear transformations, sample statistics and their properties, overall measures of dispersion in p-space, distances in p-space, simple graphical techniques
• Multivariate normal (MVN) distribution and related distribution – definition, properties, conditional distributions, the Wishart and Hotelling T-squared distribution, sampling distributions of the sample mean vector and covariance matrix, maximum likelihood estimation of the mean vector and covariance matrix
• Inferences about mean structures – hypothesis testing and confidence intervals (one sample and two independent sample procedures), generalised likelihood ratio test, CI for the components of the mean vector(s), other topics such as MANOVA and profile analysis
• Inferences about covariance and correlation matrices – testing covariance structure of a single covariance matrix, testing equality of covariance matrices

 

Part B – Advanced techniques in multivariate analysis

• Bayesian inference for MVN – including conjugate models with potential exploration of approximation techniques and Monte Carlo methods
• Dimension reduction – techniques such as principal component analysis, factor analysis, canonical correlation analysis, and correspondence analysis
• Cluster Analysis – aims, K-means and hierarchical algorithms, the dendrogram
• Discriminant Analysis – LDA, QDA 

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

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.
 

• Chatfield, C. and Collins, A. J., An Introduction to Multivariate Analysis, Chapman & Hall 1983.
• Krzanowski, W. J., Principles of Multivariate Analysis: A User's Perspective, Oxford University Press 1990.
• Johnson, R. A. and Wichern, D. W., Applied Multivariate Statistical Analysis 3rd edition, Prentice Hall 1992.
• Bishop, Y M, Fienberg, S E, and Holland P W (2007) Discrete Multivariate Analysis. Springer

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

· You will normally have exercise or problem sheets, on which you might spend approximately 2-2.5hrs per week
· There may be other tasks assigned to you on Canvas, for example short quizzes, short-answer formative exercises or directed reading
· In some weeks you may be preparing coursework or revising for mid-semester tests

Together with the timetabled classes, you should be spending approximately 9 hours per week on this course unit.

The remaining independent study time comprises revision for and taking the end-of-semester assessment.

The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Canvas page.