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.

Experiments are carried out by researchers in many fields including biology, medicine, chemistry, physics, engineering and agriculture. In such experiments the results are affected both by the choice of factors to study and experimental error (such as measurement error or inherent randomness between experimental units). Choosing a good experimental design ensures that the aim of the study where it is used is achieved. Moreover, the statistical analysis of data collected from such designed experiments is simple, easier to interpret and the experimental resources are spent most efficiently. The main principles for designing and analyzing experiments will be introduced. Various standard experimental designs and the analysis of data obtained using them are covered. Criteria for optimality of experimental designs will be introduced. Methods for constructing nonstandard designs when the model is linear or nonlinear in the parameters will be presented.

Students are not permitted to take, for credit, MATH48082 in an undergraduate programme and then MATH68082 in a postgraduate programme at the University of Manchester, as the courses are identical.

Introduce statistical principles and methods for the design of experiments and analysis of the resulting data.

On successful completion of this course unit students will be able to: 

• Construct both standard and non-standard experimental designs
• Analyse data from designed experiments using a model-based approach, both by hand and using R
• Assess the statistical properties of a proposed design, such as which model(s) can be estimated and/or its performance in terms of D- or G-optimality, and compare these properties with those of other potential designs
• Explain key ideas and assumptions underpinning the statistical design and analysis of experiments and their relationship to specific examples
• Prove results in the statistical design and analysis of experiments using relevant theoretical techniques, for example the General Equivalence Theorem

1. Basic concepts: treatments and experimental units, factors, randomization.
2. Completely randomized design.
3. Block designs: randomized complete block design, balanced incomplete block design.
4. Factorial experiments: two-way layout, two-level full factorials and fractional factorials. Confounding with blocks. Construction and analysis.
5. Response surface methodology.
6. Random effects. Consequences for ANOVA tests, estimation of variance components. Nested designs.  
7. Optimal design for linear models: D-optimality and G-optimality, algorithmic approaches, General Equivalence Theorem.
8. Nonlinear models and optimal design for nonlinear models: nonlinear least squares, locally D-optimal design, Bayesian designs. 

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. 

• Take-home Coursework: weighting 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.

• A. C. Atkinson, A. N. Donev, R. D. Tobias (2007). Optimum Experimental Designs, With SAS. Oxford University Press.
• G. Casella (2008). Statistical design. Springer.
• A. Dean, D. Voss, D. Draguljić (2017). Design and analysis of experiments, 2nd edn, Springer.
• P. Goos and B. Jones (2011). Optimal design of experiments: a case study approach, Wiley.  
• J. Lawson (2015). Design and Analysis of Experiments with R. Chapman and Hall/CRC.
• D. C. Montgomery (2019). Design and Analysis of Experiments, 10th edn. Wiley.
• G. Oehlert (2010) A first course in Design and Analysis of Experiments. http://users.stat.umn.edu/~gary/Book.html
• N. Taback (2022). Design and Analysis of Experiments and Observational Studies using R, Chapman and Hall/CRC. https://designexptr.org
• C.-F. J. Wu and M. S. Hamada (2021). Experiments: planning and optimization, Wiley.