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Multivariate Analysis - MAT00021H

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  • Department: Mathematics
  • Module co-ordinator: Dr. Agostino Nobile
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2022-23
    • See module specification for other years: 2021-22

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


Additional information

Pre-requisite modules for Natural Sciences students: Statistics Option MAT00033I.

Module will run

Occurrence Teaching period
A Spring Term 2022-23

Module aims

To introduce the main ideas of multivariate statistical analysis; that is, the analysis of sets of data where there are several measurements on each of a number of individuals.

Module learning outcomes

  • A knowledge and understanding of models and methods for multivariate data.

  • A reasonable degree of familiarity with some of the main techniques of multivariate analysis.

  • Apply appropriate techniques to different sets of data.

  • Use the statistical package R to analyse multivariate data by various techniques.

Module content

 

Syllabus

  • Introduction: Aims of multivariate analysis, descriptive statistics, graphical representation, basic concepts of vectors and matrices, use of the R program for matrix algebra and multivariate analysis.
  • The Multivariate Normal Distribution: Properties of the multivariate normal, contours of constant density, marginal and conditional distribution, checking normality.
  • Hotelling's T-squared test: One-sample tests, two-sample tests, large sample inference.
  • Multvariate Analysis of Variance (MANOVA): One-way and two-way MANOVA, Wilks' Lambda and other criteria.
  • Principal component analysis: Principal components, principle component analysis by correlation matrix, choosing the number of components.
  • Factor analysis: The idea of factor analysis, estimation of loadings, choosing the number of factors.
  • Cluster analysis: Hierarchical cluster methods, dendrogram, non-hierarchical cluster methods.

Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Multivariate Analysis		 2 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Multivariate Analysis		 2 hours 100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

Richard Johnson, Dean Wichern, Applied Multivariate Statistical Analysis, Prentice Hall.

H R Neave, Statistics Tables for Mathematicians, Engineers, Economists and the Behavioural and Management Sciences, Routledge.


The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.