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