Multivariate Statistics Harry R. Erwin, PhD School of Computing and Technology University of Sunderland

Resources Everitt, BS, and G Dunn (2001) Applied Multivariate Data Analysis, London:Arnold. Everitt, BS (2005) An R and S-PLUS® Companion to Multivariate Analysis, London:Springer

Introduction Most statistical data sets are multivariate. Sometimes it’s useful to study a variable in isolation, but usually you need to examine all the variables to understand the data. The next few lectures are the core of this module. We will examine the description, exploration, and analysis of multivariate data.

Multivariate Data Natural form of multivariate data is a table or data frame. Kinds of data –Unordered categorical variables (nominal data) –Ordinal data (numbered but not measured) –Interval data (measured data) –Ratio data (numerical with a defined ‘zero’) Missing values (common)

Handling Missing Data Ignore it. –Often biased. Fill in plausible values –Known as imputation –Advanced topic Be aware this is a problem area

Summary Statistics Means –Generated by mean Variances –Generated by var Covariances –Also generated by var Correlation coefficients –Generated by cor Distances –Generated by dist

Aims Data exploration (data mining) –Looking for non-random patterns and structures –Visual and graphical displays Confirmatory analysis (later in the module) –Statistical testing

Looking at Multivariate Data Scatterplots –Demonstration “The convex hull of bivariate data” –Demonstration Chiplot –Demonstration Bivariate Boxplot –Demonstration

More Multivariate Graphics Bivariate Densities –Demonstration Other Variables in a Scatterplot –Demonstration Scatterplot Matrix –Demonstration of pairs 3-D Plots –Demonstration Conditioning Plots and Trellis Graphics –Demonstration

Summary Most statistical data are multivariate. Most multivariate data have structure. Detecting that structure is what data mining is all about. Most data mining involves data visualisation and graphing—nothing more. Most of your conclusions from data mining will be obvious—once you see them! And you really don’t need to learn very much statistics to be good at multivariate data analysis.