# Statistical Analysis

## Overview

• Credit value: 30 credits at Level 7
• Tutors: to be confirmed
• Assessment: a three-hour written examination, plus coursework amounting to 20% of the final mark

## Module description

This module provides a solid grounding in the fundamental theory and practice of statistical modelling and the analysis of observational and experimental data (including continuous, binary and categorical data). The course covers multiple linear regression, additive models, analysis of variance with fixed and random effects, generalised linear models (including logistic regression and log-linear models for contingency tables) and an introduction to the theory and analysis of multivariate data.

You will receive provide practical training and experience in the application of the theory to the statistical modelling of data from real applications, including model identification, estimation and interpretation. You will also learn how to use advanced statistical software to analyse real data from observational studies, designed experiments and other sources.

The first section is an introductory series of five lectures in parallel with five computing sessions designed to revise basic statistical concepts and models, including one-way ANOVA and multiple regression, while introducing you to the use of S-Plus for the statistical analysis of experimental and observational data. These 10 sessions are also intended to motivate some of the theory in the first term courses on Probability and Distribution Theory and Statistical Inference.

Underlying theory is developed (or anticipated) in the lectures and illustrative practical examples fully analysed. The associated computing sessions are self-paced. They are designed to introduce the statistical package SPlus and its programming language and to allow you to carry out for yourself exercises and examples that are carefully chosen to illustrate the theory and reinforce the examples in lectures.

The remaining lectures and associated computing sessions build on this introduction, introducing more complex statistical data, models and designs for data collection, and developing both the theory and practice more fully.

### indicative module content

• Introduction to the analysis of statistical data
• Analysis of designed experiments
• Generalised linear models
• Multivariate analysis

## Learning objectives

By the end of this module, you should be able to demonstrate:

• substantial knowledge and understanding of the theory of the general linear model (including multiple regression and designed experiments with fixed and random effects) and of additive models and generalised linear models (including logistic regression and log-linear models for contingency tables)
• knowledge of the fundamental distributions in multivariate normal theory: the multivariate normal distribution, the Wishart distribution and Hotelling T2 distribution
• knowledge and understanding of the maximum likelihood and union-intersection approaches to multivariate hypothesis tests and applications to one-sample, two-sample and one-way tests for mean vectors
• knowledge and understanding of linear discriminant analysis and the relationship between Fisher's linear discriminant function, the Mahalanobis distance between samples and the two-sample Hotelling T2 test
• knowledge and understanding of principal components analysis and its uses and applications
• the ability to apply principles and theory to the statistical modelling and analysis of practical problems in a variety of application areas, and to interpret results and draw conclusions in context
• the ability to abstract the essentials of a practical problem and formulate it as a statistical model in a way that facilitates its analysis and solution.