Applied Statistics



Applied Statistics - (M8 and L4+4) R. Evans & B. Tom

This is a practical course (3 units: 12 lectures and 12 classes) aiming to develop skills in analysis and interpretation of data, and communicating this in writing. Students are strongly encouraged to attend the course Statistical Theory for the theoretical background to the results used in the practical analysis of data.


The statistical methods listed below will be put into practice using R. In the practical classes, emphasis is placed on the importance of the clear presentation of the analysis, so that students are required to submit written solutions to the lecturer.

Syllabus

Michaelmas Term

Introduction to Linux and R on the Statistical Laboratory computing network. Use of LATEX for report writing. Exploratory data analysis, graphical summaries.
Linear regression and its assumptions: relevant diagnostics: residuals, leverages, Q-Q plots, Cook's distances and related methods. Hypothesis tests for linear models, ANOVA, F-tests. Factors for categorical data. [3]
Dependent data, use of linear mixed e ects models, restricted maximum likelihood. [2]
The essentials of generalized linear modelling. Discrete data analysis: binomial and Poisson regression. Multi-way contingency tables. [3]

Lent Term

Some special topics. Previous examples include generalized additive models, and longitudinal data analysis. [4]

Pre-requisite Mathematics

It is assumed that you will have done an introductory statistics course, including: elementary probabilitytheory; maximum likelihood; hypothesis tests (t-tests, χ2-tests, possibly F-tests); con dence intervals.

Literature

1. Dobson, A.J. (2002) An Introduction to Generalized Linear Models. Chapman & Hall/CRC. 2nd edition.
2. Agresti, A. (1990) Categorical Data Analysis. Wiley. 2nd edition.
3. McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models. Chapman & Hall. 2nd edition.
4. Venables, W.N. and Ripley, B.D. (2002) Modern Applied Statistics with S. Springer-Verlag. 4th edition.
5. Pawitan, Y. (2001) In All Likelihood : Statistical Modelling and Inference Using Likelihood. Oxford Science Publications.

Applied Statistics II - (L4+4) B.D.M. Tom

This is the second part of the Applied Statistics course, which consists of 4 lectures and 4 classes given in the Lent term. This course (i.e. both the first and second parts) will count as a 3 unit (24 lectures) course.

Four topics are to be covered in this part of the course. Previous topic areas consist of non-parametric density estimation; EM algorithm and mixture models; methods for survival data analysis; longitudinal data analysis and multi-state modelling; additive and generalized additive models; parametric approaches to handling over-dispersed count data; and cost-effectiveness analysis.

The four topics chosen will be lectured on and then put into practice using the R statistical software environment. In the practical classes, emphasis is placed on the importance of clear presentation and interpretation of the analysis performed. Students are recommended to submit written solutions to the lecturer for feedback.

Pre-requisite
It is assumed that you have taken the first part of this course in the Michaelmas term and previously done a basic statistics course. Familiarity with using R to read in data, produce graphical and tabular summaries, perform simple hypothesis tests (including t, χ2, F and non-parametric tests) and analyses based on linear and generalized linear models is assumed.
Literature
1. Venables, W.N. and Ripley, B.D. (2002). Modern Applied Statistics with S. Springer-Verlag (4th Edition).
Reading to complement course material
A list of references will accompany each topic covered.

 

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