Gwybodaeth Modiwlau

This module aims to give research students in the biological sciences a firm basis in statistical science. It does not aim to teach as many methods as possible, but to give an overview of the main areas of the subject. Neither does the module deal with statistical software because: (i) dealing with computer methods would detract from the teaching of statistical principles, which is the primary aim of the module; and (ii) the use of standard computer programs to perform the calculations of statistical methods, such as MINITAB or SPSS, is fairly readily learned from the appropriate computer manuals or, better, from other people who have used the software, when one has data for which a particular analysis is required. However, the teaching of this module is firmly based around large numbers of worked examples.
Another objective of the module is to enable a biological research worker to have a meaningful dialogue with a professional statistician. It cannot be too strongly emphasised that for anything other than the simplest, whenever an experiment is being designed it should be done in conjunction with a statistician. This is to ensure that the data collected can be analysed in such a way that the questions being asked of the data can be answered as unambiguously as possible. This module aims to introduce a research worker to the concepts and terminology of statistical science, as well as to detailed methods in the three broad areas which are of most use to research biologists.

Basics: Data summarisation; the concept of sample and population; Sample statistics and population parameters; tests of hypothesis, one- and two- sample t-tests; the method of confidence intervals.

Experimental Design and Analysis of Variance (ANOVA): General principles of experimental design. One-way ANOVA. Comparisons - multiple range tests, orthogonal comparisons, comparisons by regression components (after regression part of the course). Variance heterogeneity and data transformation. The randomised block design. Two-factor ANOVA. More briefly, simply to give a flavour of what designs and analyses can be done: three- and four-factor ANOVAs; incomplete factorial designs; nested designs; split-plot designs; Model I & Model II ANOVAs.
Regression Analysis: The idea of fitting a straight line (or curve) to data and performing various tests on the fitted relationship. Straight line regression - fitting, test of significance, tests on the gradient, confidence band, testing linearity. Curvilinear regression - examples where transformation achieves linearity, the distinction between linear and non-linear regression in the statistical sense, polynomial curves, other curves. Multiple regression. Generalised linear models (a mention of).
Multivariate Methods: The concept of multivariate data and analysis. Introduction to matrix algebra. Summarisation of multivariate data; Some commonly used multivariate methods: Principal Component Analysis, Canonical Variate (Discriminant Function) Analysis, Multivariate Analysis of Variance.