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Mathematics BSc (Hons)


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The following courses also include this module in their teaching programme:-

Module MS0603 - Advanced Statistical Methods

(20.00 Credits)

SYNOPSIS OF MODULE This module covers the three important areas of experimental design, multivariate techniques and regression. Experimental design is developed using analysis of variance techniques to compare treatments meaningfully using replication, factorial experiments and balanced incomplete block designs. Multivariate techniques include multivariate inference, data reduction using principal component analysis and classification with linear discriminant analysis. Regression is extended to the case where there are several explanatory variables including indicator variables. The models are examined using variable selection criteria and regression diagnostics to improve the model. Curvilinear and non-linear regression models cover the important aspect where different types of curves are appropriate for the data. The case of a binary response variable is examined and involves different methods of estimating the parameters and testing the model. The module is delivered by a combination of lectures and laboratory sessions involving the use of an appropriate statistical package such as SPSS. Assessment involves a practical assignment and a laboratory examination.


INDICATIVE READING LIST OR OTHER LEARNING RESOURCES

Montgomery, D. C. (2005) Design and Analysis of Experiments, Wiley.

Johnson, R A and Wichern, D W (2002). Applied Multivariate Statistical Analysis. Prentice Hall.

Chatfield, C and Collins, A J (1980), Introduction to Multivariate Analysis. Chapman and Hall.

Krzanowski, W J (2000), Principles of Multivariate Analysis: A User's Perspective. Clarendon Press.

Montgomery, D.C. and Peck, E. (2001) Introduction to Linear Regression Analysis, Wiley.

Ratkowsky,D.A. (1983) Nonlinear Regression Modelling: a Unified Practical Approach, Marcel Dekker.

Dobson,A.J. (2002) An Introduction to Generalised Linear Models, Chapman and Hall.


OUTLINE SYLLABUS Experimental Design (15%): Design and analysis of 2^n factorial experiments with replication, a full replicate and balanced incomplete block designs. Multivariate Techniques (35%): The multivariate normal distribution and its properties. Hotellings T^2 test for one, two and paired samples. Manova, linear discriminant analysis and principal component analysis. Multiple linear regression (35%): Least squares estimation of the parameters of the model and their properties. The analysis of variance and the extra sum of squares method. Indicator variables in the model. Variable selection techniques using Adjusted R-squared, minimum error SS and mallows statistic. Regression diagnostics, leverage, influence and multicollinearity, polynomial and curvilinear regression. Non-linear and Generalised linear models. (15%): The non-linear regression model, estimation of parameters and testing the model. Analysis of deviance and the linear logistic model. Testing the suitability of the model.


AIMS OF MODULE 1. To extend the range of experimental designs. 2. To enable the student to use the diverse range of methods of multivariate analytical techniques. 3. To provide the student with experience in using appropriate software for the analysis of multivariate techniques. 4. To analyse multiple regression models and develop the best subset model. 5. To extend regression to curvilinear and non-linear regression models. 6. To enable the linear logistic model to be formulated.


LEARNING OUTCOMES 1. Design an appropriate experiment, analyse the results and interpret using an appropriate statistical package. 2. Select and apply the appropriate hypothesis test for one or more samples of multivariate data. 3. Implement appropriate multivariate techniques for data classification or variable reduction. 4. Analyse and assess multiple linear regression models by evaluating variable selection techniques and regression diagnostics. 5. Modify regression procedures to select curvilinear and nonlinear models. 6. Construct and assess the linear logistic regression model using the generalised linear model procedures.l


PREREQUISITES None


COREQUISITE(S) None


DISTANCE LEARNING DELIVERY


LEARNING, TEACHING AND ASSESSMENT STRATEGY The main concepts and statistical methodology will be delivered in the lecture periods. Practical examples will be given in laboratory sessions where a statistical package such as SPSS will be available to analyse the data. Assessment will be a combination of a practical assignment (30%) and a laboratory examination (70%) at the end of the year. Coursework assesses Learning Outcomes 4, 5 and 6. Examination assesses Learning Outcomes 1 to 6.


IMPLICATIONS FOR CHOICE


NOTIONAL STUDENT WORKLOAD Lectures 39 Lab Work 13 Directed Learning 39 Independent Learning 69 Formal Assessment 40 Total 200 hours



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