## Module and Programme Catalogue

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## MATH2730 Analysis of Experimental Data

### 10 creditsClass Size: 200

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2006/07

### Co-requisites

MATH2710, or equivalent.

This module is approved as an Elective

### Module summary

Informal description: Experimental design investigates the general linear model via the analysis of variance technique with its wide variety of designs and also through simple linear regression. In analysis of variance, the one-way layout and two-way layout are considered with reference to fixed or random effects and interaction. The nested design is also considered. Model adequacy is examined through the analysis of residuals and assessment of fit. In simple linear regression, the distributions of model parameters are derived leading to hypothesis testing and confidence intervals for the regression line. Residuals are examined for adequacy of fit and where appropriate the lack of it is assessed. Throughout this course, many practical examples are solved and illustrated with the R statistical computing package. See the schools website or contact: a.slomson@leeds.ac.uk for more information.

### Objectives

To investigate the general linear model via the analysis of variance technique. On completion of this module, students should be able to: (a) recognise and apply various analysis of variance models; (b) interpret results of analysis of variance methods.

### Syllabus

Experimental design investigates the general linear model via the analysis of variance technique with its wide variety of designs and also through simple linear regression. In analysis of variance, the one-way layout and two-way layout are considered with reference to fixed or random effects and interaction. The nested design is also considered. Model adequacy is examined through the analysis of residuals and assessment of fit. In simple linear regression, the distributions of model parameters are derived leading to hypothesis testing and confidence intervals for the regression line. Residuals are examined for adequacy of fit and where appropriate the lack of it is assessed. Throughout this course, many practical examples are solved and illustrated with the MINITAB statistical computing package. Topics covered include: 1. Introduction to analysis of variance : one-way layout model, model adequacy; testing sub-hypotheses; random effects, components of variance. 2. Randomized complete block design. 3. Two-way analysis of variance : interaction; fixed and random effects, mixed models. 4. Nested designs. 5. Simple linear regression : properties of estimators; matrix representation; residual analysis; lack of fit testing.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures (22 hours); examples classes (6 hours) and practicals (5 hours).

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

2 hour written examination at end of semester (80%), coursework (20%).