(Last Updated:03 May 2017)

**Total Credits: **20

**Level: **Level 2

**Target Students: **Single Honours and Joint Honours from the School of Mathematical Sciences. Available to JYA/Erasmus students. * Available to JYA/Erasmus students.*

**Taught Semesters:**

Semester | Assessment |
---|---|

Full Year | Assessed by end of Spring Semester |

**Prerequisites: **Knowledge of probability as covered by G11PRB, knowledge of statistics as covered by G11STA and knowledge of core mathematical concepts, methods and techniques as taught in G11ACF, G11CAL and G11LMA.

Mnem | Title |
---|---|

G11PRB | Probability |

G11ACF | Analytical and Computational Foundations |

G11CAL | Calculus |

G11LMA | Linear Mathematics |

G11STA | Statistics |

**Corequisites: **

Mnem | Title |
---|---|

G12PMM | Probability Models and Methods |

**Summary of Content: **

The first part of this module provides an introduction to statistical concepts and methods. A wide range of statistical models will be introduced to provide an appreciation of the scope of the subject and to demonstrate the central role of parametric statistical models. The key concepts of inference including estimation and hypothesis testing will be described. Special emphasis will be placed on maximum likelihood estimation and likelihood ratio tests. While numerical examples will be used to motivate and illustrate, the content will emphasis the mathematical basis of statistics. Topics include maximum likelihood estimation, confidence intervals, likelihood ratio tests, categorical data analysis and non-parametric procedures.

The second part of the module introduces a wide class of techniques such as regression, analysis of variance, analysis of covariance and experimental design which are used in a variety of quantitative subjects. Topics covered include the general linear model, least squares estimation, normal linear models, simple and multiple regression, practical data analysis, and assessment of model adequacy. As well as developing the theory, practical experience will be obtained by the use of a statistical computer package.

**Method and Frequency of Class: **

Activity | Number Of Weeks | Number of sessions | Duration of a session |
---|---|---|---|

Lecture | 23 weeks | 1 per week | 1 hour |

Lecture | 23 weeks | 1 per week | 1 hour |

Workshop | 4 weeks | 1 per week | 1 hour |

Seminar | 23 weeks | 1 per week | 1 hour |

Activities may take place every teaching week of the Semester or only in specified weeks. It is usually specified above if an activity only takes place in some weeks of a Semester

One two-hour class and one one-hour class per week timetabled centrally, some of which may be used for examples classes and/or problem classes.

**Method of Assessment: **

Assessment Type | Weight | Requirements |
---|---|---|

Exam 1 | 75 | 2 hour 30 min written examination |

Coursework 1 | 5 | Advanced take-home exercise on statistical data analysis and hypotheses tests using software packages (end spring semester) |

Coursework 2 | 10 | Take-home exercise on statistical data analysis using software packages (mid spring semester) |

Inclass Exam 1 (Written) | 10 | Inclass test (autumn) |

**Convenor: **

Dr T Kypraios

Dr R Wilkinson

**Education Aims: **

The purpose of this module is to introduce a wide range of statistical concepts and methods fundamental to applications of statistics, and also to introduce the key concepts and theory of linear models, illustrating their application via practical examples drawn from real-life situations. Students will acquire knowledge and skills of relevance to a professional statistician.

**Learning Outcomes: **

A student who completes this module successfully will be able to:

L1 - apply methods concerning estimation of parameters in standard
statistical models; in particular the method of moments and the maximum
likelihood method.

L2 - apply methods for interval estimation; in particular,
exact and approximate confidence intervals based on asymptotic theory.

L3 - perform statistical hypotheses tests using data from studies (such as t and F-tests, comparison of models and parameter values).

L4 - apply methods for analysing categorical data and methods without
having to make distributional assumptions (non-parametric statistics).

L5 - fit a linear model to data, both manually and using statistical
software

L6 - check model fit, diagnose errors, and perform model selection
amongst the class of linear models

**Offering School: **Mathematical Sciences

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