# 2023/24 Taught Postgraduate Module Catalogue

## OMAT5101M Statistical Methods

### 15 creditsClass Size: 100

Module manager: Dr Leonid Bogachev
Email: l.v.bogachev@leeds.ac.uk

Taught: 1 May to 30 Jun (2mth)(adv yr), 1 May to 30 June, 1 Nov to 31 Dec (2mth)(adv yr) View Timetable

Year running 2023/24

### Pre-requisite qualifications

Students are required to meet the programme entry requirements prior to studying the module.

Module replaces

N/A

This module is not approved as an Elective

### Module summary

The module provides a general introduction to statistical thinking and data analysis including probability rules and distributions, methods of estimation and hypotheses testing and present the basics of Bayesian inference.

### Objectives

Through a combination of theory and examples-based practice, the material in the module will allow students to calculate statistical estimates and understand the uncertainty in those estimates as well as select, apply and interpret the outcome of statistical tests which are widely used in a range of applications.

Learning outcomes
On completion of this module students will be able to:

1. Understand and be able to explain the role of statistical models.
2. Be able to compute appropriate statistical estimates and to assess the estimation error.
3. Perform a range of statistical tests.
4. Interpret the results of statistical tests.
5. Understand the interplay of prior information and data in Bayesian inference.

Skills outcomes
The module will develop the following skills:

- Students will learn to carry out the statistical analysis described above using appropriate software.
- Making judgements based on statistical analysis.

### Syllabus

1. The role of statistical models.
2. Probability rules and distributions.
3. Statistical estimators, bias, mean squared error (MSE).
4. Standard examples of estimators (e.g. sample mean, sample variance).
5. Statistical tests, types of error and error probabilities.
6. Examples of tests (such as z-test and t-test).
7. Computing estimates and performing tests in R.

### Teaching methods

 Delivery type Number Length hours Student hours On-line Learning 1 1.50 1.50 On-line Learning 5 1.00 5.00 Discussion forum 6 2.00 12.00 Independent online learning hours 42.00 Private study hours 89.50 Total Contact hours 18.50 Total hours (100hr per 10 credits) 150.00

### Opportunities for Formative Feedback

Students will have weekly formative assignments (e.g. quizzes, problem sheets or practical tasks) for each taught unit of the module and will be given model solutions with comments.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Students will be tested predominantly using e-assessment methods or MCQs. 20.00 Assignment The assignment will require students to complete a written report which may feature components of R code, R outputs, calculations and critical analysis of results. It is expected that the assignment will be completed in one week. 80.00 Total percentage (Assessment Coursework) 100.00

It is expected that the students resitting will do so via the assignment only which can cover all learning outcomes. This will be available during the next running of the module.