Aims

To lay the foundations of statistical inference. The students will learn about the distinction between a population and a sample. They will know about the use of estimators calculated from random samples as a means of learning about properties of the population. They will be able to describe the role of likelihood methods in the derivation of estimators and their properties.

Module summary

Statistics aims to learn about populations on the basis of samples drawn from them. Population parameters, such as means, can be estimated by suitable sample statistics, but they will be in error because of sample to sample variation. Statistical inference is concerned both with estimating parameters and also with quantifying the associated sampling variation.
This module introduces fundamental notions of a standard error, confidence interval and hypothesis tests, in the context of both discrete and continuous variables. The likelihood is probably the most important concept in statistical methodology, and its introduction in the case of a scalar parameter is one of the main features of the module.

Outline Of Syllabus

Notion of an estimator: examples using means and proportions. Exploratory data analysis.
Properties of sampling distributions, including standard errors and confidence intervals.
Central Limit Theorem via simulation, no proof.
Likelihood, maximum likelihood estimators (scalar case) and their properties. Likelihood ratio test.
Introduction to hypothesis tests: rejection regions, type I and type II errors, power and significance level. Illustrations using one- and two-sample hypothesis tests for means and for proportions. Contingency table analysis.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.