# Mathematics

## ECM2709 - Statistics (2015)

MODULE TITLE CREDIT VALUE Statistics 15 ECM2709 Dr Christopher Ferro (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 150
DESCRIPTION - summary of the module content

The subject of statistics is concerned with both the practice of analysing data to learn about the world, and also the theory that underpins the methods and models used for data collection and analysis. In this module, you will learn about the key ideas of statistical modelling and inference, in which probability is used to quantify uncertainty. You will also gain experience of employing these ideas to analyse data using advanced statistical software. These ideas underpin applications in a huge range of data-intensive fields, for example in the detection and attribution of climate change, in the design and analysis of clinical trials, in the estimation of risk in the insurance sector, and in the prediction of outcomes of sports events. Overviews of such applications will be given in a series of guest lectures.

Prerequisite module: ECM1705, ECM1707 or equivalent

AIMS - intentions of the module

This module aims to lay the foundations for a thorough understanding of modern statistical theory and practice. It aims to help students to learn how to analyse and present data effectively, to select and use appropriate probability models, and to make inferences about models from data.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:
1 demonstrate knowledge and understanding of basic data analysis tools, probability models and inferential procedures including point- and interval-estimation and hypothesis testing;
2 select statistical methods appropriate for solving simple problems;
3 apply these methods to draw correct inferences from data;
4 derive properties of basic inferential procedures.
Discipline Specific Skills and Knowledge:
5 progress to study statistical modelling and inference in more detail;
6 use statistical software competently.
Personal and Key Transferable/ Employment Skills and Knowledge:
7 demonstrate data analysis skills;
8 communicate results clearly in writing;
9 demonstrate organisational and time-management skills;
10 demonstrate independent use of relevant learning resources.

SYLLABUS PLAN - summary of the structure and academic content of the module

1. Learning from data [c. 5 hours]

We discuss the role of data in learning about the world and discover how statistics can help us to do this. Then we gain some experience with numerical and graphical tools for learning from data.

2. Probability modelling [c. 3 hours]

We revise probability, random variables and distributions before learning how probability models can be formulated to describe physical processes.

3. Statistical inference [c. 2 hours]

We introduce the aims, principles and tools of statistical inference and then discuss the criteria used to assess the quality of inferential procedures, including the key concept of sampling distributions.

4. Point estimation [c. 8 hours]

We investigate how to construct point estimators, including method-of-moments estimators, and identify important properties such as bias and consistency. Then we introduce the likelihood function, the score function, information, maximum-likelihood estimators and their large-sample properties.

5. Hypothesis testing [c. 5 hours]

We introduce the framework of hypothesis testing, including simple and composite hypotheses, critical regions, size and power, and discuss how to construct test statistics. Then we discuss z-tests and t-tests.

6. Interval estimation [c. 3 hours]

We define the notion of confidence intervals and show how to construct them.

7. Statistics in action [c. 4 hours]

At appropriate points in the module we discuss the roles of statistics in important fields such as climate, sport, health and insurance.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 44 106 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 33 Lectures including examples classes Scheduled learning and teaching activities 11 Tutorials or computing classes Guided independent study 33 Studying lecture notes Guided independent study 33 Attempting unassessed exercises Guided independent study 24 Revising for examination Guided independent study 16 Completing assessments

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Weekly exercise sheets Several short exercises (c. 4 hours each week) 1 to 10 Oral feedback in tutorials and office hour

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 2 hours 1-5, 7, 8 Oral feedback at request from student
Coursework – assessed exercise 20 Short report (c. 16 hours) 1-4, 6-10 Written feedback on script and oral feedback in office hour

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

Type Author Title Edition Publisher Year ISBN Search
Set Rice, J A Mathematical Statistics and Data Analysis 3rd Brooks Cole 2007 978-0495118688 [Library]
Set Dalgaard P Introductory Statistics with R 2nd edition Springer 2008 9780387790534 [Library]
Extended Daly, F, Hand, DJ, Jones, MC Elements of Statistics Addison-Wesley 1995 978-0201422788 [Library]
Extended Freund, J E , Walpole, RE Mathematical Statistics 3rd Prentice Hall 1980 978-0135620663 [Library]
Extended Wackerly, D D, Mendenhall,W, Scheaffer, RL Mathematical Statistics with Applications 5th Thomson Learning/Duxbury 1996 978-0534209186 [Library]
Extended Maindonald J. & Braun J. Data Analysis & Graphics using R 2nd edition Cambridge University Press 2007 9780521861168 [Library]
Extended Hogg; R.V. & Tanis; E.A. Probability and Statistical Inference 8th edition Prentice Hall/Pearson 2009 978-0321636355 [Library]
Extended Larsen, R J, Marx, M L An Introduction to Mathematical Statistics and its Applications 4th Pearson 2006 978-0132018135 [Library]
Extended Zuur, Alain F, Ieno, Elena, N, Meesters, Erik HWG A Beginner's Guide to R Springer- Verlag 2009 978-0-387-93836-3 [Library]
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES ECM1707, ECM1705
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 5 No Friday 09 January 2015 Friday 09 January 2015
KEY WORDS SEARCH Statistics; mathematics; probability; data; analysis; modelling; inference.