# TOPICS IN APPLIED STATISTICS - 2024/5

Module code: MATM056

## Module Overview

This module contains the following topics:

Multivariate Models; Survival analysis; Generalized Linear Models and Binary Data.

A selection from specialised topics:

Epidemiology; Robust design and Taguchi methods; Bootstrapping.

Statistical software is used to ensure that the emphasis is on methodological considerations rather than on calculation. Computer lab sessions relating to real life situations will reinforce topics covered and, where possible, will use real data.

### Module provider

Mathematics & Physics

GODOLPHIN Janet (Maths & Phys)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 52

Lecture Hours: 33

Laboratory Hours: 9

Guided Learning: 23

Captured Content: 33

Semester 2

None.

## Module content

Indicative content includes:

Multivariate Models Graphical representations of multivariate data. Principal components and correspondence analyses. Use of clustering analysis to identify and characterize subgroups in the population. Classification and discrimination methods to assign individuals to groups. The multivariate normal distribution.

Survival Analysis Survival data, types of censoring. Failure times and hazard functions. Accelerated failure time model. Parametric models, exponential, piecewise exponential, Weibull. Nonparametric estimates: the Kaplan-Meier estimator and asymptotic confidence regions. Parametric inference. Survival data with covariates. Proportional hazards. Cox’s model and inference.

Generalized Linear Models and Binary Data Introduction to generalized linear models. Binary logistic regression with a single categorical predictor. Binary logistic regression for k-way tables. Binary logistic regression with continuous covariates. The Poisson regression model: for count data; for rate data. Model diagnostics. Log-linear models and their use for two-way and three-way contingency tables.

A selection from specialised topics such as:

Epidemiology Prevalence. Diagnostic testing – sensitivity and specificity. Receiver Operator Characteristic curves. Odds ratios/relative risk/risk difference – link between OR and RR when prevalence is low. Cross-sectional studies. Longitudinal studies: case-control/cohort.

Robust design and Taguchi methods Robust design, rooted in Taguchi methods, focuses on creating products or processes that are less sensitive to variations, enhancing reliability and performance. The methodology emphasises minimising variability and optimising performance through systematic experimentation. By identifying and controlling key factors, robust design ensures products are resilient to external influences, reducing defects and improving overall quality.

Bootstrapping Resampling methods for use with single samples from parametric and non-parametric models. Delta methods for variance approximation based on different forms of jackknife. Extension to: several samples; semiparametric and smooth models; data from a finite population; incomplete data through censoring or missing values. Bootstrap diagnostics. Monte Carlo tests, including those using Markov Chain simulation. Parametric bootstrap tests. Construction of confidence intervals.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Assessed Coursework 20
Examination End-of-Semester Examination (2 hrs) 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Analytical ability by solution of unseen problems in the exam.

• Statistical subject knowledge through the recall of key definitions, theorems and their proofs.

• An understanding of practical considerations when completing the coursework.

• The ability to analyse data, to interpret the analysis and report comprehensively on the results.

Thus, the summative assessment for this module consists of:

• One coursework worth 20% of the module mark and corresponding to Learning Outcomes 2 to 5.

• A synoptic examination (2 hours), worth 80% of the module mark, corresponding to Learning Outcomes 1 to 4.

Formative assessment
There are two formative unassessed courseworks over an 11 week period, designed to consolidate student learning.

Feedback
The written and verbal feedback from the unassessed courseworks assists students with preparation for the assessed coursework and the end-of-semester examination. Students also receive verbal and written feedback in the computer labs and office hours.

## Module aims

• Provide students with a detailed understanding of the principles and methods of several areas of statistical modelling and methodology.
• Give students practical experience of investigating data using statistical software.
• Equip students with the tools and techniques to be able to independently conduct an appropriate statistical analysis using R and provide a systematic report within the range of topics covered.

## Learning outcomes

 Attributes Developed 001 Students will demonstrate systematic understanding of key aspects of some selected topics within modern statistics. KC 002 Students will demonstrate the capability to use established approaches appropriately and accurately to analyse and solve problems in modern statistical modelling and statistical methods. KCPT 003 Students will be able to apply key aspects of selected topics in statistics in well-defined contexts, showing judgement in the selection and application of tools and techniques. KCP 004 Students will show judgement in the application of R and in the interpretation of R output. KCPT 005 Students will be able to analyse experimental data and interpret and write up the results in a way comprehensible to a layman. KCPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A comprehensive treatment of principles and methods underlying a selection of statistical topics.

• Experience in problem solving for the cognitive skills.

• Practical experience in statistical analysis and reporting.

The learning and teaching methods include:

• Three one-hour lectures per week for eleven weeks, with typeset notes to complement the lectures. The lectures provide a structured learning environment with opportunities for students to ask questions and to practice methods taught.

• One one-hour computer lab session per week for 9 weeks. Students will gain experience in using R to analyse data from experimental designs.

• Assessed coursework to give students practical experience of implementing techniques covered in lectures and lab sessions in an extended piece of work.

• There are two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.

Lectures may be recorded. Lecture recordings are intended to give students the opportunity to review parts of the session that they might not have understood fully and should not be seen as an alternative to attendance at lectures.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MATM056

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourceness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:

Digital Capabilities: The computer lab sessions and assessed coursework are specifically designed to help students cultivate digital data manipulation, modelling and analysis skills using the statistical software R.

Employability: The statistical techniques covered enable students to navigate complex data scenarios, enhancing adaptability in diverse professional settings.

Global and Cultural Capabilities: Student engagement in discussions during lectures and in computer lab sessions naturally cultivates the sharing of the different cultures that the students originate from.

Resourcefulness and Resilience: The statistical analysis skills developed through MATM056 enhance resilience as students problem-solving, model fitting, and data analysis skills develop. Their statistical expertise leads to resourcefulness, with the students able to appropriately apply statistical methods to problems of a variety of types.

Sustainability: Students equipped with statistical knowledge and skills can play a pivotal role in implementing and optimising sustainable solutions across various sectors, fostering a more environmentally resilient future.

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics MMath 2 Compulsory A weighted aggregate mark of 50% is required to pass the module
Mathematics MMath 2 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics MSc 2 Optional A weighted aggregate mark of 50% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.