## MA321-7-SU-CO:Applied Statistics

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Summer
Postgraduate: Level 7
Current
Tuesday 22 April 2025
Friday 27 June 2025
15
23 May 2024

Requisites for this module
(none)
(none)
(none)
(none)

(none)

## Key module for

MSC G304JP Data Science with Professional Placement,
MSC G304JS Data Science

## Module description

This module covers three application areas of statistics: multivariate methods, demography and epidemiology and sampling.

## Module aims

The aim of this module is:

• To foster statistical thinking and create data scientists that have both theoretic knowledge and application skills.

## Module learning outcomes

By the end of this module, students will be expected to be able to:

1. Understand and to apply multivariate methods.

2. Assess the results of discriminant analysis, principal components, cluster analysis and multivariate analysis of variance.

3. Understand and to apply demographical and epidemiological methods.

4. Understand and to use the notion of support vector machines, with applications to classification.

5. Understand and to apply sampling methods.

## Module information

Indicative syllabus

• Multivariate methods

Vectors of expected values. Covariance and correlation matrices. Discriminant analysis, choice between two populations, calculation of discriminant function, and probability of misclassification, test and training samples, leave-one-out and k-fold cross-validation, idea of extension to several populations. Principal components; definition, interpretation of calculated components, use in regression. Cluster analysis, similarity measures, single-link and other hierarchical methods, k-means. Informal approaches to checking for multivariate Normality. Tests and confidence regions for multivariate means.

• Demography and epidemiology

Population pyramids. Life tables. Standardised rates (e.g. mortality). Incidence and prevalence. Design and analysis of cohort (prospective) studies. Design and analysis of case-control (retrospective) studies. Confounding and interaction.
Matched case control design and analyses, using McNemar's test. Causation.
Relative risk. Odds ratio. Estimation and confidence intervals for 2x2 tables.
Mantel-Haenszel procedure. Sensitivity, specificity, ROC curves, positive predictive value, negative predictive value.

• Sampling

Census and sample survey design. Target and study populations, uses and limitations of non-probability sampling methods, sampling frames, sampling fraction.
Simple random sampling. Estimators of totals, means and proportions; bias. Estimated standard errors, confidence intervals and precision. Sampling fraction and finite population correction. Ratio and regression estimators. Stratified random sampling. Estimators of totals, means and proportions; bias. Estimated standard errors, confidence intervals and precision. Cost functions. Proportional and optimal allocations. Limitations of stratified sampling. One-stage cluster sampling. Estimators for totals, means and proportions with equal cluster sizes and with different cluster sizes. Estimated standard errors, confidence intervals and precision. Link with systematic sampling. Description of two-stage sampling and of multi-stage sampling. Limitations.

## Learning and teaching methods

Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

(none)

## Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Exam  Main exam: In-Person, Open Book (Restricted), 180 minutes during September (Reassessment Period)
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 180 minutes during January

### Exam format definitions

• Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
• In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
• In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
• In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Coursework Exam
20% 80%

### Reassessment

Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Danilo Petti, email: d.petti@essex.ac.uk.
Dr Danilo Petti; Dr Xu Chen
maths@essex.ac.uk

Availability
No
No
Yes

## External examiner

No external examiner information available for this module.
Resources
Available via Moodle
No lecture recording information available for this module.

Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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