Applied Statistics

The details
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Undergraduate: Level 6
Monday 13 January 2025
Friday 21 March 2025
23 May 2024


Requisites for this module



Key module for

BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC I1G3 Data Science and Analytics,
BSC I1GB Data Science and Analytics (Including Placement Year),
BSC I1GC Data Science and Analytics (Including Year Abroad),
BSC I1GF Data Science and Analytics (Including Foundation Year)

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 the module, students will be expected 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 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.


The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Assignment 1 (Initial Task)    25% 
Coursework   Assignment 2 (Group Project)    75% 
Exam  Main exam: In-Person, Open Book (Restricted), 180 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 180 minutes during September (Reassessment Period) 

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.

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Stella Hadjiantoni, email:
Dr Stella Hadjiantoni; Dr Oludare Ariyo



External examiner

Dr Yinghui Wei
University of Plymouth
Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Available via Moodle
Of 30 hours, 25 (83.3%) hours available to students:
5 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.


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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