ST514: Multivariate Statistical Analysis

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N360001102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor

STADS ID (UVA): N360001101
ECTS value: 5

Date of Approval: 12-10-2022

Duration: 1 semester

Version: Approved - active


The course is read together with DS805 Multivariate statistical analysis.

Entry requirements

The course cannot be followed by students who have passed ST811 or DS805.

Academic preconditions

Students taking the course are expected to:
  • Have skills in statistics corresponding to ST520 Applied statistics or ST521 Mathematical statistics, and calculus corresponding to one of the calculus courses on the first year on the study programmes at the Faculty of Science, SDU.
  • Be able to use the statistical software R.
  • A full first year in Science or an equivalent study programme.

Course introduction

The aim of the course is to enable the student to work systematically with data sets with several variables, which is important in regard to performing statistical analyses in a broad range of research areas, such as biology and epidemiology.

The course builds on the knowledge acquired in the courses such as ST520 Applied statistics or ST521 Mathematical statistics, and the calculus course in the respective study programme, and gives an academic basis for studying topics such as biometry, that are part of the degree, as well as bachelor or master projects where multivariate methods are employed.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give the competence to evaluate and choose between different methods for the analysis of multivariate data sets.
  • Give skills to perform analyses of multivariate data sets using the statistical software R.
  • Give knowledge and understanding of the fundamental ideas and methods for analyzing measurements on several variables.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

  • Reproduce key theoretical results concerning elementary operations on random variables and random vectors.
  • Work with the concepts and models, both in scalar and matrix/vector representation.
  • Understand and identify problems that can be solved using multivariate techniques.
  • Perform a practical data analysis with the techniques from the course.
  • Perform programming relevant to the content of the course in the statistical package used in the course.
  • Identify and interpret relevant information in the output of the statistical package used in the course.
  • Summarize the results of an analysis in a statistical report.


The following main topics are contained in the course:
  • random vectors
  • the multivariate normal distribution
  • inference about a mean vector
  • comparison of several mean vectors
  • principal component analysis
  • discriminant analysis and classification


See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)




Written exam




Second examiner: Internal


7-point grading scale


Student Identification Card


Normally, the same as teaching language


Written exam - 2½ hours

Examination aids

Written exam:  All common aids are allowed e.g. books, notes, computer programmes which do not use internet etc. 

Internet is not allowed during the exam. However, you may visit system DE-Digital Exam when answering the multiple-choice questions. If you wish to use course materials from itslearning, you must download the materials to your computer the day before the exam. During the exam itslearning is not allowed.  

ECTS value


Indicative number of lessons

48 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.
These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

  • Intro phase (lectures) - 24 hours
  • Training phase: 24 hours,

In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours aor the study phase hours.

Educational activities

  • Work on problems not covered in the training phase.
  • Discussion of the concepts and terms of the topic.

Teacher responsible

Name E-mail Department
Jing Qin Data Science


Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration


Offered in


Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.