Course Basic Statistical Analysis

The course Basic Statistical Analysis is offered by the Graduate School of Natural Sciences/GSNS and Graduate School of Technical Sciences/GSTS, Aarhus University, fall 2025.

Name of course: Basic Statistical Analysis

ECTS credits: 4.0 ECTS

Course parameters: No. of contact hours/hours in total incl. preparation, assignment(s) or the like: four weeks with 6h lecturing per week distributed in two days and 2h per week of consultation. Additionally, the participants should write a report on the assignments involving three relevant full statistical analyses proposed.

Objectives of the course:
The aim of the course is to introduce the PhD student to basic notions of statistical analysis and give an idea of a typical statistical modelling process.

Learning outcomes and competences:
At the end of the course, the student should be able to:

1) Identify the key assumptions and critically evaluate some chosen (simple) statistical models

2) Perform basic inference and conclude from those models under supervision

3) Present (orally) and report (written) the results of those analyses.

Course contents:
The course aims to introduce the PhD student to basic notions of statistical analyses and give an idea of a typical statistical modelling process. The course does not intend to systematically cover key statistical models or to supply a large applicable statistical toolbox in the research area of the PhD student. Instead, the idea is to build a solid basis on general statistical principles, allowing the PhD student to understand and apply more complex statistical models used in their research area or other statistical courses. The examples used are based on relatively simple real cases occurring in life and environmental sciences strategically chosen for pedagogical purposes.

The course starts with a quick review of basic probability principles, including definition and basic properties of probability, probability independence, expectation, variance and covariance, the law of large numbers and the central limit theorem. The first statistical model (a simple binomial model for binary data) is presented and the notions of statistical parametrisation, parameter estimation, hypothesis test and confidence intervals are introduced using those simple models as the first examples. Two other families of statistical models are then presented: Poisson models for counting data and Normal models (t-test, F-test, regression, analysis of variance and analysis of covariance) for continuous data. The basic notions of estimation and hypotheses tests are revisited and applied in examples involving the three families of statistical models already introduced. Finally, two techniques of model control are presented: residual analysis and model embedding in larger models.

The course ends with a supervised analysis of some key examples involving some of the techniques studied in the course where the PhD student is supposed to: 1) perform a statistical analysis of a simple practical problem, 2) write a short report on that analysis and 3) report and discuss this analysis orally. 

Prerequisites:
It is not presupposed that the PhD student masters statistic techniques beforehand. For those who have some experience in the use of statistical tools the course could be used as an opportunity to review and re-think basic concepts of statistics from a different perspective.

The course will use the software R as a tool, but it is NOT a course on R. It will be assumed that the PhD students have the software R installed on their computers and that they know the basic notions of R programming. This includes knowing to: read and write data in R, perform basic operations with variables and vectors, make simple tabulations, use simple functions, use repeated and conditional calculations and draw simple graphs. These skills in R can be obtained in the course “Introduction to R” (link).

Name of lecturer and course responsible: Rodrigo Labouriau

Type of course/teaching methods:
Lectures alternated with supervised exercise, self-study including the elaboration of a report on three relevant full statistical analyses proposed at the beginning of the course. The course responsible will offer the participants to give a feedback to a draft of the reports, provided the draft is delivered before a deadline established at the beginning of the course by the course responsible.

Literature and course material:
Lecture notes and a collection of tutorials and demonstration programs (in R) written by R. Labouriau (distributed during the course, for internal use).

Course homepage:
A general description of the course, further details and software can be found at https://tildeweb.au.dk/au33031/Courses/PhDBasicStatisticalAnalysis

Course assessment:
Attendance to 80% of the lectures is a necessary condition to participation in the oral examination.

In the last part of the course, there will be a final project (three datasets that should be analysed). The final examination constitutes a written report on the final project and an oral examination based on the report. Using the oral examination and the written report, it will be evaluated whether the PhD student has passed the course.

Provider:
Applied Statistics Laboratory (aStatLab) at the Department of Mathematics, Aarhus University in collaboration with the GSNS. Course responsible: Rodrigo Labouriau (aStatLab, MATH AU).

Time:
Weeks 44-47 Tuesdays and Wednesdays from 9:15 to 12:00, oral exam 10th and 11th December 2025.

Place:
Department of Mathematics if held physically otherwise online. If held physically the course will not be simultaneously transmitted online.

No show fee:
Course participants on our transferable skills courses, who do not show up at the course or cancel their course participation after the course cancellation deadline (without providing a doctor’s note), may have to pay a no-show fee, unless someone from the waiting list is able to take part in the course instead.

The no-show fee is DKK 1,200 (the price of one ECTS). The no-show fee has been introduced due to many late cancellations, thus preventing people from the waiting lists to have a seat at the courses.

Registration: 

• Participation in the course is without cost for PhD students from Aarhus University

Due to an Agreement between Danish Universities coming into force as of 1 January 2011, participants from other universities than Aarhus University will have to pay DKK 1,200 per ECTS. In principle this also applies to external parties, but exemption can be granted under specific circumstances.

Please be aware that your registration for the course not necessarily equals your admission for the course. You will receive an e-mail after the registration deadline regarding whether you are admitted for the course or if you are registered on the waiting list. Please note that seats are allocated on a first-come-first-served basis.

Course dates:

• 28 October 2025 09:15 - 12:00
• 29 October 2025 09:15 - 12:00
• 04 November 2025 09:15 - 12:00
• 05 November 2025 09:15 - 12:00
• 11 November 2025 09:15 - 12:00
• 12 November 2025 09:15 - 12:00
• 18 November 2025 09:15 - 12:00
• 19 November 2025 09:15 - 12:00
• 10 December 2025
• 11 December 2025