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Applied statistics in Nanoscience

ECTS credits:

Course parameters:
Language: English
Level of course: PhD course
Time of year: January 2021
No. of contact hours/hours in total incl. preparation, assignment(s): 18/50
Capacity limits: 40 participants

Objectives of the course:
Graduate statistics course giving an introduction to statistics and data analysis applied to nanoscience. The course will cover error propagation, ChiSquare, fitting, Probability Distribution Functions, and simple hypothesis testing. Specific examples from nanoscience and research at iNANO will be given. Furthermore, the relevance of different types of analyses and hypotheses in different fields as well as common misuse and misconceptions will be discussed. The course will be taught in Python (V3.8), but MatLab® alternatives will also be provided.

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

  • Determine mean, standard deviation, uncertainty on mean, and correlations.
  • Understand the concept of a probability distribution.
  • Be able to understand and propagate uncertainties.
  • Understand the concept of fitting data with a model in terms of minimizing a ChiSquare.
  • Have a basic understanding of what a hypothesis test is.
  • Understand pitfalls and misuses of hypothesis and significance testing in the sciences.
  • Apply the above tools in a critical manner to research in nanoscience.

Compulsory programme:
The student should attend all 7 sessions (18 contact hours), and do all the corresponding 4 assignments. Work in groups are both allowed and in fact recommended.

Course contents:

Below is the preliminary course outline, subject to changes throughout the course. All details and exercises for Session 1-4 can be found on www.nbi.dk/~petersen/Teaching/IntroductionToStatistics2020.html

Session 1 Troels C. Petersen - Thursday the 7th of January, 10-17 (at iNANO, Aarhus University):

  • 10:15-12:00: Intro to course and statistics in general.
    Lecture on central limit theorem, mean, RMS, estimators, correlations, significant digits, and histograms.
  • 13:15-14:00: Lecture on error propagation.
  • 14:15-16:00: Exercise on error propagation (and all of the above).
  • 16:15-17:00: Discussion of exercise and introduction to next three sessions.

Session 2 Troels C. Petersen - Thursday the 14th of January, 10-12 (Zoom, recorded):

  • 10:15-11:00: Lecture on ChiSquare and fitting.
  • 11:15-12:00: Exercises on using and interpreting ChiSquare.

Session 3 Troels C. Petersen - Tuesday the 19th of January, 10-12 (Zoom, recorded):

  • 10:15-11:00: Lecture on Probability Distribution Functions (PDFs).
  • 11:15-12:00: Exercises on PDFs, specifically Binomial, Poisson, and Gaussian.

Session 4 Troels C. Petersen - Thursday the 21st of January, 10-12 (Zoom, recorded):

  • 10:15-11:00: Lecture introducing hypothesis testing.
  • 11:15-12:00: Exercises on simple hypothesis testing.

Session 5 Morten Foss: The date is to be decided, 2x45 min (at iNANO, Aarhus University):

  • Practical examples from iNANO research with actual data from both materials and biomedical science projects.

Session 6 Jesper W. Schneider: The date is to be decided, 2x45 min (at iNANO)

  • Lecture 1: Introduction: The use of “hypothesis testing” in the sciences, its origins and relevance to different fields.
  • Lecture 2: Null Hypothesis Significance Testing (NHST), its logic and assumptions.

Session 7 Jesper W. Schneider: The date is to be decided, 3x45 min (at iNANO)

  • Lecture 1: Misconceptions of NHST.
  • Lecture 2: Misuses of NHST.
  • Lecture 3: What to do, current debates about good practices.

Sessions 6 and 7 will be a mix of lectures, discussions and some minor excises. Suggested readings for the two lectures will follow in due time.

Following the 7 sessions, participants will be divided into study groups based on their scientific field to allow for discussion, application and implementation of the learned statistical tools in their individual PhD projects.

Basic mathematics (linear algebra and calculus) and basic programming (preferably in either Python or MatLab)

Name of lecturer[s]:

  • Associate professor Troels Christian Petersen, Niels Bohr Institute, University of Copenhagen,
  • Professor Jesper Wiborg Schneider, Department of Political Sciences, Aarhus University
  • Senior Researcher Morten Foss, Interdisciplinary Nanoscience Center (iNANO), Aarhus University


Type of course/teaching methods:
Combination of lectures (physical and online), exercises and study groups


Roger Barlow: Statistics: A guide to the use of statistics.

Philip R. Bevington: Data Reduction and Error Analysis.

Course homepage:


Course assessment:
Pass/fail based on the four exercises, which contains questions that should be answered by all students individually, though the students may work in groups.


Special comments on this course:
PhD students from the Nanoscience PhD programme will have preference. If there are more available seats when the registration closes, students will be prioritized based on first-come-first-served.


Register via this webpage: https://events.au.dk/appliedstatistics2021

If you have any questions, please contact Maria Kragelund, e-mail: maria@inano.au.dk

PhD students from the Nanoscience PhD programme will have preference. If there are more available seats when the registration closes, students will be prioritized based on first-come-first-served.

19825 / i43