# Applied Statistics: From Data to Results

### Course content

The course will give the student an introduction to and a basic knowledge of statistics and data analysis. The focus will be on the application of statistics and thus proofs are omitted, while examples and use of computers take their place. For this reason, programming plays a central role and is an essential requirement (see below).

The course will cover the following subjects:

• Introduction to statistics.
• Distributions - Probability Density Functions.
• Error propagation.
• Correlations.
• Monte Carlo - using simulation.
• Statistical tests.
• Parameter estimation - philosophy and methods of fitting data.
• Chi-Square and Maximum Likelihood fits.
• Simulation and planning of an experiment.
• Multidimensional data and Fisher Discriminant.
• Introduction to Machine Learning.
• The power and limit of statistics.
Education

MSc Programme in Climate Change

MSc Programme in Environmental Science
MSc Programme in Nanoscience
MSc Programme in Physics
MSc Programme in Physics with a minor subject

Learning outcome

Skills
The student should in the course obtain the following skills:

• Determining mean, width, uncertainty on mean, and correlations.
• Understanding how to use probability distribution functions.
• Be able to calculate, propagate and interpret uncertainties.
• Be capable of fitting data sets and obtain parameter values with uncertainties.
• Know the use of simulation in planning experiments and data analysis.
• Select and apply appropriate statistical tests.

Knowledge
The student will obtain knowledge about statistical concepts and procedures, more specifically:

• Binomial, Poisson and Gaussian distributions and origins.
• Error propagation formula – use and applicability.
• ChiSquare as a measure of Goodness-of-fit.
• Calculation and interpretation of p-values.
• Determination and treatment of potential outliers in data.
• The applicability of Machine Learning.

Competences
This course will provide the students with an understanding of statistical methods and knowledge of data analysis, which enables them to analyse data from essentially ALL fields of science. The students should be capable of handling uncertainties, fitting data, applying hypothesis tests and extracting conclusions from data, and thus produce statistically sound scientific work.

Lectures, exercises by computers, and discussion/projects.

See Absalon for final course material. The following is an example of expected course literature.

Primary literature: Statistics - A Guide to the Use of Statistical Methods in the Physical Sciences, Roger Barlow.
Additional literatur: Statistical Data Analysis, Glen Cowan. Data Reduction and Error Analysis, Philip R. Bevington. Statistical Methods in Experimental Physics.

Programming is an essential tool and is therefore necessary for the course (we will use Python). The student should be familiar with different types of variables, loops, if-sentences, functions, and the general line of thinking in programming. Elementary mathematics (calculus, linear algebra, and combinatorics) is also required.

Academic qualifications equivalent to a BSc degree is recommended (in particular for non-physics students), but not required.

It is expected that the student brings a laptop.

There will be an introduction the week before the course begins. You will be informed about time and place later (on the course webpage and by Email).

Written
Oral
Individual
Collective
Continuous feedback during the course of the semester
Peer feedback (Students give each other feedback)
ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Written assignment, 36 hours
Type of assessment details
The final grade is given based on the continuous evaluation as well as on the take-home exam with the following weight;
20% from a project, 20% from a problem set, and 60% from a 36 hours take-home exam.
Aid
All aids allowed
Marking scale
Censorship form
No external censorship
several internal examiners
Re-exam

The exam form is identical to the regular exam; the project and/or problem set that were approved during the course can be re-used. The remaining project and/or problem set should be approved 2 weeks before the re-exam.

##### Criteria for exam assessment

Seelearning outcome.

Single subject courses (day)

• Category
• Hours
• Lectures
• 56
• Preparation
• 98
• Theory exercises
• 28
• Exam
• 24
• English
• 206

### Kursusinformation

Language
English
Course number
NFYK13011U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 2
Schedulegroup
B
Capacity
No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Studyboard
Study Board of Physics, Chemistry and Nanoscience
##### Contracting department
• The Niels Bohr Institute
##### Contracting faculty
• Faculty of Science
##### Course Coordinator
• Troels Christian Petersen   (8-756a796a77786a734573676e33707a336970)
Saved on the 15-02-2024

### Are you BA- or KA-student?

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Courseinformation of students