# Applied Statistics: From Data to Results

### Course content

The course will give the student an introduction to and a basic knowledge on statistics. The focus will be on application and thus proofs are omitted, while examples and use of computers take their place.

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.
• The power and limit of statistics. The frontier.
Education

MSc Programme in Physics
MSc Programme in Nanoscience
MSc Programme in Environmental Science
MSc Programme in Physics w. minor subject

Learning outcome

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

•   Determining mean, width, uncertainty on mean and correlations.
•   Understading how to use probability distribution functions.
•   Be able to calculate, propagate and interprete uncertainties.
•   Be capable of fitting data sets and obtain parameter values.
•   Know the use of simulation in planing experiments and data analysis.

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

•   Binomial, Poisson and Gaussian distributions and origins.
•   Error propagation formula and how to apply it.
•   ChiSquare as a measure of Goodness-of-fit.
•   Calculation and interpretation of ChiSquare probability.

Competences
This course will provide the students with an understanding of statistical methods and knowledge of data analysis, which enables them to analyse data in 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 with interface to CERN’s ROOT software, both free and working on all platforms). 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 needed.

Course webpage: www.nbi.dk/​~petersen/​Teaching/​AppliedStatistics2015.html
The course webpage is administered by: Troels C. Petersen (petersen@nbi.dk)

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 above course webpage).

ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Written assignment, 28 hours
The final grade is normally given based on the continuous evaluation as well as on the take-home exam with the following weight;
25% from projects, 15% from problem sets, and 60% from 28 hours take-home exam.
It is possible to some extent to arrange a different weight in individual cases in agreement between the student and course responsible, if this can be justified.
Aid
All aids allowed
Marking scale
Censorship form
No external censorship
More internal examiners
##### Criteria for exam assessment

Seelearning  outcome.

Single subject courses (day)

• Category
• Hours
• Lectures
• 56
• Theory exercises
• 28
• Preparation
• 122
• English
• 206