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Advanced Statistics


Admission requirements

Advice: Knowledge of:
Basic statistics: t-test, ANOVA and linear regression.
Basic probability theory: Normal, Binomial and Poisson distributions.

In order to test your statistical knowledge, a test, with accompanying video lectures, will be made available. If the result of the test is unsatisfactory, we advise you to follow the introductory course Basic Statistics for Master students first; please contact the study advisor for further details.

N.B. For the combination master programs (Business Studies, Education and Science Communication) Advanced Statistics is not compulsory. These students can also choose to take Basic Statistics for Master students.


This course discusses probabilistic theory, experimental design, statistical analysis and statistical modelling in the context of research in the life sciences. Leading concepts in statistics are introduced from the perspective of empirical inquiry and study design. Basic statistics are quickly reviewed and more advanced statistical methods are introduced to deal with data that cannot be analyzed using the standard classical methods:

  • Mixed models are introduced to deal with data that are not independent, like repeated and nested designs.

  • Generalized models to deal with deviations from normality and heteroscedasticity.

  • Machine learning methodologies are discussed to deal with high dimensional data allowing for both prediction and conformational statistics.

  • Some of the statistics discussed will be evaluated in the context of bioinformatics.

  • In a short detour, we explain important statistical perspectives like the Bayesian view on statistics, information entropy, GAM’s and statistical network theory. These topics might vary depending on interests.

  • All statistical examples and assignments are done in R and Rstudio, including simulation of data based on your own experimental designs.

Course Objectives

After completion of the course, students are able to:  
1. Apply methods discussed in GRS/Basic Statistics with extensions to generalized and mixed-model methods, supervised & unsupervised learning methodologies. 
2. Identify key data properties of complex study designs from which the student can infer the correct statistical methods to be used and analytic strategies to be followed.
3. Identify statistical pitfalls and fallacies that can occur in statistical analysis. 
4. Motivate the use of statistics based on the fundamental principles of a disbalance between the degree of freedom of the model and the data, infer the expected distribution of the residuals and apply this knowledge to the interpretation of statistical results.
5. Deduce and interpret generic mathematical formulas of important statistical concepts. 
6. Reason why a particular test statistic takes on certain values under the null hypothesis. 
7. Combine statistical data from different literature sources, combine them in a meta-analysis and relate the underlying methodology to mixed models. 
8. Convert complex data to tidy format, create subsets and detailed data summaries using a scientific programming language (e.g., R). 
9. Simulate and analyze complex data in a scientific programming language (e.g., R). 
10. Produce publication-grade figures in a scientific programming language (e.g., R), using basic and advanced plotting routines. 


You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

Mode of instruction

Lectures, tutorials and assignments. Some lectures must be prepared by the students with the use of web lectures and tutorials.

Assessment method

Written exam and a group assignment.
A weight of 75 % for exam and 25% for the group assignment.

Reading list

Set of chapters from the Springer-link library will be published on Brightspace. These chapters can be downloaded for free.


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.


Coordinator: Dr. H.G.J. van Mil


A timetable will be communicated through Brightspace.