Master Biomedical Engineering, M2 track Bioengineering and Innovation in Neuroscience

The whole statistics module is shared with the BioMat and BioMech tracks, as part of UE 3.2 "Research Methodology".
Parts I, II, III of the statistics module will be the subject of a 1h30 multiple-choice-questions test, followed by a 2h debriefing session. Part IV is the subject of a 3h+2h lecture, and of a R tutorial (4h computer session), which is relevant to UE 3.7-8 "Brain-computer interfaces : from modeling to engineering".

• Introduction (pdf)

• I. Probability space (pdf)
  Sample space and events
  The axioms of probability
  Conditional probability, independence and Bayes theorem
  Application to the evaluation of a diagnostic test
  

• II. Random variables (pdf)
  Definitions, descriptive statistics
  Discrete probability distributions
  Continuous probability distributions
  

• III. Point and interval estimation (pdf)
  Point estimation
  Interval estimation
  Examples drawn from publications
  

• IV. Statistical hypothesis testing (pdf)
  Decision and probabilities of error
  Comparing two samples
  P-value and type I error risk
  Chi-square tests
  One-way analysis of variance
  Summary of the tests
  Corrections for multiple testing
  

STATISTICAL TABLES

• Standard normal (jpg)
• Student (pdf)
• Pearson (pdf)
• Fisher (pdf)
• Poisson (pdf)

TUTORIAL WITH R

• Tutorial (pdf)
  
• R template (script)
  
• Data files : dataA.txt, dataB.txt, dataC.txt
  

THE R SOTFWARE FOR STATISTICAL COMPUTING

• Link to the R software
• Link to R Studio (choose the free version)
• R pour les débutants (E. Paradis)
• An Introduction to R (W. N. Venables & D. M. Smith)
• Practical Regression and Anova using R (J. J. Faraway)
• Useful R commands in English and in French

RECOMMENDED BOOKS

• In French, rather for engineers : G. Saporta (2011), Probabilités, analyse des données et Statistique, Editions TECHNIP.
• In English, rather for engineers : A. Hayter (2013), Probability and statistics for engineers and scientists, Brooks/Cole.
• Also in English, less technical with many exercises : R. B. Schinazi (2012), Probability with statistical applications, Birkhaüser.
  In case you may want to have look at these books before purchasing them, I have copies at my lab.

RECOMMENDED STATISTICS SITE

• Graziano & Raulin’s Statistical Ressources