1. Analysis of RT distributions with R Emil Ratko-Dehnert WS 2010/ 2011

2. About meme Studied Mathematics (LMU) – „Kalman Filter, State-space models and EM-algorithm“ Dr. candidate under Prof. Müller, Dr. Zehetleitner Research Interest: – Visual attention and memory – Formal modelling and systems theory – Philosophy of mind 2

3. About the students Your name and origin? Your educational background? Your research interests/ experience? Any statistical/ programming skills? What are your expectations about the course? 3

4. Concept of the course Where:CIP-Pool 001, Martiusstr. 4 When:Tuesdays, 0800 – 1000 Introduction to probability theory, statistics with focus on instruments for RT distribution analysis Part theory, part programming (in R) Tailored to the students state of knowledge and speed Follow-up course next semester is planned 4

5. Literature This course is loosely based on... – Trisha Van Zandt: Analysis of RT distributionsAnalysis of RT distributions – John Verzani: simpleR – Using R for introductory statisticsUsing R for introductory statistics 5

6. MOTIVATION FOR THE COURSE 6 RT

7. Why use response times (RT)? measured easily and (in principle) with high precision are ratio-scaled, thus a large amount of statistical/ mathematical tools can be applied 7 RT

8. Response times in research RTs are of paramount importance for empirical investigations in biological, social and clinical psychology with over 29.000 abstracts in PsychInfo database 8 RT

9. But... Although RTs have been used for over a century, still basic issues arise – NP H 0 testing are routinely applied to RTs even though normality and independence are violated – analysis at the level of means most often too conservative, uninformative, concealing... 9 RT

10. Recently... Publications with in-depth investigation of RT distributions were issued – Ulrich 2007, Ratcliff 2006, Maris 2003, Colonius 2001,... Why not earlier? – Mathematical theories are not very accessible for non- mathematicians – Implementation with current statistical software is generally not easy to use 10 RT

11. GNU R Project R was created by Ross Ihaka and Robert Gentleman at the University of Auckland (NZ) R has become a de facto standard among statisticians for the development of statistical software and is widely used for statistical software development and data analysis. 11

12. Advantages of R R is free - R is open-source and runs on UNIX, Windows and Mac R has an excellent built-in help system R has excellent graphing capabilities R has a powerful, easy to learn syntax with many built-in statistical functions R is highly extensible with user-written functions 12

13. „Downsides“ of R R is a computer programming language, so users must learn to appreciate syntax issues etc. It has a limited graphical interface There is no commercial support 13

14. Useful links for R Book of the course: – http://wiener.math.csi.cuny.edu/UsingR/index.html/ http://wiener.math.csi.cuny.edu/UsingR/index.html/ – http://mirrors.devlib.org/cran/doc/contrib/Verzani-SimpleR.pdf http://mirrors.devlib.org/cran/doc/contrib/Verzani-SimpleR.pdf Manuals: – http://cran.r-project.org/doc/manuals/R-intro.html http://cran.r-project.org/doc/manuals/R-intro.html – http://www.statmethods.net/index.html http://www.statmethods.net/index.html – http://www.cyclismo.org/tutorial/R/ http://www.cyclismo.org/tutorial/R/ – http://math.illinoisstate.edu/dhkim/Rstuff/Rtutor.html http://math.illinoisstate.edu/dhkim/Rstuff/Rtutor.html 14

15. Links for packages http://cran.r-project.org/web/views/ http://cran.r-project.org/web/packages/index.html http://crantastic.org/ 15

16. Course roadmap Introduction to probability theory Random variables and their characterization Estimation Theory Model testing 16 I II III IV

17. INTRODUCTION TO PROBABILITY THEORY 17 I

18. Interpretations of probability Laplacian Notion – „events of interest“ / „all events“ Frequentistic Notion – Throwing a dice 1000 times  „real“ probability Subjective probabilities/ Bayesian approach – How likely would you estimate the occurence of e.g. being struck by a lightning? – Updating estimation after observing evidence 18 I

19. Randomness in mathematics Probability theory – Axiomatic system of Kolmogorov; measure theory – Stochastic processes (e.g. Wiener process) Mathematical statistics – Test and estimation theory; modelling 19 I

20. Randomness in the brain? Neural level – Neurons are non-linear system and have intrinsic noise Stimulus level – BU: Ambiguous sensory evidence may lead to conflict/ deliberation Subject level – TD: expectations, intertrial and learing effects alter the per se deterministic decision loop Measurement device – May have subpar precision or sampling rate 20 I

21. Mathematical Modelling 21 „Reality“Model space I

22. AND NOW TO 22