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Analysis of RT distributions with R Emil Ratko-Dehnert WS 2010/ 2011 About me • 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 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 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 Literature • This course is loosely based on... – Trisha Van Zandt: Analysis of RT distributions – John Verzani: simpleR – Using R for introductory statistics 5 RT MOTIVATION FOR THE COURSE 6 Why use response times (RT)? RT • measured easily and (in principle) with high precision • are ratio-scaled, thus a large amount of statistical/ mathematical tools can be applied 7 Response times in research RT • RTs are of paramount importance for empirical investigations in biological, social and clinical psychology with over 29.000 abstracts in PsychInfo database 8 But... RT • Although RTs have been used for over a century, still basic issues arise – NP H0 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 Recently ... RT • 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 nonmathematicians – Implementation with current statistical software is generally not easy to use 10 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 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 „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 Useful links for R • Book of the course: – http://wiener.math.csi.cuny.edu/UsingR/index.html/ – http://mirrors.devlib.org/cran/doc/contrib/Verzani-SimpleR.pdf • Manuals: – http://cran.r-project.org/doc/manuals/R-intro.html – http://www.statmethods.net/index.html – http://www.cyclismo.org/tutorial/R/ – http://math.illinoisstate.edu/dhkim/Rstuff/Rtutor.html 14 Links for packages • http://cran.r-project.org/web/views/ • http://cran.r-project.org/web/packages/index.html • http://crantastic.org/ 15 Course roadmap I Introduction to probability theory II Random variables and their characterization III Estimation Theory IV Model testing 16 I INTRODUCTION TO PROBABILITY THEORY 17 Interpretations of probability I • 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 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 Randomness in the brain? I • 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 Mathematical Modelling „Reality“ I Model space 21 AND NOW TO 22