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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
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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?
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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
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Literature
• This course is loosely based on...
– Trisha Van Zandt: Analysis of RT distributions
– John Verzani: simpleR – Using R for
introductory statistics
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RT
MOTIVATION FOR THE COURSE
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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
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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
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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 ...
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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
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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.
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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
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„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
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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
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Links for packages
• http://cran.r-project.org/web/views/
• http://cran.r-project.org/web/packages/index.html
• http://crantastic.org/
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Course roadmap
I
Introduction to probability theory
II
Random variables and their characterization
III
Estimation Theory
IV
Model testing
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I
INTRODUCTION TO
PROBABILITY THEORY
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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
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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
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Randomness in the brain?
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• 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
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Mathematical Modelling
„Reality“
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Model space
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AND NOW TO
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