Analysis of RT distributionswith R

Emil Ratko-DehnertWS 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 planned4

Literature

• This course is loosely based on...

– Trisha Van Zandt: Analysis of RT distributions

– John Verzani: simpleR –

Using R for introductory statistics

5

MOTIVATION FOR THE COURSE

6

RT

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

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

But...

• 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

RT

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 use10

RT

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 functions12

„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

Introduction to probability theory

Random variables and their characterization

Estimation Theory

Model testing

16

I

II

III

IV

INTRODUCTION TOPROBABILITY THEORY

17

I

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 evidence18

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

I

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

Mathematical Modelling

21„Reality“ Model space

I

AND NOW TO

22