How to use MATLAB to fit the ex-Gaussian and other probability functions to a distribution of response times
Bibliographic record
Abstract
This article discusses how to characterize response time (RT) frequency distributions in terms of probability functions and how to implement the necessary analysis tools using MATLAB.The first part of the paper discusses the general principles of maximum likelihood estimation.A detailed implementation that allows fitting the popular ex-Gaussian function is then presented followed by the results of a Monte Carlo study that shows the validity of the proposed approach.Although the main focus is the ex-Gaussian function, the general procedure described here can be used to estimate best fitting parameters of various probability functions.The proposed computational tools, written in MATLAB source code, are available through the Internet.In recent years there has been an upsurge of interest in the response times (RT) of cognitive processes.This can be attributed in part to the wide availability of computer programs that allow experiments to be conducted automatically and RT to be measured with millisecond precision.However, and perhaps more importantly, many researchers see RT as major constraints when testing models of cognitive processes.Although RT are now routinely measured and frequently reported, there is a lack of standard tools for characterizing RT distributions.The difficulty is that simple descriptive statistics usually do not provide an adequate characterization of the data, and a
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.016 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.048 | 0.027 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".