Psychometric Function Slope
Evaluate a logistic psychometric response and local derivative with explicit guessing, lapse, midpoint and stimulus-unit scale.
Description
A logistic psychometric model links stimulus level to response probability.
A logistic psychometric model links stimulus level to response probability. Guess and lapse rates restrict its lower and upper asymptotes.
The tool returns responseProbability (response probability); probabilitySlopePerStimulus (probability slope per stimulus). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Psychometric Function Slope
Use Psychometric Function Slope when you already have stimulus, midpoint, logisticScale, guessRate, lapseRate and want responseProbability, probabilitySlopePerStimulus. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Psychometric Function Slope and understand its results
- Enter stimulus, midpoint, logisticScale, guessRate, lapseRate using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read responseProbability, probabilitySlopePerStimulus. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| stimulus | Stimulus | number | Required |
| midpoint | Midpoint | number | Required |
| logisticScale | Logistic scale | number | Required |
| guessRate | Guess rate | number | Required |
| lapseRate | Lapse rate | number | Required |
Use positive scale, guess and lapse in [0,1] with their sum below one. Evaluate a numerically stable logistic value and its local derivative.
L = logistic((stimulus−midpoint)/scale); probability = guess+(1−guess−lapse)L; slope = (1−guess−lapse)L(1−L)/scale The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"stimulus": 0,
"midpoint": 0,
"logisticScale": 2,
"guessRate": 0.5,
"lapseRate": 0.1
},
"output": {
"responseProbability": 0.7,
"probabilitySlopePerStimulus": 0.05
}
}Limitations and assumptions
Parameters are supplied rather than fitted. The local slope differs from a threshold estimate and has units of probability per stimulus unit.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Two-Point Discrimination: Interpolate a two-point tactile discrimination criterion from monotone trial-count psychometric data; out-of-range criteria remain unestimated. Grating Orientation Threshold: Estimate grating-orientation threshold by interpolation in log groove width at a supplied probability criterion; unlike linear two-point separation interpolation.
Methodological background: The psychometric function: fitting, sampling, and goodness of fit.1
References
-
The psychometric function: fitting, sampling, and goodness of fit — Wichmann and Hill; Perception & Psychophysics
Similar or alternative tools
- Two-Point Discrimination
Interpolate a two-point tactile discrimination criterion from monotone trial-count psychometric data; out-of-range criteria remain unestimated.
- Grating Orientation Threshold
Estimate grating-orientation threshold by interpolation in log groove width at a supplied probability criterion; unlike linear two-point separation interpolation.