Two-Point Discrimination

Interpolate a two-point tactile discrimination criterion from monotone trial-count psychometric data; out-of-range criteria remain unestimated.

Description

A two-point psychometric threshold is the separation at which observed correct-response probability reaches a chosen criterion.

A two-point psychometric threshold is the separation at which observed correct-response probability reaches a chosen criterion. Interpolation requires a measured bracket around that criterion.

The tool returns interpolatedThresholdMm (interpolated threshold mm); bracketingSeparationsMm (bracketing separations mm). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Two-Point Discrimination

Use Two-Point Discrimination when you already have separationsMm, correctCounts, trialCounts, criterionFraction and want interpolatedThresholdMm, bracketingSeparationsMm. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Two-Point Discrimination and understand its results

Enter separationsMm, correctCounts, trialCounts, criterionFraction 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 interpolatedThresholdMm, bracketingSeparationsMm. 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
separationsMm	Separations mm	list of number	Required
correctCounts	Correct counts	list of number	Required
trialCounts	Trial counts	list of number	Required
criterionFraction	Criterion fraction	number	Required

Form response fractions from integer counts, require nondecreasing rates and increasing nonnegative separations, and linearly interpolate the first qualifying bracket.

threshold = lowSeparation + (high−low) × (criterion−lowRate)/(highRate−lowRate)

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "separationsMm": [
      1,
      2,
      3
    ],
    "correctCounts": [
      5,
      7,
      9
    ],
    "trialCounts": [
      10,
      10,
      10
    ],
    "criterionFraction": 0.75
  },
  "output": {
    "interpolatedThresholdMm": 2.25,
    "bracketingSeparationsMm": [
      2,
      3
    ]
  }
}

Limitations and assumptions

No extrapolation, psychometric fitting or uncertainty estimation is performed; a criterion already reached at the first level is rejected.

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

Grating Orientation Threshold: Estimate grating-orientation threshold by interpolation in log groove width at a supplied probability criterion; unlike linear two-point separation interpolation. Psychometric Function Slope: Evaluate a logistic psychometric response and local derivative with explicit guessing, lapse, midpoint and stimulus-unit scale.

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

Grating Orientation Threshold
Estimate grating-orientation threshold by interpolation in log groove width at a supplied probability criterion; unlike linear two-point separation interpolation.
Psychometric Function Slope
Evaluate a logistic psychometric response and local derivative with explicit guessing, lapse, midpoint and stimulus-unit scale.