Signal Detection d Prime
Compute d′ from trial counts with an explicit Hautus loglinear half-count correction, preserving finite extreme-count estimates; assumes equal-variance signal detection.
Description
Signal-detection sensitivity separates hits from false alarms through normal quantiles.
Signal-detection sensitivity separates hits from false alarms through normal quantiles. A half-count adjustment keeps rates finite even at zero or perfect observed counts.
The tool returns correctedHitRate (corrected hit rate); correctedFalseAlarmRate (corrected false alarm rate); dPrime (d prime). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Signal Detection d Prime
Use Signal Detection d Prime when you already have hits, signalTrials, falseAlarms, noiseTrials and want correctedHitRate, correctedFalseAlarmRate, dPrime. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Signal Detection d Prime and understand its results
- Enter hits, signalTrials, falseAlarms, noiseTrials 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 correctedHitRate, correctedFalseAlarmRate, dPrime. 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 |
|---|---|---|---|
| hits | Hits | integer | Required |
| signalTrials | Signal trials | integer | Required |
| falseAlarms | False alarms | integer | Required |
| noiseTrials | Noise trials | integer | Required |
Apply the same correction to noise trials, then use an approximate inverse-normal function. Counts are integers bounded by positive trial totals.
hitRate = (hits+0.5)/(signalTrials+1); d′ = Φ⁻¹(hitRate)−Φ⁻¹(falseAlarmRate) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"hits": 8,
"signalTrials": 10,
"falseAlarms": 2,
"noiseTrials": 10
},
"output": {
"correctedHitRate": 0.7727272727272727,
"correctedFalseAlarmRate": 0.22727272727272727,
"dPrime": 1.4957171882410376
}
}Limitations and assumptions
This assumes the equal-variance normal signal-detection model. It returns sensitivity only, without confidence intervals or response-bias estimates.
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. Psychometric Function Slope: Evaluate a logistic psychometric response and local derivative with explicit guessing, lapse, midpoint and stimulus-unit scale.
Methodological background: Corrections for extreme proportions and their biasing effects on estimated values of d′.1
References
-
Corrections for extreme proportions and their biasing effects on estimated values of d′ — Hautus; Behavior Research Methods, Instruments, & Computers
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.
- Psychometric Function Slope
Evaluate a logistic psychometric response and local derivative with explicit guessing, lapse, midpoint and stimulus-unit scale.