@decidables/detectable-mathEquations for Calculating Signal Detection Theory in d′etectable

Helper functions for calculations related to Signal Detection Theory for d′etectable.

Usage

Install

yarn add @decidables/detectable-math

Use

import SDTMath from '@decidables/detectable-math';

A class providing static functions for calculating Signal Detection Theory equations

Contents

SDTMath

Single class exposing static functions for SDT calculations. Each function takes values for one or more variables and returns the value of another variable. The functions are named with a list of the input variables followed by a '2' followed by the output variable, in camelcase. For example, hM2Hr takes as input the number of hits, H, and the number of misses, M, and outputs the hit rate, HR

Variable names

• H = hits
• M = misses
• FA = false alarms
• CR = correct rejections
• HR = hit rate
• zHR = Z-transformed hit rate
• FAR = false alarm rate
• zFAR = Z-transformed false alarm rate
• ACC = accuracy
• PPV = positive predictive value
• FOMR = false omission rate (used FOMR to avoid keyword FOR!)
• d' = sensitivity (d' for equal variance, d_a for unequal variance)
• c = response bias (c for equal variance, c_a for unequal variance)
• s = standard deviation of signal distribution, with standard deviation of noise distribution = 1
• muN = mean of noise distribution
• muS = mean of signal distribution
• l = lambda, threshold location, with l = 0 indicating no response bias
• h = height of signal distribution

Function names

• Z = z-score
• Z^-1 = inverse z-score

Methods w/implemented equations

Many methods take an optional s for unequal variance. A different equation, marked with a * is used in these cases.

• hM2Hr(h, m)
  • HR = H / (H + M)
• faCr2Far(fa, cr)
  • FAR = FA / (FA + CR)
• hMFaCr2Acc(h, m, fa, cr)
  • ACC = (H + CR) / (H + M + FA + CR)
• hrFar2Acc(hr, far)
  • ACC = (HR + (1 - FAR)) / 2
• hFa2Ppv(h, fa)
  • PPV = H / (H + FA)
• mCr2Fomr(m, cr)
  • FOMR = M / (M + CR)
• hrFar2D(hr, far, s = 1)
  • d' = Z^-1(HR) - Z^-1(FAR)
  • * d' = (2 / (s^2 + 1))^(1/2) * (s * Z^-1(HR) - Z^-1(FAR))
• hrFar2C(hr, far, s = 1)
  • c = -(Z^-1(HR) + Z^-1(FAR))/2
  • * c = (2 / (s^2 + 1))^(1/2) * (s / s + 1) * -(Z^-1(HR) + Z^-1(FAR))
• dC2Hr(d, c, s = 1)
  • HR = Z(d'/2 - c)
  • * HR = Z(((s^2 + 1) / 2)^(1/2) * (d' / (s + 1) - c / s))
• dC2Far(d, c, s = 1)
  • FAR = Z(-d'/2 - c)
  • * FAR = Z(((s^2 + 1) / 2)^(1/2) * -(d' / (s + 1) + c))
• dFar2Hr(d, far, s = 1)
  • HR = Z(d' + Z^-1(FAR))
  • * HR = Z(((s^2 + 1) / 2)^(1/2) * d' + Z^-1(FAR) / s)
• cFar2Hr(c, far, s = 1)
  • HR = Z(-2c - Z^-1(FAR))
  • * HR = Z(-((s^2 + 1) / 2)^(1/2) * ((s + 1) / s) * c - Z^-1(FAR))
• d2MuN(d, s = 1)
  • muN = -d'/2
  • * muN = -((s^2 + 1) / 2)^(1/2) * (1 / (s + 1)) * d'
• muN2D(muN, s = 1)
  • d' = -2 * muN
  • * d' = -(2 / (s^2 + 1))^(1/2) * (s + 1) * muN
• d2MuS(d, s = 1)
  • muS = d'/2
  • * muS = ((s^2 + 1) / 2)^(1/2) * (s / (s + 1)) * d'
• muS2D(muS, s = 1)
  • d' = 2 * muS
  • * d' = (2 / (s^2 + 1))^(1/2) * ((s + 1) / s) * muS
• c2L(c, s = 1)
  • l = c
  • * l = ((s^2 + 1) / 2)^(1/2) * c
• l2C(l, s = 1)
  • c = l
  • * c = (2 / (s^2 + 1))^(1/2) * l
• s2H(s = 1)
  • h = 1 / (s * (2 * pi)^(1/2))
• h2S(h)
  • s = 1 / (h * (2 * pi)^(1/2))
• hr2Zhr(hr)
  • zHR = Z(HR)
• far2Zfar(far)
  • zFAR = Z(FAR)
• zhr2Hr(zhr)
  • HR = Z^-1(zHR)
• zfar2Far(zfar)
  • FAR = Z^-1(zFAR)

Development

Features/Bugs/Notes

• Unequal variance
  • Ambiguity about with what to hold constant when varying other parameters in the context of unequal variance
  • d' vs d_a, and c vs c_a
  • muN != muS != d'
  • lambda != c
  • distinction between parameter s and sigma

Package Scripts

• yarn lint
  • Lints markdown, scripts and styles
• yarn test
  • Runs all tests and reports coverage in test/coverage/
• yarn test:watch
  • Runs all tests in watch mode and reports coverage in test/coverage/
• yarn test:file <filename>
  • Runs tests for a single file and reports coverage in test/coverage/
• yarn build
  • Builds bundles from src/ to lib/

File Organization

• decidables-elements/
  • lib/ (Bundles created from src/ by build) [autogenerated]
  • src/ (Source files)
  • test/ (Testing files)
    • coverage/ (Code coverage results) [autogenerated]
  • CHANGELOG.md (Based on conventional commits) [autogenerated]
  • gulpfile.js (Tasks for gulp)
  • package.json (Package config for yarn and npm)
  • README.md (This file)
  • rollup-stats.html (Report on js bundle composition and size) [autogenerated]

License

The content of this project is licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC-BY-SA-4.0) and the source code of this project is licensed under GNU General Public License v3.0 or any later version (GPL-3.0-or-later).