Template:Confusion matrix terms/sandbox

Terminology and derivations
from a confusion matrix
condition positive (P) the number of real positive cases in the data condition negative (N) the number of real negative cases in the data true positive (TP) eqv. with hit true negative (TN) eqv. with correct rejection false positive (FP) eqv. with false alarm, type I error or underestimation false negative (FN) eqv. with miss, type II error or overestimation sensitivity, recall, hit rate, or true positive rate (TPR) $\mathrm {TPR} ={\frac {\mathrm {TP} }{\mathrm {P} }}={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN} }}=1-\mathrm {FNR}$ specificity, selectivity or true negative rate (TNR) $\mathrm {TNR} ={\frac {\mathrm {TN} }{\mathrm {N} }}={\frac {\mathrm {TN} }{\mathrm {TN} +\mathrm {FP} }}=1-\mathrm {FPR}$ precision or positive predictive value (PPV) $\mathrm {PPV} ={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FP} }}=1-\mathrm {FDR}$ negative predictive value (NPV) $\mathrm {NPV} ={\frac {\mathrm {TN} }{\mathrm {TN} +\mathrm {FN} }}=1-\mathrm {FOR}$ miss rate or false negative rate (FNR) $\mathrm {FNR} ={\frac {\mathrm {FN} }{\mathrm {P} }}={\frac {\mathrm {FN} }{\mathrm {FN} +\mathrm {TP} }}=1-\mathrm {TPR}$ fall-out or false positive rate (FPR) $\mathrm {FPR} ={\frac {\mathrm {FP} }{\mathrm {N} }}={\frac {\mathrm {FP} }{\mathrm {FP} +\mathrm {TN} }}=1-\mathrm {TNR}$ false discovery rate (FDR) $\mathrm {FDR} ={\frac {\mathrm {FP} }{\mathrm {FP} +\mathrm {TP} }}=1-\mathrm {PPV}$ false omission rate (FOR) $\mathrm {FOR} ={\frac {\mathrm {FN} }{\mathrm {FN} +\mathrm {TN} }}=1-\mathrm {NPV}$ prevalence threshold (PT) ${\begin{aligned}\mathrm {PT} &={\frac {{\sqrt {\mathrm {TPR} (-\mathrm {TNR} +1)}}+\mathrm {TNR} -1}{(\mathrm {TPR} +\mathrm {TNR} -1)}}\\&={\frac {\sqrt {\mathrm {FPR} }}{{\sqrt {\mathrm {TPR} }}+{\sqrt {\mathrm {FPR} }}}}\end{aligned}}$ threat score (TS) or critical success index (CSI) $\mathrm {TS} ={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN} +\mathrm {FP} }}$ accuracy (ACC) ${\begin{aligned}\mathrm {ACC} &={\frac {\mathrm {TP} +\mathrm {TN} }{\mathrm {P} +\mathrm {N} }}\\&={\frac {\mathrm {TP} +\mathrm {TN} }{\mathrm {TP} +\mathrm {TN} +\mathrm {FP} +\mathrm {FN} }}\end{aligned}}$ balanced accuracy (BA) $\mathrm {BA} ={\frac {TPR+TNR}{2}}$ F1 score is the harmonic mean of precision and sensitivity ${\begin{aligned}\mathrm {F} _{1}&=2\times {\frac {\mathrm {PPV} \times \mathrm {TPR} }{\mathrm {PPV} +\mathrm {TPR} }}\\&={\frac {2\mathrm {TP} }{2\mathrm {TP} +\mathrm {FP} +\mathrm {FN} }}\end{aligned}}$ Matthews correlation coefficient (MCC) $\mathrm {MCC} ={\frac {\mathrm {TP} \times \mathrm {TN} -\mathrm {FP} \times \mathrm {FN} }{\sqrt {\begin{aligned}&(\mathrm {TP} +\mathrm {FP} )\times (\mathrm {TP} +\mathrm {FN} )\\\times &(\mathrm {TN} +\mathrm {FP} )\times (\mathrm {TN} +\mathrm {FN} )\end{aligned}}}}$ Fowlkes–Mallows index (FM) ${\begin{aligned}\mathrm {FM} &={\sqrt {{\frac {TP}{TP+FP}}\times {\frac {TP}{TP+FN}}}}\\&={\sqrt {PPV\times TPR}}\end{aligned}}$ informedness or bookmaker informedness (BM) $\mathrm {BM} =\mathrm {TPR} +\mathrm {TNR} -1$ markedness (MK) or deltaP (Δp) $\mathrm {MK} =\mathrm {PPV} +\mathrm {NPV} -1$ Sources: Fawcett (2006),^[1] Piryonesi and El-Diraby (2020),^[2] Powers (2011),^[3] Ting (2011),^[4] CAWCR,^[5] D. Chicco & G. Jurman (2020, 2021),^[6]^[7] Tharwat (2018).^[8]