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)

A test result that correctly indicates the presence of a condition or characteristic

true negative (TN)

A test result that correctly indicates the absence of a condition or characteristic

false positive (FP), Type I error

A test result which wrongly indicates that a particular condition or attribute is present

false negative (FN), Type II error

A test result which wrongly indicates that a particular condition or attribute is absent

sensitivity, recall, hit rate, or true positive rate (TPR)

${\displaystyle \mathrm {TPR} ={\frac {\mathrm {TP} }{\mathrm {P} }}={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN} }}=1-\mathrm {FNR} }$

specificity, selectivity or true negative rate (TNR)

${\displaystyle \mathrm {TNR} ={\frac {\mathrm {TN} }{\mathrm {N} }}={\frac {\mathrm {TN} }{\mathrm {TN} +\mathrm {FP} }}=1-\mathrm {FPR} }$

precision or positive predictive value (PPV)

${\displaystyle \mathrm {PPV} ={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FP} }}=1-\mathrm {FDR} }$

negative predictive value (NPV)

${\displaystyle \mathrm {NPV} ={\frac {\mathrm {TN} }{\mathrm {TN} +\mathrm {FN} }}=1-\mathrm {FOR} }$

miss rate or false negative rate (FNR)

${\displaystyle \mathrm {FNR} ={\frac {\mathrm {FN} }{\mathrm {P} }}={\frac {\mathrm {FN} }{\mathrm {FN} +\mathrm {TP} }}=1-\mathrm {TPR} }$

fall-out or false positive rate (FPR)

${\displaystyle \mathrm {FPR} ={\frac {\mathrm {FP} }{\mathrm {N} }}={\frac {\mathrm {FP} }{\mathrm {FP} +\mathrm {TN} }}=1-\mathrm {TNR} }$

false discovery rate (FDR)

${\displaystyle \mathrm {FDR} ={\frac {\mathrm {FP} }{\mathrm {FP} +\mathrm {TP} }}=1-\mathrm {PPV} }$

false omission rate (FOR)

${\displaystyle \mathrm {FOR} ={\frac {\mathrm {FN} }{\mathrm {FN} +\mathrm {TN} }}=1-\mathrm {NPV} }$

Positive likelihood ratio (LR+)

${\displaystyle \mathrm {LR+} ={\frac {\mathrm {TPR} }{\mathrm {FPR} }}}$

Negative likelihood ratio (LR-)

${\displaystyle \mathrm {LR-} ={\frac {\mathrm {FNR} }{\mathrm {TNR} }}}$

prevalence threshold (PT)

${\displaystyle \mathrm {PT} ={\frac {\sqrt {\mathrm {FPR} }}{{\sqrt {\mathrm {TPR} }}+{\sqrt {\mathrm {FPR} }}}}}$

threat score (TS) or critical success index (CSI)

${\displaystyle \mathrm {TS} ={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN} +\mathrm {FP} }}}$

Prevalence

${\displaystyle {\frac {\mathrm {P} }{\mathrm {P} +\mathrm {N} }}}$

accuracy (ACC)

${\displaystyle \mathrm {ACC} ={\frac {\mathrm {TP} +\mathrm {TN} }{\mathrm {P} +\mathrm {N} }}={\frac {\mathrm {TP} +\mathrm {TN} }{\mathrm {TP} +\mathrm {TN} +\mathrm {FP} +\mathrm {FN} }}}$

balanced accuracy (BA)

${\displaystyle \mathrm {BA} ={\frac {TPR+TNR}{2}}}$

F1 score

is the harmonic mean of precision and sensitivity: ${\displaystyle \mathrm {F} _{1}=2\times {\frac {\mathrm {PPV} \times \mathrm {TPR} }{\mathrm {PPV} +\mathrm {TPR} }}={\frac {2\mathrm {TP} }{2\mathrm {TP} +\mathrm {FP} +\mathrm {FN} }}}$

phi coefficient (φ or r_φ) or Matthews correlation coefficient (MCC)

${\displaystyle \mathrm {MCC} ={\frac {\mathrm {TP} \times \mathrm {TN} -\mathrm {FP} \times \mathrm {FN} }{\sqrt {(\mathrm {TP} +\mathrm {FP} )(\mathrm {TP} +\mathrm {FN} )(\mathrm {TN} +\mathrm {FP} )(\mathrm {TN} +\mathrm {FN} )}}}}$

Fowlkes–Mallows index (FM)

${\displaystyle \mathrm {FM} ={\sqrt {{\frac {TP}{TP+FP}}\times {\frac {TP}{TP+FN}}}}={\sqrt {PPV\times TPR}}}$

informedness or bookmaker informedness (BM)

${\displaystyle \mathrm {BM} =\mathrm {TPR} +\mathrm {TNR} -1}$

markedness (MK) or deltaP (Δp)

${\displaystyle \mathrm {MK} =\mathrm {PPV} +\mathrm {NPV} -1}$

Diagnostic odds ratio (DOR)

${\displaystyle \mathrm {DOR} ={\frac {\mathrm {LR+} }{\mathrm {LR-} }}}$

Sources: Fawcett (2006),[1] Piryonesi and El-Diraby (2020),[2] Powers (2011),[3] Ting (2011),[4] CAWCR,[5] D. Chicco & G. Jurman (2020, 2021, 2023),[6][7][8] Tharwat (2018).[9] Balayla (2020)[10]