Template:Confusion matrix terms

This template is currently being merged with Template:diagnostic testing diagram.
This template is being merged with another template, according to the specific instructions at Wikipedia:Templates for discussion/Holding cell, after which it will be redirected or deleted. The decision to merge this template was made following this discussion initiated on 6 April 2023 at Templates for discussion.
Note: Please review this template's instructions at Wikipedia:Templates for discussion/Holding cell before proceeding with any type of merging.

{| class="wikitable floatright" width=35% style="margin-left:0.5em; padding:0.25em; background:#f1f5fc; font-size:98%;"

|+ Terminology and derivations
from a confusion matrix |- style="vertical-align:top;" |

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): A test result which wrongly indicates that a particular condition or attribute is present
false negative (FN): A test result which wrongly indicates that a particular condition or attribute is absent

sensitivity, recall, hit rate, or true positive rate (TPR): $T P R = \frac{T P}{P} = \frac{T P}{T P + F N} = 1 - F N R$
specificity, selectivity or true negative rate (TNR): $T N R = \frac{T N}{N} = \frac{T N}{T N + F P} = 1 - F P R$
precision or positive predictive value (PPV): $P P V = \frac{T P}{T P + F P} = 1 - F D R$
negative predictive value (NPV): $N P V = \frac{T N}{T N + F N} = 1 - F O R$
miss rate or false negative rate (FNR): $F N R = \frac{F N}{P} = \frac{F N}{F N + T P} = 1 - T P R$
fall-out or false positive rate (FPR): $F P R = \frac{F P}{N} = \frac{F P}{F P + T N} = 1 - T N R$
false discovery rate (FDR): $F D R = \frac{F P}{F P + T P} = 1 - P P V$
false omission rate (FOR): $F O R = \frac{F N}{F N + T N} = 1 - N P V$
Positive likelihood ratio (LR+): $L R + = \frac{T P R}{F P R}$
Negative likelihood ratio (LR-): $L R - = \frac{F N R}{T N R}$
prevalence threshold (PT): $P T = \frac{\sqrt{F P R}}{\sqrt{T P R} + \sqrt{F P R}}$
threat score (TS) or critical success index (CSI): $T S = \frac{T P}{T P + F N + F P}$

Prevalence: $\frac{P}{P + N}$
accuracy (ACC): $A C C = \frac{T P + T N}{P + N} = \frac{T P + T N}{T P + T N + F P + F N}$
balanced accuracy (BA): $B A = \frac{T P R + T N R}{2}$
F1 score: is the harmonic mean of precision and sensitivity: $F_{1} = 2 \times \frac{P P V \times T P R}{P P V + T P R} = \frac{2 T P}{2 T P + F P + F N}$
phi coefficient (φ or r_φ) or Matthews correlation coefficient (MCC): $M C C = \frac{T P \times T N - F P \times F N}{\sqrt{(T P + F P) (T P + F N) (T N + F P) (T N + F N)}}$
Fowlkes–Mallows index (FM): $F M = \sqrt{\frac{T P}{T P + F P} \times \frac{T P}{T P + F N}} = \sqrt{P P V \times T P R}$
informedness or bookmaker informedness (BM): $B M = T P R + T N R - 1$
markedness (MK) or deltaP (Δp): $M K = P P V + N P V - 1$
Diagnostic odds ratio (DOR): $D O R = \frac{L R +}{L R -}$

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] |}

Template documentation

Editors can experiment in this template's sandbox (create | mirror) and testcases (create) pages.
Subpages of this template.

↑ Fawcett, Tom (2006). "An Introduction to ROC Analysis" (PDF). Pattern Recognition Letters. 27 (8): 861–874. doi:10.1016/j.patrec.2005.10.010.
↑ Piryonesi S. Madeh; El-Diraby Tamer E. (2020-03-01). "Data Analytics in Asset Management: Cost-Effective Prediction of the Pavement Condition Index". Journal of Infrastructure Systems. 26 (1): 04019036. doi:10.1061/(ASCE)IS.1943-555X.0000512.
↑ Powers, David M. W. (2011). "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation". Journal of Machine Learning Technologies. 2 (1): 37–63.
↑ Ting, Kai Ming (2011). Sammut, Claude; Webb, Geoffrey I., eds. Encyclopedia of machine learning. Springer. doi:10.1007/978-0-387-30164-8. ISBN 978-0-387-30164-8. Search this book on
↑ Brooks, Harold; Brown, Barb; Ebert, Beth; Ferro, Chris; Jolliffe, Ian; Koh, Tieh-Yong; Roebber, Paul; Stephenson, David (2015-01-26). "WWRP/WGNE Joint Working Group on Forecast Verification Research". Collaboration for Australian Weather and Climate Research. World Meteorological Organisation. Retrieved 2019-07-17.
↑ Chicco D.; Jurman G. (January 2020). "The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation". BMC Genomics. 21 (1): 6-1–6-13. doi:10.1186/s12864-019-6413-7. PMC 6941312 Check |pmc= value (help). PMID 31898477.
↑ Chicco D.; Toetsch N.; Jurman G. (February 2021). "The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation". BioData Mining. 14 (13): 1-22. doi:10.1186/s13040-021-00244-z. PMC 7863449 Check |pmc= value (help). PMID 33541410 Check |pmid= value (help).
↑ Chicco D.; Jurman G. (2023). "The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification". BioData Mining. 16 (1). doi:10.1186/s13040-023-00322-4. PMC 9938573 Check |pmc= value (help).
↑ Tharwat A. (August 2018). "Classification assessment methods". Applied Computing and Informatics. doi:10.1016/j.aci.2018.08.003.
↑ Balayla, Jacques (2020). "Prevalence threshold (ϕe) and the geometry of screening curves". PLoS One. 15 (10). doi:10.1371/journal.pone.0240215.

This template "Confusion matrix terms" is from Wikipedia if otherwise notified

[1] Fawcett, Tom (2006). "An Introduction to ROC Analysis" (PDF). Pattern Recognition Letters. 27 (8): 861–874. doi:10.1016/j.patrec.2005.10.010.

[2] Piryonesi S. Madeh; El-Diraby Tamer E. (2020-03-01). "Data Analytics in Asset Management: Cost-Effective Prediction of the Pavement Condition Index". Journal of Infrastructure Systems. 26 (1): 04019036. doi:10.1061/(ASCE)IS.1943-555X.0000512.

[3] Powers, David M. W. (2011). "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation". Journal of Machine Learning Technologies. 2 (1): 37–63.

[4] Ting, Kai Ming (2011). Sammut, Claude; Webb, Geoffrey I., eds. Encyclopedia of machine learning. Springer. doi:10.1007/978-0-387-30164-8. ISBN 978-0-387-30164-8. Search this book on

[5] Brooks, Harold; Brown, Barb; Ebert, Beth; Ferro, Chris; Jolliffe, Ian; Koh, Tieh-Yong; Roebber, Paul; Stephenson, David (2015-01-26). "WWRP/WGNE Joint Working Group on Forecast Verification Research". Collaboration for Australian Weather and Climate Research. World Meteorological Organisation. Retrieved 2019-07-17.

[6] Chicco D.; Jurman G. (January 2020). "The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation". BMC Genomics. 21 (1): 6-1–6-13. doi:10.1186/s12864-019-6413-7. PMC 6941312 Check |pmc= value (help). PMID 31898477.

[7] Chicco D.; Toetsch N.; Jurman G. (February 2021). "The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation". BioData Mining. 14 (13): 1-22. doi:10.1186/s13040-021-00244-z. PMC 7863449 Check |pmc= value (help). PMID 33541410 Check |pmid= value (help).

[8] Chicco D.; Jurman G. (2023). "The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification". BioData Mining. 16 (1). doi:10.1186/s13040-023-00322-4. PMC 9938573 Check |pmc= value (help).

[9] Tharwat A. (August 2018). "Classification assessment methods". Applied Computing and Informatics. doi:10.1016/j.aci.2018.08.003.

[10] Balayla, Jacques (2020). "Prevalence threshold (ϕe) and the geometry of screening curves". PLoS One. 15 (10). doi:10.1371/journal.pone.0240215.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]