Confusion Matrix

Definition(s)

A two-by-two table listing values for the number of True Negatives (TN), False Negatives (FN), True Positives (TP), and False Positives (FP) resulting from a search or review effort. As shown below, all of the standard evaluation measures are algebraic combinations of the four values in the Confusion Matrix. Also referred to as a Contingency Table. An example of a Confusion Matrix (or Contingency Table) is provided immediately below. 1

Coded RelevantCoded Non-Relevant
Truly RelevantTrue Positives (TP)False Negatives (FN)
Truly Non-RelevantFalse Positives (FP)True Negatives (TN)

Accuracy = 100% – Error = (TP + TN) / (TP + TN + FP + FN)
Elusion = 100% – Negative Predictive Value = FN / (FN + TN)
Error = 100% – Accuracy = (FP + FN) / (TP + TN + FP + FN)
Fallout = False Positive Rate = 100% – True Negative Rate = FP / (FP+TN)
False Negative Rate = 100% ‒ True Positive Rate = FN / (FN+TP)
Negative Predictive Value = 100% – Elusion = TN / (TN + FN)
Precision = Positive Predictive Value = TP / (TP + FP)
Prevalence = Yield = Richness = (TP + FN) / (TP + TN + FP + FN)
Recall = True Positive Rate = Sensitivity = TP / (TP+FN)
True Negative Rate = Specificity = TN / (TN + FP)

Notes

  1. Maura R. Grossman and Gordon V. Cormack, EDRM page & The Grossman-Cormack Glossary of Technology-Assisted Review, with Foreword by John M. Facciola, U.S. Magistrate Judge2013 Fed. Cts. L. Rev. 7 (January 2013).