Template:SensSpecPPVNPV

Relationships among terms
 Condition (as determined by "Gold standard") Condition Positive Condition Negative Test Outcome Test Outcome Positive True Positive False Positive (Type I error) Positive predictive value = Σ True Positive Σ Test Outcome Positive Test Outcome Negative False Negative (Type II error) True Negative Negative predictive value = Σ True Negative Σ Test Outcome Negative Sensitivity = Σ True Positive Σ Condition Positive Specificity = Σ True Negative Σ Condition Negative
A worked example
A diagnostic test with sensitivity 67% and specificity 91% is applied to 2030 people to look for a disorder with a population prevalence of 1.48%
 Patients with bowel cancer (as confirmed on endoscopy) Condition Positive Condition Negative Fecal Occult Blood Screen Test Outcome Test Outcome Positive True Positive (TP) = 20 False Positive (FP) = 180 Positive predictive value = TP / (TP + FP) = 20 / (20 + 180) = 10% Test Outcome Negative False Negative (FN) = 10 True Negative (TN) = 1820 Negative predictive value = TN / (FN + TN) = 1820 / (10 + 1820) ≈ 99.5% Sensitivity = TP / (TP + FN) = 20 / (20 + 10) ≈ 67% Specificity = TN / (FP + TN) = 1820 / (180 + 1820) = 91%

Related calculations

• False positive rate (α) = type I error = 1 − specificity = FP / (FP + TN) = 180 / (180 + 1820) = 9%
• False negative rate (β) = type II error = 1 − sensitivity = FN / (TP + FN) = 10 / (20 + 10) = 33%
• Power = sensitivity = 1 − β
• Likelihood ratio positive = sensitivity / (1 − specificity) = 66.67% / (1 − 91%) = 7.4
• Likelihood ratio negative = (1 − sensitivity) / specificity = (1 − 66.67%) / 91% = 0.37

Hence with large numbers of false positives and few false negatives, a positive screen test is in itself poor at confirming the disorder (PPV = 10%) and further investigations must be undertaken; it did, however, correctly identify 66.7% of all cases (the sensitivity). However as a screening test, a negative result is very good at reassuring that a patient does not have the disorder (NPV = 99.5%) and at this initial screen correctly identifies 91% of those who do not have cancer (the specificity).

Note: This template is used as a portion of the articles on sensitivity, specificity, likelihood ratios in diagnostic testing, etc. See those articles for additional citations.