Evaluation Metrics

False-Positive Rate Uses Actual Negatives

False-positive rate reads the actual negative side of the confusion grid. This lesson keeps FP, TN, and the shared denominator visible.

highlighted = computed this step

Start from fixed counts

This grid has TP=2, FN=1, FP=1, and TN=2. The false-positive-rate row will read only the actual negative side.

TP=2,  FN=1,  FP=1,  TN=2TP=2,\;FN=1,\;FP=1,\;TN=2
False-positive rate uses actual negativesExact side rate from the actual negative row group.false-positive rate from actual negativesoutputpositivenegativeactualpositivenegativeTP2FN1FP1TN2FPR=1/3specificity=2/3actual-negative side ratesrowexact fractionvaluefalse-positive rateFP/(FP+TN)=1/31/3specificityTN/(TN+FP)=2/32/3complement1/3+2/31both rows use FP+TN, the actual-negative denominatorfalse-positive rate reads actual negatives only; one displayed grid; not a claim about future rows; NOT trainingthreshold fixed first; metric alone is not a claim; NOT training

Use actual negatives

The denominator is FP+TN, because both cells came from actual negative rows. Here FP+TN=1 + 2 = 3.

FP+TN=1+2=3FP+TN = 1 + 2 = 3
False-positive rate uses actual negativesExact side rate from the actual negative row group.false-positive rate from actual negativesoutputpositivenegativeactualpositivenegativeTP2FN1FP1TN2FPR=1/3specificity=2/3actual-negative side ratesrowexact fractionvaluefalse-positive rateFP/(FP+TN)=1/31/3specificityTN/(TN+FP)=2/32/3complement1/3+2/31both rows use FP+TN, the actual-negative denominatorfalse-positive rate reads actual negatives only; one displayed grid; not a claim about future rows; NOT trainingthreshold fixed first; metric alone is not a claim; NOT training

Compute the rate

False-positive rate is FP divided by FP+TN. The exact value is 1/3 because FP=1 out of 3 actual negatives.

FPR=FPFP+TN=13=1/3FPR={FP\over FP+TN} = {1\over3} = 1/3
False-positive rate uses actual negativesExact side rate from the actual negative row group.false-positive rate from actual negativesoutputpositivenegativeactualpositivenegativeTP2FN1FP1TN2FPR=1/3specificity=2/3actual-negative side ratesrowexact fractionvaluefalse-positive rateFP/(FP+TN)=1/31/3specificityTN/(TN+FP)=2/32/3complement1/3+2/31both rows use FP+TN, the actual-negative denominatorfalse-positive rate reads actual negatives only; one displayed grid; not a claim about future rows; NOT trainingthreshold fixed first; metric alone is not a claim; NOT training

Specificity is the complement

Specificity reads the same denominator from the TN side: 2/3. Together they sum to 1. This is one displayed grid only; not a claim about future rows.

13+23=1{1\over3} + {2\over3} = 1
False-positive rate uses actual negativesExact side rate from the actual negative row group.false-positive rate from actual negativesoutputpositivenegativeactualpositivenegativeTP2FN1FP1TN2FPR=1/3specificity=2/3actual-negative side ratesrowexact fractionvaluefalse-positive rateFP/(FP+TN)=1/31/3specificityTN/(TN+FP)=2/32/3complement1/3+2/31both rows use FP+TN, the actual-negative denominatorfalse-positive rate reads actual negatives only; one displayed grid; not a claim about future rows; NOT trainingthreshold fixed first; metric alone is not a claim; NOT training