Metrics from a confusion matrix

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Problem

A classifier has $\mathrm{TP}=18$ , $\mathrm{FP}=6$ , $\mathrm{FN}=2$ , and $\mathrm{TN}=24$ . Compute accuracy, precision, recall, specificity, and $F_1$ for the positive class.

Reveal answer or reference solution

There are $50$ examples. The metrics are

\begin{aligned} \text{accuracy} &= \frac{18+24}{50}=0.84,\\ \text{precision} &= \frac{18}{24}=0.75,\\ \text{recall} &= \frac{18}{20}=0.90,\\ \text{specificity} &= \frac{24}{30}=0.80. \end{aligned}

Finally,

F_1=\frac{2\,\mathrm{TP}}{2\,\mathrm{TP}+\mathrm{FP}+\mathrm{FN}}=\frac{36}{44}=\frac{9}{11}\approx 0.8181818.

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Metrics from a confusion matrix

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