Definition of “Precision” seems incorrect...

[Scoodood]

On this page at ClassificationReport

For binary classifier, the part “not to label an instance positive that is actually negative” sounded like “to correctly classified a negative”, which is the definition of True Negative right? I think the first sentence should be removed to avoid confusion.

[bbengfort]

@Scoodood I agree that we could make it more clear; however I don't think we can necessarily simply remove the first sentence; do you have an edit to suggest?

[Scoodood]

Hi @bbengfort,

If we simplified the first sentence it will become
"Precision is the ability of a classifier to correctly label a negative instance as negative."

That definition is wrong, because it belongs to the True Negative Rate, not Precision. According to the wikipedia,
Precision = TP / (TP + FP) = Positive Predictive Value (PPV)

The denominator term TP + FP also means total predicted output. So the whole equation means for all cases that were labeled by the classifier as positive, what percent of those were actually correct. But your second sentence said this already.

Besides, the formula of TPR (True Positive Rate) and PPV is very similar, and yet their interpretation is different.
TPR = The ability of classifier to recognize positive instance
PPV = The ability of classifier to give relevant positive output

So if you insist to keep the first sentence, then I would like to suggest something like this
Precision measures the ability of a classifier to give relevant positive output.

But I really think your second sentence is clear enough even without the first sentence.