100 people, 50 false alarms, 1 actual problem alerted and 49 marked as safe correctly = 50/(50+49) = ~50%.
I agree it can be confusing, but I think people would also make the opposite mistake if it were defined differently.
See https://en.m.wikipedia.org/wiki/Precision_and_recall for a table of different terms.
False positive = (Machine says positive but grand truth is negative) / (Machine says is positive)
In English, a false positive is when the machine declares something as positive but it is actually negative.
This fits a sanity test because ~50% of people that pass through a detector do not get patted down. The truth is closer to 10%. Even then, a true positive probably includes someone with two pennies in their pocket.
In statistics and ML it’s (FP) / (FP + TN) aka (false positives) / (actual negatives samples). This is by far the most common definition.
Here ML using the common definition see fall-out: https://en.m.wikipedia.org/wiki/Precision_and_recall
> In English, a false positive is when the machine declares something as positive but it is actually negative.
Yes, and the rate is based on the frequency this happens in your negative set.
>This fits a sanity test because ~50% of people that pass through a detector do not get patted down.
The 50% figure may be wrong, but my definition of what a false positive rate is not.
See https://en.m.wikipedia.org/wiki/Precision_and_recall for a table of different terms.