A finding from Qubix University
A 99% accurate alarm is wrong half the times it fires
A detector that is 99% accurate, looking for something that happens 1% of the time, is right about half the times it goes off.
| Deliveries | 10,000 | |
|---|---|---|
| Actually late | 100 | of which 99 are flagged |
| Actually on time | 9,900 | of which 99 are flagged anyway |
| Alarms in total | 198 | about half are genuine |
Accuracy describes how the detector behaves on each delivery. It says nothing about how many of its alarms are genuine, because that also depends on how rare the thing is.
Take 10,000 deliveries. 100 are late, and the detector catches 99 of them. The other 9,900 are on time, and it wrongly flags 1% of those: another 99.
That is 198 alarms, of which 99 are real. The detector did exactly what it promised. The population it was pointed at is what makes half its alarms false.
Arithmetic: 99 true flags and 99 false flags out of 198.
Taught in Chapter 8 · What you already know changes the number.
Qubix University is a data-science course being written in the open. Volume 0 is a draft: it has not been through final review, and nothing in it is accredited. The finding above is arithmetic, and stands on its own.