A false positive (type I error in statistical hypothesis testing) is about receiving a positive result when expecting a negative one, an indication of a condition’s presence while in reality, it is not present. On the other hand, a false negative (type II error in statistical hypothesis testing) is the opposite. It is about receiving a negative result while expecting a positive one, about something happening while not expecting it.
Now in machine learning terms, a false positive is when a data point is classified as a positive example while it is actually negative (classified as “1” while it is “0”), and a false negative is when a data point is classified as “0” while it is actually “1”.
Below a confusion matrix, showing the true and false positive/negative, and the accuracy/error rates calculation:
False positive and false negative are both false results, but, can one be better than the other?
As shown in the precedent photo, a type I error seems like a warning while a type II error looks more like an issue. A false fire alarm (false positive) is better than a fire alarm not going on when there is fire all around (false negative). A false positive test of a patient showing he has cancer while he doesn’t, and taking medicines while he shouldn’t, is less harmful than a false negative test of him, missing out on crucial treatments.
Many may say that a type II error is worse than a type I error as something not happening is better than something happening while not expecting it, but, is it always the case? Isn’t a false positive alcohol test result leading to arrest a sober driver, less harmful than a false negative alcohol test result leaving a drunk driver on the road as a threat for himself and other drivers?
What about finding someone guilty while he is not (false positive) and putting to prison? Is it better than leaving a thief free (false negative)? It may be worst but what if the thief was also a criminal and a big threat to society?
Not having false positives and false negatives is the best result to obtain, but since a perfect sample rarely occurs, it is a case by case to define whether the false positive is better or worse than the false negative.
Innocent until proven guilty or guilty unless proven innocent?
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