Line 210:
> "Gay and heterosexual people were represented in equal numbers."
According to Gallup Polling, around 4% of the American population is homosexual. So, let's be generous and say that their classifier has a 80% accuracy given balanced inputs while humans have 60%.
Let's sample 100 people of the dataset, 50 of which are homosexual (and the rest heterosexual). If the classifier has 80% accuracy (let's assume false_positive_rate = false_negative_balance since I didn't find information about that), it means that 80 people were correctly classified, 10 heterosexuals were misclassified as homosexuals and 10 homosexuals as heterosexuals.
According to the Bayes theorem, "Given a random person, probability of being homosexual assuming that the classifier said so" = "Probability of being homosexual of a random person (the so-called prior)" <times> "Probability of classifier saying it's homosexual, assuming it's indeed homosexual <divided by> "Given a random person, probability of saying it's homosexual".
Substituting, we get: P = 0.04 * 0.8 / 0.5 = 0.064
If instead of the classifier we use human "feeling", we get: P=0.04 * 0.6 / 0.5 = 0.048
In summary, 4% of the people are homosexual. If a human thinks someone is homosexual, the probability "increases" to 4.8%. If on the contrary their algorithm believes it's homosexual, the probability of actually being homosexual increases to 6.4%.
Not very groundbreaking...
According to Gallup Polling, around 4% of the American population is homosexual. So, let's be generous and say that their classifier has a 80% accuracy given balanced inputs while humans have 60%.
Let's sample 100 people of the dataset, 50 of which are homosexual (and the rest heterosexual). If the classifier has 80% accuracy (let's assume false_positive_rate = false_negative_balance since I didn't find information about that), it means that 80 people were correctly classified, 10 heterosexuals were misclassified as homosexuals and 10 homosexuals as heterosexuals.
According to the Bayes theorem, "Given a random person, probability of being homosexual assuming that the classifier said so" = "Probability of being homosexual of a random person (the so-called prior)" <times> "Probability of classifier saying it's homosexual, assuming it's indeed homosexual <divided by> "Given a random person, probability of saying it's homosexual".
Substituting, we get: P = 0.04 * 0.8 / 0.5 = 0.064
If instead of the classifier we use human "feeling", we get: P=0.04 * 0.6 / 0.5 = 0.048
In summary, 4% of the people are homosexual. If a human thinks someone is homosexual, the probability "increases" to 4.8%. If on the contrary their algorithm believes it's homosexual, the probability of actually being homosexual increases to 6.4%.
Not very groundbreaking...