7 ms·
My favorite professor used to describe this statistical error as a major cause behind racism. E.g. it may be true that most criminals in an area are of a certa
by schrodinger 8y ago
My favorite professor used to describe this statistical error as a major cause behind racism.
E.g. it may be true that most criminals in an area are of a certain race; that says nothing about the probability of a single person of that race being a criminal. Same with Islamaphobia–even if most acts of terrorism were performed by Muslims (which isn’t even true!), that’d say nothing about the likelihood that a randomly chosen Muslim person you meet is a terrorist.
Edit: changed likelihood to probability
- alexis_fr 8y agoThat’s what I believed. Until my daughter got raped.
- rco8786 8y agoI’m sorry to hear about your daughter. But don’t let an anecdote change your mind about the field of statistics.
- mj_olnir 8y agoAs someone who has also lived through that nightmare - I'm deeply sorry for your daughter. However, you have to remember that this is an anecdote - you don't want to throw people into boxes they don't fit.
- deleted 8y ago[deleted]
- grkvlt 8y agoWhich goes to show how terrible people are at dealing rationally with anything when they are affected personally or emotionally.
- sokoloff 8y agoI am interested in the stats error here. If there are 100 balls in a bag, 10 of each rainbow color and 30 blank, and I tell you 3 of the green balls have property X, while 10 total of the balls in the bag have property X. You blindly draw a ball from the bag; do you know anything about the likelihood of that ball having property X? You now inspect it and find it’s green. Do you now know anything different about that likelihood? If I offered you “pay $100 to win $900 if you drew a property X ball, with the option to double your wager after seeing the color”, you would be happy indeed to see that you’d drawn a green ball and would double your wager. Regardless of the colors, ratios, and desirability of property X, it seems to me like you do know something new about the likelihood after learning the color. It also seems to hold if there are 300 million balls, 10 balls with property X, and 3 of those are green, just at a strong cause to believe “this specific ball does not have property X” overall (such as the case in the people examples you gave).
- SmirkingRevenge 8y agoI'm sure there is a better term for it, but its a kind of unwarranted generalization, with respect to population sizes, e.g.: - Nearly all murderers are men. - Bob is a man. - Therefore Bob is probably a murderer. There's obviously a problem there. The population of murderers is an infinitesimal fraction of the male population. While you can say its more likely that any given male is a murderer, than any given female, its not really useful for making judgements about individuals.
- dominotw 8y ago> - Therefore Bob is probably a murderer. You are mixing logic and probability. "its not really useful for making judgements about individuals." is not equal to "tells you nothing"
- testvox 8y agoYeah it certainly still tells you something, but most people's intuitions about probability mislead them about the amount of information contained. Its like how people can be lead to believe they have a very rare disease if they test positive for it. Just because most people who have the disease test positive for it doesn't mean you can just ignore the prior probability that the disease is extremely rare in the first place, so you still likely don't have it. https://en.wikipedia.org/wiki/Base_rate_fallacy https://en.wikipedia.org/wiki/Base_rate_fallacy
- dominotw 8y agoThats the prototypical example used in all bayes theorem explantions :D.
- iguy 8y agoThe related mistake here is to jump from "not really useful for making judgements about individuals" to "not useful for making judgements about averages". Sometimes you are trying to predict about an individual. Sometimes you are trying to predict a population average. Sticking with medical examples, the first matters for "does this guy have this disease?" The second matters for "how many doses should we order?" Or, more controversially, "how many of the doctors we train today will still be working in 30 years?" Which came up as a question regarding the increasing proportion of women in medical school. And many people were loudly offended that this might be something to take into consideration. Because they read it as the first kind of question, "will this individual...". But that's different.
- dominotw 8y agoI don't get it. Why not?
- AlexTWithBeard 8y agoWell, because it does. Let's say we have a group of 1000 animals: 900 rabbits and 100 foxes. We also know that there are about 10 crimes happening every year and for every crime there's 50% chance of it being committed by a fox. Then according to Bayes' formula: P(fox is a criminal) = P(criminal is a fox) * P(animal is a criminal) / P(animal is a fox) = 0.5 * 0.01/0.1 = 0.05 = 5% chance for every given fox to be a criminal. For every given rabbit the same formula gives 0.5 * 0.01/0.9 which is roughly 0.6%.
- __s 8y agoLet's say I show you a muslim. Do we investigate him as a terrorist? We'll assume 100% of terrorists are muslims. Let's say there are 1000 muslim terrorists, & 100000000 muslims. There's a 0.001% chance of finding a terrorist per random sampling. In order to find 0.001% of terrorists you will have to pick through 99999 innocent muslims. This is immensely far from the original 100% number. If you think 1:100000 is worth it, you'll want to extend your model with: 1. Real numbers 2. What's the probability you misclassify someone innocent? 3. What's the probability you misclassify someone guilty? 4. How many people are going to get busted over some unrelated crime like marijuana, which you would find at the same rate if you investigated non-muslims with the same gusto? 2 & 3 will tend to cause you to fail to achieve the original goal. 4 will cause you to create a systematic racist bias edit: I mismathed my random numbers
- sokoloff 8y ago> In order to find 0.001% of terrorists you will have to pick through 999 innocent muslims. 99,999, not 999 innocents and 1:100,000, not 1:1000 (making your point stronger)
- AlexTWithBeard 8y agoNot every animal in Australia is a kangaroo. Nevertheless, if you want to find a kangaroo in a wild, heading to Australia, would probably be your best bet.
- ad_hominem 8y ago> it may be true that most criminals in an area are of a certain race; that says nothing about the likelihood of a single person of that race being a criminal Huh? If 10% of purple people in an area have been incarcerated, and you select one individual from the purple people population of that area at random, the odds are 10% the individual you selected will have been incarcerated. That's fundamental to how sampling works.
- tnzn 8y agoExcept that's not what happens.
- schrodinger 8y agoThe situation isn’t that 10% of purple have been incarcerated; if it was, you’d be correct. Instead, the situation is that 90% of those incarcerated are purple. You can’t draw any meaningful conclusions from that without knowing the number that you were referring to: what percentage of purple people that makes up.
- imgabe 8y agoYou are flipping around the percentages. Parent says "10% of incarcerated people are purple". This does not imply that "10% of purple people are incarcerated".
- fludlight 8y agoRandom sampling doesn't work well with small sample sizes.
- titanix2 8y agoStill the thing is if you have zero muslim in a given area you will have 0 murders committed by them. So it is a totally reasonable public policy for countries who don’t have them to no accept them. Also "islamophobia" is a term coined and used by radical muslims to spread their ideology so don’t use it like if it were a normal and conscensual concept. If you care the slightest about women & LGBT rights and lives of non-muslim people you better start read the Quran now and understand what is on the menu for them.
- stdbrouw 8y agoI think you meant probability instead of likelihood. That is: it may be true that most criminals in an area are of a certain race; that says nothing about the probability of a single person of that race being a criminal because you'd need to know about the prevalence of crime. (In statistics, the likelihood is the probability of the data conditional on the hypothesis, so in this case the probability of being of a certain race given that one is a criminal.)
- schrodinger 8y agoThanks! I’m pretty ignorant on the specific terminology behind statistics, and realize how important it is to be accurate in this case.
- deleted 8y ago[deleted]