statistics question

MengerSponge

OK, this is sort of an odd question, but I can't think of how to word my position to my friend. We're discussing profiling, such as profiling muslims in an airport to find terrorists. I remember reading some statistical argument that proved that, even if (for a completely hypothetical example) most terrorists are muslim, that doesn't mean that a particular muslim individual is more likely to be a terrorist than a non-muslim individual. That's my position as to why profiling doesn't work, but he asserts that if most terrorists are muslim, then scrutinizing muslims more makes sense, because there's a better chance that a muslim will be a terrorist than another individual will be. However, I can't remember what this misconception is called, or how to explain it (I don't even know for sure that it's correct, but I really think I remember reading it somewhere). Can anyone offer an explanation, or at least the name of this misconception so that I can research it more? Or if it's wrong, yell at me and tell my why my friend's right.

Edit: I'm not looking for moral reasons against profiling, that's not the issue; I'm just trying to find the statistical reasoning that shows that racial profiling doesn't work, and can't seem to remember the proof that this guy used.

Ain't No Sunshine

Circumvent him by showing him this.

http://abcnews.go.com/International/wireStory?id=1851494

I'm not sure what the proper statistical argument is. I drew a Venn diagram ('looks terrist' vs. 'don't look terrist' as independent areas where 'don't look terrist' was a much larger area, then added 'terrist' as overlapping both but with a higher proportion of overlap in the 'looks terrist' area than the 'don't look terrist' area.) By a very primitive assessment, it looks like racial profiling would work, until the terrorists alter recruiting tactics to shift the boxes (as they have already done even with the threat of profiling emerging).

MengerSponge

Yeah, there's the factor of terrorists recruiting people who don't "look the part", which lends support to the idea that racial profiling doesn't work. However, I'm really looking for someone who can offer a statistical rationalization, because neither of us can seem to come up with it. We make simplified examples, but they all seem to show that profiling should work.

Thanks for the link though.

Chenjesu

I remembered seeing this argument before, that totally random searches work better than any sort of profiling, even if criminals don't try to actively guess the profiling criteria and avoid them.

I believe this is the article I read. You may want to look into the source and verify how trustworthy it is before you use it. (I say that not because I distrust it, just that it's a site I'm not really familiar with.)
http://www.acfnewsource.org/science/random_security.html

Feral

If you're looking for an academic-sounding phrase, "Hasty Generalization" will work. It's basing a generalization (most hijackers are Muslims) on an incomplete sample (the 9-11 hijackers were Muslims). It's a sign of fuzzy thinking.

If you want counter-arguments, there are plenty. The biggest act of terrorism perpetrated on American soil prior to 9-11 was committed by a blonde white dude. (Other examples of non-Muslim hijackers.) As a security measure, racial profiling is stupid because all it takes is for the "bad guys" to find somebody sympathetic to their cause who doesn't look Middle Eastern. Need I point out that "Muslim" is not an ethnicity? You can be any skin color and Islamic. Behavioral profiling and random profiling are demonstrably more effective at finding potential threats.

EggyToast

I believe you need to look at sample variance and sampling distributions. What that covers is what the probability is of selecting a particular sample among the range of sampling possibilities, based on an estimated proportion.

So if, say, .1 % of muslims are terrorists, what is the likelihood of selecting a sample that contains that .1% out of a larger sample. The "sample" in this case are people who are detained and questioned. It's not feasible to detain and question each muslim-looking passenger, so a sample is selected. Needless to say, given the number of muslims that travel, the probability of selecting a sample that would contain the .1% is infinitesimally small. So small to the point that profiling based on race is a waste of time.

That, combined with the whole "not all terrorists are muslim" thing. Since it's saint patrick's day, you shouldn't forget about the IRA. No racial profiling happened then, because there's no natural xenophobia. Which is what racial profiling ultimately comes down to.

MengerSponge

EggyToast wrote: »

I believe you need to look at sample variance and sampling distributions. What that covers is what the probability is of selecting a particular sample among the range of sampling possibilities, based on an estimated proportion.

So if, say, .1 % of muslims are terrorists, what is the likelihood of selecting a sample that contains that .1% out of a larger sample. The "sample" in this case are people who are detained and questioned. It's not feasible to detain and question each muslim-looking passenger, so a sample is selected. Needless to say, given the number of muslims that travel, the probability of selecting a sample that would contain the .1% is infinitesimally small. So small to the point that profiling based on race is a waste of time.

That, combined with the whole "not all terrorists are muslim" thing. Since it's saint patrick's day, you shouldn't forget about the IRA. No racial profiling happened then, because there's no natural xenophobia. Which is what racial profiling ultimately comes down to.

Yeah, I did ask him if he thought that there would be the same degree of profiling for other groups. My counter-example was bringing up the trench-coat mafia and the supposed correlation between video games and violence. My friend wears a black trench-coat and plays video games, so does he think that he himself should be scrutinized? His reply on this was vague. So aggravating.

I have been thinking of the sampling problems; even if x% of muslims are terrorists, that doesn't mean that x% of the muslims in the airport are; could be more or less. Maybe this is what I was thinking of. I'm also vaguely recalling something about, even if you focus on one group that supposedly has a higher chance of being guilty, you get so many false positives and miss so many real positives from other groups that it's ineffective. (My stats teacher would be so ashamed of how much I've forgotten.)

All good ideas so far, anyone have anything else to add? This entire discussion has made me really want to get a few statistics books.

Valkun

In the hypothetical situation you described, it does not mean that a Muslim is more likely to be a terrorist because the percentage of the populations who are terrorists is not defined.

Therefore you could have something like this:

In our sample we have
10 Muslim terrorists and 1 non-Muslim terrorist
90 Muslim non-terrorists and 4 non-Muslim non-terrorists

Although 90.91% of all terrorists are Muslims, only 10% of Muslims are terrorists. In contrast, only 9.1% of all terrorists are non-Muslims but 20% of all non-Muslims are terrorists. Even though Muslims make up the vast majority of terrorists, they are less likely to be one.

I could have sworn there was a named paradox that was associated with this but I can't seem to find it on wikipedia.

It came up in my statistics courses in a hypothetical cancer screening where positive results were more likely to come about as false positives rather than true positives due to the difference in the number of patients without cancer compared to with cancer.

RocketScience

The false positives problems relate to Bayes Theorem.

MengerSponge

I seem to remember examples about drug test effectiveness, cancer screenings, etc. also. That might be what I'm thinking of; I also read the article on Bayes' Theorem, and that sounds familiar too. Thanks everyone, I just have to put all this together and hopefully I can come up with something.