20 ms·

Are mass shootings really random events? A look at the US numbers

156 points by jipumarino 14y ago

omershapira 14y ago
"If mass shootings are really occurring at random, then this suggests that they are extreme, unpredictable events, and are not the most relevant measure of the overall harm caused by gun violence." In my Undergrad years I would get crucified for arguing that a computational model works and concluding that it is therefore the way reality works. Seriously though, can anyone reading this fathom a way to formalize the event "Guns are available"? What's the probability of getting a gun if it's not available in shops? You need to model a different country for that. The same reasoning can be used to show that the probability of a mass shooting given the availability of guns is lower given a lack thereof. In other words, this: http://www.youtube.com/watch?v=KsN0FCXw914 http://www.youtube.com/watch?v=KsN0FCXw914 . And if they are indeed rare events, what's the metric for that? If we have a chance of stopping a rare, unexpected event that would add quite a lot to the expected value of deaths per year, would it not matter significantly in our efforts of stopping it?
- jlgreco 14y ago
  I don't think the author is attempting to imply anything other than "Assuming mass shootings are random unrelated events, 7 mass shootings in 1 year does not necessarily signal a significant change from the past 30 years. (Though if it happens again, it does.)"
  - omershapira 14y ago
    I thought so too until I read the last 3 paragraphs. "Those numbers check out" is totally valid. But concluding with the relevance of the measure of gun harm is an observation about reality, not Statistics, which is debatable, but has no relevance to what was previously mentioned. We haven't yet defined the goals. Unless "Minimum amount of gun-related deaths" is the goal (clearly, it isn't that simple in this country), in which case his highlighted claim is definitely false - we don't know much about effective metrics. Are the psychological effects of a mass shooting similar to a snowball effect? Maybe in the long run? There's a lot more to research before saying 'insignificant', especially if you don't describe the model. One more thought: could you define 'mass shooting'? Usually the media is responsible for that definition, whereas a random murder isn't called that.
    - jlgreco 14y ago
      The conclusion about the relevance of the measure of gun harm seems to me the "mass shootings in 1 year does not necessarily signal a significant change from the past 30 years" part. It means that discussions along the line of "Why the change?", or "How can we go back to the way it was before?" are premature, though it does not say anything at all about discussions along the line of "How do we reduce mass shootings?". Mother Jones probably did a pretty decent job of defining 'mass shooting', I assume they errored on the side of inclusion (I only recall 2 this year). The authors analysis seems to make it pretty clear it is only considering that definition. I'm really not reading this as an attack on discussions of gun violence in general, as it seems you are.
- Jayschwa 14y ago
  > If we have a chance of stopping a rare, unexpected event that would add quite a lot to the expected value of deaths per year, would it not matter significantly in our efforts of stopping it? I wouldn't characterize the number of deaths via mass shootings as "quite a lot". It's probably in the same ballpark as death by lightning strike (~50/year, according to Wikipedia).
SoftwareMaven 14y ago
This was a great article, but I'm not convinced mass shootings are completely independent. Given the media attention, it is very likely that event n+1 was, in some way, impacted by event n. I don't have any evidence to back this up, so I could be (and I hope I am) completely wrong. But if I'm right, then I think it would imply we need to reduce the correlation between events. And it is likely the media that provides that correlation. Instead of reporting about the <insert your word here> that causes these events, report on the impacts of these events. It would, hopefully, stop deifying the perpetrator, which might reduce the likelihood of other perpetrators from doing the same.
- jeremyjh 14y ago
  There should be some way to formalize this into a hypothesis. Testable with the same data I mean. If you were correct we should see more clustering then we do with a random sample.
  - carbocation 14y ago
    Perhaps looking at the time between mass shootings would be more interesting than simply looking at mass shootings per year.
    - vsbuffalo 14y ago
      You'd get weird mixture model type systems. There are certain subclasses: school-based vs non-school-based. You'd have to control for this since school-based shootings are highly temporally correlated. But then maybe there's crossover too. Like everything, estimating these things with more complex models is hard to do right, and findings are usually overstated.
- waterlesscloud 14y ago
  The media coverage may play a role, but I don't know that it's the entirely the fame angle at work. What if the goal in large part is to inflict the most possible suffering on the world? Out of anger or hurt or whatever the case may be. Then cutting out coverage on the person isn't as important, it's the entirety of the coverage that matters.
jQueryIsAwesome 14y ago
I have flagged this article; is not only link bait using the subject everyone is talking about; is being extremely disingenuous using statistics about a so ambiguous concept as "mass shootings" to draw conclusions about a real world situation.
- mitchi 14y ago
  I come here to gain knowledge about things related to science and computers. I'm tired of all the "humanities"
  - vitalique 14y ago
    I'd say if you are going to learn about or do any kind of serious science, resist putting labels left and right just because you are tired, on this site and elsewhere. There's nothing wrong with humanities in terms of being able to benefit from applying CS to them.
  - Tyr42 14y ago
    Hey, this is stats. At least where I'm from, Stats is in the Math faculty. Same as the CS departement.
- Daishiman 14y ago
  If you actually understood how a Poisson process works and how a hypothesis test works you would understand that his conclusions are very, very much important.
rdl 14y ago
This seems like trying to use a hammer (statistics) because you have a hammer, not because it's the right tool for the job. Essentially, if you look at the incidents, you see enough common factors (increasingly, using semiautomatic carbines, carrying multiple weapons, attacking schools, wearing armor or load bearing gear, etc.) to think there is some common factor at work. The population of random people on the street doesn't pick the AR-15 to do anything, and certainly doesn't pick a school as a target for anything. The solution space here isn't "spree shootings at schools through time", it is traits of spree shootings themselves -- location, methods, etc. They're pretty tightly clustered. Either there is a common hidden factor, or these incidents are feeding on each other. I personally don't think gun control is the major tool to deal with this, and don't think violent video games are the problem, but rather the non-stop multi-day press coverage by the media of each of these incidents. Some insignificant douchebags from a Colorado school became about as famous as the 9/11 terrorists (and far more than fortune 50 CEOs or scientists or classical musicians) by murdering their classmates. (Columbine essentially as as big a deal for the 'how to respond to shootings' world as 9/11 was to aviation security; previously, you cordoned off the area and called in SWAT to negotiate, thinking it was a hostage situation -- now, the first 1-2 responders on scene move directly to the threat with whatever weapons they have on them at the time, ignore any wounded victims, close, and engage/destroy -- similarly, hijacked airliners are now viewed as air to ground missiles vs. hostage negotiations.) Every time the media talks about the shooters in one of these situations, making them famous, it reinforces the rational (if defective) choice of someone who wants to be famous at the cost of doing evil to copycat. The mythological/historical example is Herostratus, who burned the temple of artemis just to be famous.
- potatolicious 14y ago
  I don't buy this explanation over the alternatives. It's logically sound but is based on the assumption that spree shooters do so in large part to gain infamy and notoriety. Given what we know of spree shooters around the world and in the US, they strike me as predominantly desperate, mentally ill people. We had the Columbine shooters who seemed to be more vengeful than fame-seeking. We had the Aurora shooter who didn't do any grandstanding when apprehended, or in fact talk to the media at all. And of course, we had the Newtown shooter who didn't leave behind any notes, manifestos, or in fact any evidence that he wanted to be infamous (even if posthumously). These don't strike me as people who are driven by the ensuing media coverage. Don't get me wrong - I've been appalled by the news media surrounding the Newtown shooting, particularly CNN's journalistically abhorrent fingering of an innocent individual, but I don't think the coverage is really the crux of it, and I don't think taking it away will stop them.
dizzystar 14y ago
I think a better methodology would be using linear time clusters and measuring the possible impact of the Werther Effect. Look at the regional areas where the news may not have spread out. Look at the attempts that were stopped and see if they clustered. The stopped attempts are probably a better indicator as people, after hearing the news, are naturally more alert to the indicators that something may happen. The other problem with the data is that there is no way, from looking at the graph, if an event happening in December affected an event happening in January, thus delimiting by years is arbitrary.
joe_the_user 14y ago
The question probably requires a more detailed treatment. For example, even the distribution of killings by frequency looked poisson, if the number were uniformly increasing year by year, it would look like a trend.
lostlogin 14y ago
This hits HN as another shooting covers front pages. A new dark twist for extra newsworthiness. http://www.nytimes.com/2012/12/25/nyregion/2-firefighters-killed-in-western-new-york.html?hp&_r=0 http://www.nytimes.com/2012/12/25/nyregion/2-firefighters-ki... Edit: it is unclear at this stage if this event would qualify for inclusion in the numbers according to the criteria in the article. Below are the used criteria. The killings were carried out by a lone shooter. (Except in the case of the Columbine massacre and the Westside Middle School killings, both of which involved two shooters.) The shootings happened during a single incident and in a public place. (Public, except in the case of a party in Crandon, Wisconsin, and another in Seattle.) Crimes primarily related to armed robbery or gang activity are not included. The shooter took the lives of at least four people. An FBI crime classification report identifies an individual as a mass murderer—as opposed to a spree killer or a serial killer—if he kills four or more people in a single incident (not including himself), and typically in a single location. If the shooter died or was hurt from injuries sustained during the incident, he is included in the total victim count. (But we have excluded cases in which there were three fatalities and the shooter also died, per the previous criterion.) We included six so-called "spree killings"—prominent cases that fit closely with our above criteria for mass murder, but in which the killings occurred in multiple locations over a short period of time.
aes256 14y ago
There is absolutely an observed trend of copycat school shootings which flies in the face of randomness. That said, I think this trend is hidden from this dataset because it relates specifically to mass shootings, including only those incidents in which the shooter took the lives of at least four people. I would hypothesize that each major shooting is followed in the succeeding months by a number of slapdash copycat shootings, in many of which less than four people are killed by the shooter.
beloch 14y ago
Mass shootings are rare enough that you're going to get poor stats due to granularity. It might be more interesting to look at stats like homicide rate. The U.S. has a homicide rate that is second only to Russia in the G8, and is more than 3 times higher that of any G8 nation besides Russia. This sets off warning bells for me... Normally I'd love to dig a little deeper, but it's time for me to play Santa. Merry Christmas!
- tomjen3 14y ago
  The sad truth is that if you exclude innercity slums, themurder rate in the us plummets to mostly normal levels.
  - robbiep 14y ago
    Yes, let's exclude statistics in order to normalise them. Because if we cut out the bits of statistics that sway them, we can claim the distribution is the same as elsewhere!
    - d2vid 14y ago
      By grouping statistics into these things we call "countries" we are also "excluding" certain statistics. For instance, why are we ignoring cartel murders just south of the US/Mexican border even though the US drug market is the driving factor? The parent comment is providing a better, more specific grouping that helps shed light on where murders are actually happening in the US and points us towards where we need to focus our efforts if we want to actually change the murder rate in the US. Inner city interventions will result in the greatest improvements to the murder rate, whereas focusing efforts elsewhere has literally zero chance of bringing the murder rate into line with the rest of the G8 because that's not where the murders are happening.
      - robbiep 14y ago
        The parent comment is introducing a new variable which may or may not be useful in, as you suggest, providing targeted approaches to reducing deaths by firearms. It still flies in te face of convention which still treats a whole country as a whole country, in the perhaps naive assumption that by averaging the nations stats you will be able to get a good comparison of what the average citizen puts up with an thus providing a ground for comparison with other average citizens in other nation-states, regardless of their level of development, or even, indeed, if they have 'inner city slums'. And all that is leaving aside the matter of whether the statement is actually true, as questioned by a number of other threads
clarkm 14y ago
Since mass shootings are such a rare events, the data is overdispersed, so a negative binomial distribution is likely more appropriate than a Poisson distribution. This, along with quasi poisson, is commonly used by criminologists to account for such problems. See this paper for a more detailed discussion: http://www.crim.upenn.edu/faculty/papers/berk/regression.pdf http://www.crim.upenn.edu/faculty/papers/berk/regression.pdf
- dbecker 14y ago
  Deviations from the Poisson distribution are exactly what he is testing for. The paper you referenced discusses how to model in the presence of overdispersion. Not how to test that as a hypothesis. Moreover Poisson distributions are generated from events that occur in a very small fraction of all opportunities, but with many opportunities each time period. So, unless the timing of shootings is correlated (again, the thing he is testing for), this is a perfect use case for the Poisson distribution.
clarkm 14y ago
Since mass shootings are such a rare events, the data is overdispersed, so a negative binomial distribution is likely more appropriate than a Poisson distribution. This, along with quasi poisson, is commonly used by criminologists to account for such problems. See this paper for a more detailed discussion: http://www.crim.upenn.edu/faculty/papers/berk/regression.pdf http://www.crim.upenn.edu/faculty/papers/berk/regression.pdf
phaselock 14y ago
The auther does a horrible job. He takes it as an assumption that the reader doesn't know statistics, and when he gets to the actual meat he just states as fact, "i calculate k=32.5 m/j" " what does this mean? It means I'm right" he should as a minimum either assume completely that the reader knows everything nessesary to interpret the hypothesis test or actually make an effort to explain to layman what the p-value means.
RyanZAG 14y ago
All these comments about statistics don't seem to even begin to understand statistics. 1) Yes, we can use the chi-squared test here - the small number of events is built into the p value. 2) No, we do not need to include all murders, as we are not testing for murders. We are testing for mass shootings. This line of reasoning is the same as saying we cannot test for rotten apples only, we can only test if all fruit is rotten. Statistics on categories is acceptable and meaningful if apples are a specific kind of fruit, or mass shootings are a specific kind of crime. We can't draw an conclusion about crime, but we can draw a conclusion about mass shootings. 3) These statistics prove only a single thing: mass shootings in USA are likely random events and have a mean value of ~2. The following conclusions are applicable: - Mass shootings are likely not a 'copycat' crime, and each event is likely completely independent of any other event occurring. - You should expect about 10 mass shootings over the next 5 years. Not so nice... Following conclusions are NOT applicable: - Gun laws have any effect. Gun laws may or may not decrease the average, these statistics do not say. - No measures that have been put in place to reduce mass shootings (I assume there are?) have had any effect so far. They may have had a positive or negative effect, but these effects may be small or may be cancelled out by other, opposite effects. - The chance of a mass shooting is stable, and no increase or decrease in events seems to be happening. The distribution fit test only shows us on the aggregate data, and that it does fit that distribution. The correct way to check for this is to break the data set in half, and compare the first set against the second set. And now we return you to our regular statistics hate... EDIT: Or not - nobody is questioning the real possible problem here: the data itself? http://www.bradycampaign.org/xshare/pdf/major-shootings.pdf http://www.bradycampaign.org/xshare/pdf/major-shootings.pdf This seems to imply there are FAR more mass shootings per year than indicated by the data. None of my conclusions above are correct if the data itself is wrong, and I don't even live in the USA so I can't vouch for the correctness of the data.
- RyanZAG 14y ago
  I blame Christmas and lack of sleep - I misread the actual article. Article is completely wrong. " ... found a p-value of 0.18. What does this mean? It suggests that there is no evidence of clustering beyond what you would expect from a random process ... " Above is incorrect. What the author is actually testing is the following statement: The mass shooting data points come from a Poisson distribution with an average value of 2 However, the test he is using can only prove this statement to be false: it CANNOT prove that the statement is true. So the only thing the author proved is that the statement may or may not be true. (For more, read up on a null hypotheses, the scientific term for this.) All the author has proven is that there is an 18% chance that the data does not come from a Poisson distribution. ~1 in 5 chance of being wrong is not something you assume to be right. Author needs to learn statistics.
chewxy 14y ago
For anyone who's interested, this blog post piqued a very morbid interest in me, and so I decided to have a look at the data. Here's a distribution of the number of days before the previous incidents (as reported by MotherJones. I'm personally not familiar with the number of shootings in the US, which according to different sources ranges from very few to way too many): http://imgur.com/Onoxv http://imgur.com/Onoxv . The colours represent the group of how many incidents happened in the 180 days prior to the incident. Here is the distribution of the number of incidents 180 days prior to an incident: http://imgur.com/9VTjQ http://imgur.com/9VTjQ Draw your own conclusions
archgoon 14y ago
Kudos to the author for attacking the question this way, it's always important to look at data and try to model it. (and it's a lot of work!) Unfortunately, I'm pretty sure there's a fatal flaw in the analysis. Suppose we had two types of years, both following a Poisson Distributino, but one with a higher incidence, the other with a lower incidence, and they alternated[1]. Now sample each type of year separately. Each will give you a Poisson distribution. To get the distribution of all years you'd just add bins of the two types together. The sum of two poisson distributions is a poisson distribution (with a different mean), therefore, we cannot conclude anything about how the mean value is changing with time (and thus, answering the question: is the incidence rate rising) unless we actually bin the data by year, and see if the mean value is changing with time. Unfortunately, by splitting time up, we reduce the already small sample sizes for each bracket. Time series analysis is a more appropriate tool to tackle this question. [1] This is unchanged if the rate is continuously increasing, the setup was so that you can actually think of collecting the same data over multiple years.
waldrews 14y ago
Statistician here. Saying nothing about the substance of the argument or whether their data source appropriately classifies what counts as this kind of crime, the methodology is on the right track but not optimal. Of course binning the events by year throws away data about specific timing. Having actual event times would allow fitting a hazard rate model. There are two simple alternative hypotheses - explanations for a deviation from the Poisson assumption. What they're calling "random" is really "occuring at a homogeneous rate;" so we have to ask - as opposed to what? 1) clustering/overdispersion, because the events happen more often alongside each other (copycat effect or whatever; risk of a new event is a function of time since last event) 2) secular trend (the rate of events is changing over time) We can't really distinguish between these two without explicitly modeling, and it doesn't look like we have enough data to do that. The tool to do it would be a generalized linear model with an overdispersed Poisson dependent variable. It's kind of bad form to estimate the Poisson mean from the data, and then use that to fit the distribution you're testing against. You're using the data twice, so the p-value isn't what you think it is. You should be conditioning on the total number of events in the sample. Also, chi-square distribution comparison is for large samples. This is a meh-kinda-borderline-midsize sample, to use a technical term. The test they want that has neither of these problems is Fisher's exact test for equal proportions. If the events were generated by a Poisson process, the number in each year would be conditionally binomial, and they'd add up to the total observed event count. The test is: is the data explained by all the years getting events randomly at the same rate (null hypothesis) vs. each year having its own rate (alt hypothesis). And finally, yes, you get a p-value. But you also need to think about the power of the test detect an anomaly if there was one (type II error). For something like this, you could do power analysis by a simple simulation, but you'd need to specify what kind of anomaly you'd want power to detect (e.g. all events cluster together in one year, to pick an extreme). Otherwise, all you have is a design that has a correct p-value. If you reject the null hypothesis at 5%, but you have low power, you might as well toss a coin and declare the data "nonrandom" 5% of of the time. This might be as good a test as we can get with the data available, but p-value isn't the only thing you can look at.
chrisringrose 14y ago
Beware: the whole point of this is article (and train of thought) is to cast a shadow of doubt over gun control. It's to remind us how these are random and extreme events. Yes, mass-shootings are random and extreme. A layperson can conclude this without having to look at any statistics. But unfortunately this distracts from the real problem. Machine guns. And how they're legal, and easy, for anyone to buy. And ammo. And modifications for guns. When the constitution was written to allow citizens the right to bare arms, the only arms in the legislators' wildest dreams took a minute to load one bullet, likely would miss, and probably wouldn't kill with one shot. Since the world is very different today, shouldn't the laws change too? Look at the success of gun control in the United Kingdom. Enough of this nonsense. It reminds me of climate change deniers pointing out "Yeah but it's snowing now."

156 points by jipumarino 14y ago

"If mass shootings are really occurring at random, then this suggests that they are extreme, unpredictable events, and are not the most relevant measure of the overall harm caused by gun violence." In my Undergrad years I would get crucified for arguing that a computational model works and concluding that it is therefore the way reality works. Seriously though, can anyone reading this fathom a way to formalize the event "Guns are available"? What's the probability of getting a gun if it's not available in shops? You need to model a different country for that. The same reasoning can be used to show that the probability of a mass shooting given the availability of guns is lower given a lack thereof. In other words, this: http://www.youtube.com/watch?v=KsN0FCXw914 http://www.youtube.com/watch?v=KsN0FCXw914 . And if they are indeed rare events, what's the metric for that? If we have a chance of stopping a rare, unexpected event that would add quite a lot to the expected value of deaths per year, would it not matter significantly in our efforts of stopping it?

jlgreco 14y ago
I don't think the author is attempting to imply anything other than "Assuming mass shootings are random unrelated events, 7 mass shootings in 1 year does not necessarily signal a significant change from the past 30 years. (Though if it happens again, it does.)"
- omershapira 14y ago
  I thought so too until I read the last 3 paragraphs. "Those numbers check out" is totally valid. But concluding with the relevance of the measure of gun harm is an observation about reality, not Statistics, which is debatable, but has no relevance to what was previously mentioned. We haven't yet defined the goals. Unless "Minimum amount of gun-related deaths" is the goal (clearly, it isn't that simple in this country), in which case his highlighted claim is definitely false - we don't know much about effective metrics. Are the psychological effects of a mass shooting similar to a snowball effect? Maybe in the long run? There's a lot more to research before saying 'insignificant', especially if you don't describe the model. One more thought: could you define 'mass shooting'? Usually the media is responsible for that definition, whereas a random murder isn't called that.
  - jlgreco 14y ago
    The conclusion about the relevance of the measure of gun harm seems to me the "mass shootings in 1 year does not necessarily signal a significant change from the past 30 years" part. It means that discussions along the line of "Why the change?", or "How can we go back to the way it was before?" are premature, though it does not say anything at all about discussions along the line of "How do we reduce mass shootings?". Mother Jones probably did a pretty decent job of defining 'mass shooting', I assume they errored on the side of inclusion (I only recall 2 this year). The authors analysis seems to make it pretty clear it is only considering that definition. I'm really not reading this as an attack on discussions of gun violence in general, as it seems you are.
Jayschwa 14y ago
> If we have a chance of stopping a rare, unexpected event that would add quite a lot to the expected value of deaths per year, would it not matter significantly in our efforts of stopping it? I wouldn't characterize the number of deaths via mass shootings as "quite a lot". It's probably in the same ballpark as death by lightning strike (~50/year, according to Wikipedia).

SoftwareMaven 14y ago

This was a great article, but I'm not convinced mass shootings are completely independent. Given the media attention, it is very likely that event n+1 was, in some way, impacted by event n. I don't have any evidence to back this up, so I could be (and I hope I am) completely wrong. But if I'm right, then I think it would imply we need to reduce the correlation between events. And it is likely the media that provides that correlation. Instead of reporting about the <insert your word here> that causes these events, report on the impacts of these events. It would, hopefully, stop deifying the perpetrator, which might reduce the likelihood of other perpetrators from doing the same.

jeremyjh 14y ago
There should be some way to formalize this into a hypothesis. Testable with the same data I mean. If you were correct we should see more clustering then we do with a random sample.
- carbocation 14y ago
  Perhaps looking at the time between mass shootings would be more interesting than simply looking at mass shootings per year.
  - vsbuffalo 14y ago
    You'd get weird mixture model type systems. There are certain subclasses: school-based vs non-school-based. You'd have to control for this since school-based shootings are highly temporally correlated. But then maybe there's crossover too. Like everything, estimating these things with more complex models is hard to do right, and findings are usually overstated.
waterlesscloud 14y ago
The media coverage may play a role, but I don't know that it's the entirely the fame angle at work. What if the goal in large part is to inflict the most possible suffering on the world? Out of anger or hurt or whatever the case may be. Then cutting out coverage on the person isn't as important, it's the entirety of the coverage that matters.

jQueryIsAwesome 14y ago

I have flagged this article; is not only link bait using the subject everyone is talking about; is being extremely disingenuous using statistics about a so ambiguous concept as "mass shootings" to draw conclusions about a real world situation.

mitchi 14y ago
I come here to gain knowledge about things related to science and computers. I'm tired of all the "humanities"
- vitalique 14y ago
  I'd say if you are going to learn about or do any kind of serious science, resist putting labels left and right just because you are tired, on this site and elsewhere. There's nothing wrong with humanities in terms of being able to benefit from applying CS to them.
- Tyr42 14y ago
  Hey, this is stats. At least where I'm from, Stats is in the Math faculty. Same as the CS departement.
Daishiman 14y ago
If you actually understood how a Poisson process works and how a hypothesis test works you would understand that his conclusions are very, very much important.

rdl 14y ago

This seems like trying to use a hammer (statistics) because you have a hammer, not because it's the right tool for the job. Essentially, if you look at the incidents, you see enough common factors (increasingly, using semiautomatic carbines, carrying multiple weapons, attacking schools, wearing armor or load bearing gear, etc.) to think there is some common factor at work. The population of random people on the street doesn't pick the AR-15 to do anything, and certainly doesn't pick a school as a target for anything. The solution space here isn't "spree shootings at schools through time", it is traits of spree shootings themselves -- location, methods, etc. They're pretty tightly clustered. Either there is a common hidden factor, or these incidents are feeding on each other. I personally don't think gun control is the major tool to deal with this, and don't think violent video games are the problem, but rather the non-stop multi-day press coverage by the media of each of these incidents. Some insignificant douchebags from a Colorado school became about as famous as the 9/11 terrorists (and far more than fortune 50 CEOs or scientists or classical musicians) by murdering their classmates. (Columbine essentially as as big a deal for the 'how to respond to shootings' world as 9/11 was to aviation security; previously, you cordoned off the area and called in SWAT to negotiate, thinking it was a hostage situation -- now, the first 1-2 responders on scene move directly to the threat with whatever weapons they have on them at the time, ignore any wounded victims, close, and engage/destroy -- similarly, hijacked airliners are now viewed as air to ground missiles vs. hostage negotiations.) Every time the media talks about the shooters in one of these situations, making them famous, it reinforces the rational (if defective) choice of someone who wants to be famous at the cost of doing evil to copycat. The mythological/historical example is Herostratus, who burned the temple of artemis just to be famous.

potatolicious 14y ago
I don't buy this explanation over the alternatives. It's logically sound but is based on the assumption that spree shooters do so in large part to gain infamy and notoriety. Given what we know of spree shooters around the world and in the US, they strike me as predominantly desperate, mentally ill people. We had the Columbine shooters who seemed to be more vengeful than fame-seeking. We had the Aurora shooter who didn't do any grandstanding when apprehended, or in fact talk to the media at all. And of course, we had the Newtown shooter who didn't leave behind any notes, manifestos, or in fact any evidence that he wanted to be infamous (even if posthumously). These don't strike me as people who are driven by the ensuing media coverage. Don't get me wrong - I've been appalled by the news media surrounding the Newtown shooting, particularly CNN's journalistically abhorrent fingering of an innocent individual, but I don't think the coverage is really the crux of it, and I don't think taking it away will stop them.

dizzystar 14y ago

I think a better methodology would be using linear time clusters and measuring the possible impact of the Werther Effect. Look at the regional areas where the news may not have spread out. Look at the attempts that were stopped and see if they clustered. The stopped attempts are probably a better indicator as people, after hearing the news, are naturally more alert to the indicators that something may happen. The other problem with the data is that there is no way, from looking at the graph, if an event happening in December affected an event happening in January, thus delimiting by years is arbitrary.

joe_the_user 14y ago

The question probably requires a more detailed treatment. For example, even the distribution of killings by frequency looked poisson, if the number were uniformly increasing year by year, it would look like a trend.

lostlogin 14y ago

This hits HN as another shooting covers front pages. A new dark twist for extra newsworthiness. http://www.nytimes.com/2012/12/25/nyregion/2-firefighters-killed-in-western-new-york.html?hp&_r=0 http://www.nytimes.com/2012/12/25/nyregion/2-firefighters-ki... Edit: it is unclear at this stage if this event would qualify for inclusion in the numbers according to the criteria in the article. Below are the used criteria. The killings were carried out by a lone shooter. (Except in the case of the Columbine massacre and the Westside Middle School killings, both of which involved two shooters.) The shootings happened during a single incident and in a public place. (Public, except in the case of a party in Crandon, Wisconsin, and another in Seattle.) Crimes primarily related to armed robbery or gang activity are not included. The shooter took the lives of at least four people. An FBI crime classification report identifies an individual as a mass murderer—as opposed to a spree killer or a serial killer—if he kills four or more people in a single incident (not including himself), and typically in a single location. If the shooter died or was hurt from injuries sustained during the incident, he is included in the total victim count. (But we have excluded cases in which there were three fatalities and the shooter also died, per the previous criterion.) We included six so-called "spree killings"—prominent cases that fit closely with our above criteria for mass murder, but in which the killings occurred in multiple locations over a short period of time.

aes256 14y ago

There is absolutely an observed trend of copycat school shootings which flies in the face of randomness. That said, I think this trend is hidden from this dataset because it relates specifically to mass shootings, including only those incidents in which the shooter took the lives of at least four people. I would hypothesize that each major shooting is followed in the succeeding months by a number of slapdash copycat shootings, in many of which less than four people are killed by the shooter.

beloch 14y ago

Mass shootings are rare enough that you're going to get poor stats due to granularity. It might be more interesting to look at stats like homicide rate. The U.S. has a homicide rate that is second only to Russia in the G8, and is more than 3 times higher that of any G8 nation besides Russia. This sets off warning bells for me... Normally I'd love to dig a little deeper, but it's time for me to play Santa. Merry Christmas!

tomjen3 14y ago
The sad truth is that if you exclude innercity slums, themurder rate in the us plummets to mostly normal levels.
- robbiep 14y ago
  Yes, let's exclude statistics in order to normalise them. Because if we cut out the bits of statistics that sway them, we can claim the distribution is the same as elsewhere!
  - d2vid 14y ago
    By grouping statistics into these things we call "countries" we are also "excluding" certain statistics. For instance, why are we ignoring cartel murders just south of the US/Mexican border even though the US drug market is the driving factor? The parent comment is providing a better, more specific grouping that helps shed light on where murders are actually happening in the US and points us towards where we need to focus our efforts if we want to actually change the murder rate in the US. Inner city interventions will result in the greatest improvements to the murder rate, whereas focusing efforts elsewhere has literally zero chance of bringing the murder rate into line with the rest of the G8 because that's not where the murders are happening.
    - robbiep 14y ago
      The parent comment is introducing a new variable which may or may not be useful in, as you suggest, providing targeted approaches to reducing deaths by firearms. It still flies in te face of convention which still treats a whole country as a whole country, in the perhaps naive assumption that by averaging the nations stats you will be able to get a good comparison of what the average citizen puts up with an thus providing a ground for comparison with other average citizens in other nation-states, regardless of their level of development, or even, indeed, if they have 'inner city slums'. And all that is leaving aside the matter of whether the statement is actually true, as questioned by a number of other threads

clarkm 14y ago

Since mass shootings are such a rare events, the data is overdispersed, so a negative binomial distribution is likely more appropriate than a Poisson distribution. This, along with quasi poisson, is commonly used by criminologists to account for such problems. See this paper for a more detailed discussion: http://www.crim.upenn.edu/faculty/papers/berk/regression.pdf http://www.crim.upenn.edu/faculty/papers/berk/regression.pdf

dbecker 14y ago
Deviations from the Poisson distribution are exactly what he is testing for. The paper you referenced discusses how to model in the presence of overdispersion. Not how to test that as a hypothesis. Moreover Poisson distributions are generated from events that occur in a very small fraction of all opportunities, but with many opportunities each time period. So, unless the timing of shootings is correlated (again, the thing he is testing for), this is a perfect use case for the Poisson distribution.

clarkm 14y ago

phaselock 14y ago

The auther does a horrible job. He takes it as an assumption that the reader doesn't know statistics, and when he gets to the actual meat he just states as fact, "i calculate k=32.5 m/j" " what does this mean? It means I'm right" he should as a minimum either assume completely that the reader knows everything nessesary to interpret the hypothesis test or actually make an effort to explain to layman what the p-value means.

RyanZAG 14y ago

All these comments about statistics don't seem to even begin to understand statistics. 1) Yes, we can use the chi-squared test here - the small number of events is built into the p value. 2) No, we do not need to include all murders, as we are not testing for murders. We are testing for mass shootings. This line of reasoning is the same as saying we cannot test for rotten apples only, we can only test if all fruit is rotten. Statistics on categories is acceptable and meaningful if apples are a specific kind of fruit, or mass shootings are a specific kind of crime. We can't draw an conclusion about crime, but we can draw a conclusion about mass shootings. 3) These statistics prove only a single thing: mass shootings in USA are likely random events and have a mean value of ~2. The following conclusions are applicable: - Mass shootings are likely not a 'copycat' crime, and each event is likely completely independent of any other event occurring. - You should expect about 10 mass shootings over the next 5 years. Not so nice... Following conclusions are NOT applicable: - Gun laws have any effect. Gun laws may or may not decrease the average, these statistics do not say. - No measures that have been put in place to reduce mass shootings (I assume there are?) have had any effect so far. They may have had a positive or negative effect, but these effects may be small or may be cancelled out by other, opposite effects. - The chance of a mass shooting is stable, and no increase or decrease in events seems to be happening. The distribution fit test only shows us on the aggregate data, and that it does fit that distribution. The correct way to check for this is to break the data set in half, and compare the first set against the second set. And now we return you to our regular statistics hate... EDIT: Or not - nobody is questioning the real possible problem here: the data itself? http://www.bradycampaign.org/xshare/pdf/major-shootings.pdf http://www.bradycampaign.org/xshare/pdf/major-shootings.pdf This seems to imply there are FAR more mass shootings per year than indicated by the data. None of my conclusions above are correct if the data itself is wrong, and I don't even live in the USA so I can't vouch for the correctness of the data.

RyanZAG 14y ago
I blame Christmas and lack of sleep - I misread the actual article. Article is completely wrong. " ... found a p-value of 0.18. What does this mean? It suggests that there is no evidence of clustering beyond what you would expect from a random process ... " Above is incorrect. What the author is actually testing is the following statement: The mass shooting data points come from a Poisson distribution with an average value of 2 However, the test he is using can only prove this statement to be false: it CANNOT prove that the statement is true. So the only thing the author proved is that the statement may or may not be true. (For more, read up on a null hypotheses, the scientific term for this.) All the author has proven is that there is an 18% chance that the data does not come from a Poisson distribution. ~1 in 5 chance of being wrong is not something you assume to be right. Author needs to learn statistics.

chewxy 14y ago

For anyone who's interested, this blog post piqued a very morbid interest in me, and so I decided to have a look at the data. Here's a distribution of the number of days before the previous incidents (as reported by MotherJones. I'm personally not familiar with the number of shootings in the US, which according to different sources ranges from very few to way too many): http://imgur.com/Onoxv http://imgur.com/Onoxv . The colours represent the group of how many incidents happened in the 180 days prior to the incident. Here is the distribution of the number of incidents 180 days prior to an incident: http://imgur.com/9VTjQ http://imgur.com/9VTjQ Draw your own conclusions

archgoon 14y ago

Kudos to the author for attacking the question this way, it's always important to look at data and try to model it. (and it's a lot of work!) Unfortunately, I'm pretty sure there's a fatal flaw in the analysis. Suppose we had two types of years, both following a Poisson Distributino, but one with a higher incidence, the other with a lower incidence, and they alternated[1]. Now sample each type of year separately. Each will give you a Poisson distribution. To get the distribution of all years you'd just add bins of the two types together. The sum of two poisson distributions is a poisson distribution (with a different mean), therefore, we cannot conclude anything about how the mean value is changing with time (and thus, answering the question: is the incidence rate rising) unless we actually bin the data by year, and see if the mean value is changing with time. Unfortunately, by splitting time up, we reduce the already small sample sizes for each bracket. Time series analysis is a more appropriate tool to tackle this question. [1] This is unchanged if the rate is continuously increasing, the setup was so that you can actually think of collecting the same data over multiple years.

waldrews 14y ago

Statistician here. Saying nothing about the substance of the argument or whether their data source appropriately classifies what counts as this kind of crime, the methodology is on the right track but not optimal. Of course binning the events by year throws away data about specific timing. Having actual event times would allow fitting a hazard rate model. There are two simple alternative hypotheses - explanations for a deviation from the Poisson assumption. What they're calling "random" is really "occuring at a homogeneous rate;" so we have to ask - as opposed to what? 1) clustering/overdispersion, because the events happen more often alongside each other (copycat effect or whatever; risk of a new event is a function of time since last event) 2) secular trend (the rate of events is changing over time) We can't really distinguish between these two without explicitly modeling, and it doesn't look like we have enough data to do that. The tool to do it would be a generalized linear model with an overdispersed Poisson dependent variable. It's kind of bad form to estimate the Poisson mean from the data, and then use that to fit the distribution you're testing against. You're using the data twice, so the p-value isn't what you think it is. You should be conditioning on the total number of events in the sample. Also, chi-square distribution comparison is for large samples. This is a meh-kinda-borderline-midsize sample, to use a technical term. The test they want that has neither of these problems is Fisher's exact test for equal proportions. If the events were generated by a Poisson process, the number in each year would be conditionally binomial, and they'd add up to the total observed event count. The test is: is the data explained by all the years getting events randomly at the same rate (null hypothesis) vs. each year having its own rate (alt hypothesis). And finally, yes, you get a p-value. But you also need to think about the power of the test detect an anomaly if there was one (type II error). For something like this, you could do power analysis by a simple simulation, but you'd need to specify what kind of anomaly you'd want power to detect (e.g. all events cluster together in one year, to pick an extreme). Otherwise, all you have is a design that has a correct p-value. If you reject the null hypothesis at 5%, but you have low power, you might as well toss a coin and declare the data "nonrandom" 5% of of the time. This might be as good a test as we can get with the data available, but p-value isn't the only thing you can look at.

chrisringrose 14y ago

Beware: the whole point of this is article (and train of thought) is to cast a shadow of doubt over gun control. It's to remind us how these are random and extreme events. Yes, mass-shootings are random and extreme. A layperson can conclude this without having to look at any statistics. But unfortunately this distracts from the real problem. Machine guns. And how they're legal, and easy, for anyone to buy. And ammo. And modifications for guns. When the constitution was written to allow citizens the right to bare arms, the only arms in the legislators' wildest dreams took a minute to load one bullet, likely would miss, and probably wouldn't kill with one shot. Since the world is very different today, shouldn't the laws change too? Look at the success of gun control in the United Kingdom. Enough of this nonsense. It reminds me of climate change deniers pointing out "Yeah but it's snowing now."