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Your point 3 is incorrect. The analysis fails to show that the data observed can be distinguished from data drawn randomly from a Poisson distribution of mean 2.

The double negative here and concept of "distinguishing from" is important. In particular, this result does not rule out being underpowered by which we'd mean to say that given infinite tragic observations we may be able to make a case to distinguish the data from the random distribution, but since we only had a little that effect was buried.

Again, you cannot even say things like "are likely not" and "should expect" because those are epistemologically reversed from what we can state. What we can say, in parallel, is

    - We do not have evidence here suggesting that mass shootings are copycat crimes (if we buy that copycat crimes would lead to non-Poisson distribution of mass shootings).

    - We have not been able to show it flawed to predict 10 mass shootings over the next 5 years.

It's definitely a pain in the ass to rework all your statements this way, but it's also necessary for them to mean anything resembling truth. Statistics is a fickle beast, especially frequentist methods interpreted predictively. This song and dance, however, is required to make the general process of using statistical tests trustworthy enough over time.

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.

All any statistical twst can do is give you a probability. Nothing can be "proven". In any event, the possibilities are not "random" and "not random", e.g. We could be seeing a poisson distribution with a very small copycat effect.

What is pretty clear is that the US has an obscenely high rate of gun violence, which is what we ahould be debating. Several thousand children die each year, and nearly one and a half Sandy Hook's occur each day.

All the author has proven is that there is an 18% chance that the data does not come from a Poisson distribution.

This isn't right either. You've committed the inverse fallacy [1].

The correct way to read that p-value is: "If the data came from a Poisson(2) process, it would be 18% likely to have deviations at least as different from poisson(2) as the observed data."

The test gives no insight into the probability that the true distribution is Poisson or Poisson(2).

[1] http://en.wikipedia.org/wiki/Confusion_of_the_inverse

Worth saying "18% of independent repetitions would be so severe" as well! :)

The Brady list includes many incidents of types excluded by the OP's data source, including gang-related violence, incidents that occurred in non-public locations such as private residences, and cases where fewer people were killed.

The Brady data is flawed because they count folks who likely could shoot each other (e.g. two gangs). Also, it is best to get data from advocates verified by independent sources. I tend to use the CDC or someone who explains clearly their methodology.

>These statistics prove only a single thing: mass shootings in USA are likely random events and have a mean value of ~2.

The whole "it is random" BS is based on the pre-assigned value of 2 per year. Why pre-suppose that 2 per year is an acceptable norm, that is not problematic in itself?

Consider a US with a mean value of 10,000 mass shootings per year, with the occasional 0, 20.000 or 50,000 etc mass shootings fitting the poisson distribution. Using the same methodology as the article, the same "conclusion" would have been reached, that mass shootings are random.

This is a major misunderstanding at what "random" implies in this context. It just means that the motives and decisions at the individual level to "go for it" are triggered independently and with the specific year bearing no influence. That is, it proves that the specific events are not co-ordinated.

This is mighty fine, but it doesn't at all mean that the cultural / law / etc climate that makes even considering an attempt at one of these events possible (much more for a median of 2 a year) is "random" or non changeable by human intervention.

Way to misapply statistics. As they say, there are lies, damned lies, and statistics.

As an extreme example, in a country where there are no guns (either legal or illegal), there would be no mass shootings AT ALL. No "spontaneous random activity" pertaining to mass shootings could change that.

In a similar, but more practical way, if other western countries have a median of about 0 mass shootings per year for decades (with the occasional exception), this tells us that even if the number of mass shootings per year in the US is random, the fact that it has mass shooting at all is not random but a cultural/structural result.

A minor point here, but relevant since the OP is emphasizing the importance of understanding the Poisson distribution - if the mean really was 10,000, any observation outside the range [9,500, 10,500] would be extremely unlikely.

http://en.wikipedia.org/wiki/Poisson_distribution

Thanks, I should correct for that, but don't have the "edit" link anymore.

Why pre-suppose that 2 per year is an acceptable norm, that is not problematic in itself?

No one does. The rest of your comment is a riff on that point, so I won't respond to that. This (brief) analysis was trying to answer the question: are there more mass shootings now than in the past? The answer was no, and that there are about 2 a year.

This point is entirely independent from the question, what can we do to decrease the number of mass shootings?

>The whole "it is random" BS is based on the pre-assigned value of 2 per year. Why pre-suppose that 2 per year is an acceptable norm, that is not problematic in itself?

There is no such presupposition. The way that you estimate the mean parameter in a Poisson distribution is by taking the average over your sample. "2 per year" is not a normative statement; it's an observation of history.

In statistics, you don't get to make a moral judgment when estimating parameters. If you do that, you will get the Wrong Answer.

Apples is a clear easily distinguished subset of fruits wish is useful to predict its taste, expiration date, gastric tolerance, etc.

There is many widely different definitions of what a mass-shooting is (about apples we don't); the article is using a definition from the motherjones website; their definition is strict but randomly chosen; like somebody claiming that only red apples are real apples and the other ones are not; with no data to support that this definition creates any useful subset that can or should be statistically analysed; the statistical sample is already biased by absolutist and arbitrary boolean conditionals which render null any conclusion extracted from its statistical analysis (e.g shooter killed 3 people instead of 4 and therefore is not a mass-shooter)

I actually found the author's comparison to a poisson distribution with a mean of 2 a bit disturbing.

Why should americans expect an average of 2 mass shootings a year? What the heck is wrong with that country that you can expect TWO mass murderings a year?

If you compare the statistics to a poisson distribution with a mean of say, 0 (you know, like most countries, you don't expect ANY mass shootings in a year AT ALL), then you cannot claim randomness any more.

The premise is what bugged me the most - that a mean of 2 is acceptable

You seem to be confused. There's no claim that a mean of 2 is acceptable or anything like that. The fact is that in the last 31 years, we've had 62 mass shootings, and that comes out to an average of 2 per year. You don't get to compare to a Poisson distribution with a mean of zero because you have to use the actual mean, which is 2.

This analysis has nothing to do with whether or not there are too many shootings. It's about whether the shootings occur at a fixed rate, and are independent of each other.

You have it correct in your last sentence although your previous sentence had it quite wrong.

You are correct that the analysis is about whether the shootings occur at a fixed rate. The author had set the expected value of 2 at a given time period, which is to say the author assumes that the 'natural rate' of a mass shooting murder is 2 a year.

The mean across the years has got nothing to do with this IMO. It may have been a good rule of thumb to compare against, but it's not a good one to do an analysis upon. It leads to all sorts of mistaken conclusions, like the one the author made.

You're all partialy wrong. The author wants to test if there is an incrase of mass murders, so he wants to test if the large number of mass murders that occured in 2012 is likely to be due by chance or not. he wants to know if 2012 is an exceptional year or not regarding the average. We dont care what the average is, we want to know if this observed number of mass murder is not likely to be observed regarding the average. His pvalue is small but not small enough to conclude that the distribution of observed mass murders does not fit the model.

No, there's no assumption of "natural rate" or anything like that. The ordinary way of estimating the mean parameter for a Poisson distribution is by taking average value over the sample period (http://en.wikipedia.org/wiki/Poisson_distribution#Maximum_li...).

>The mean across the years has got nothing to do with this IMO.

Well, that's all well and good, but your opinion is irrelevant. This is simply how this statistical tool is used. And crucially, the data fits this model, so objecting to its completely standard parameters is very silly.

take a step back and consider: size of population and history.

Norway has had 0 mass murders since ww2. Yet 18 months ago Norway faced one of the worst mass murdrs in peacetime. Maybe the percentage of people wanting to do such stupid things are the same in Norway as in US, only the population is so small it takes years between everytime there is someone with high enough iq to plan this kind of cruelty and low enough respect of life to actually do it.

Also take a look at Japan. Few shootings but at least during the nineties a couple of attempted mass murders using poisenous gas.

Insanity is distributed fairly evenly across mankind. Access to weapons is not.

weapons are pretty well distributed too. Witness pipe bombs, IEDs, and suicide bombers in very poor / resource poor areas.

Except those areas are also fairly well armed with guns. It just turns out IEDs and suicide bombers are more effective in kill rate than guns in certain situations.

An awful lot of those weapons are provided to those places by outside interests for proxy wars and similar circumstances, at east for more advanced types of weapons. Yes, you can improvise killing tools from a great many things, but the more effective methods tend to be at least somewhat advanced.

Organised terrorism is very different to a lone gunman.

Aum Shinrikyo were a remarkable terrorist cult who achieved pretty scarry things. (https://en.wikipedia.org/wiki/Aum_Shinrikyo)

It's worth noting that the population of Norway is tiny, around 5 million, while the USA has ~310m. At 2 shootings a year for 310m Americans, that suggests something like 1 shooting per 155m; 155m is 31x Norway's 5m, suggesting 1 shooting every >30 years.

Assume a lower base rate, and you make just 1 mass murder in the 67 years since WWII a fairly plausible outcome. I'd note that before Breivik, the previous record-setting mass murder was a South Korean policeman, also a small country not known for violence or crime.