5 ms·

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 event

by 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.
- Tloewald 14y ago
  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.
- dbecker 14y ago
  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 http://en.wikipedia.org/wiki/Confusion_of_the_inverse
  - tel 14y ago
    Worth saying "18% of independent repetitions would be so severe" as well! :)
DennisP 14y ago
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.
chewxy 14y ago
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
- mistercow 14y ago
  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.
  - chewxy 14y ago
    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.
    - mykosmos 14y ago
      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.
tel 14y ago
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.
pretoriusB 14y ago
>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.
- svantana 14y ago
  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 http://en.wikipedia.org/wiki/Poisson_distribution
  - pretoriusB 14y ago
    Thanks, I should correct for that, but don't have the "edit" link anymore.
- 14y ago
protomyth 14y ago
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.
jQueryIsAwesome 14y ago
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)

by RyanZAG 14y ago

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.

Tloewald 14y ago
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.
dbecker 14y ago
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 http://en.wikipedia.org/wiki/Confusion_of_the_inverse
- tel 14y ago
  Worth saying "18% of independent repetitions would be so severe" as well! :)

DennisP 14y ago

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.

chewxy 14y ago

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

mistercow 14y ago
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.
- chewxy 14y ago
  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.
  - mykosmos 14y ago
    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.

tel 14y ago

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.

pretoriusB 14y ago

>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.

svantana 14y ago
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 http://en.wikipedia.org/wiki/Poisson_distribution
- pretoriusB 14y ago
  Thanks, I should correct for that, but don't have the "edit" link anymore.
14y ago

protomyth 14y ago

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.

jQueryIsAwesome 14y ago

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)