Another shooting in the USA. Remind me about the reason for having guns again.

Al_B on 7/9/2012 at 08:35

Speaking as someone who never liked statistics, why not?

If all other factors are equivalent between the two countries including population level, social conditions, legal issues such as speed limits, insurance provisions, etc. then surely your correllation could indicate causation in this instance?

SubJeff on 7/9/2012 at 08:53

(http://lmgtfy.com/?q=correlation+vs+causation) I think you find this helps.

Unless you have erased all other forms of confounding you cannot even begin to suggest it. You have to have ALL factors equivalent, and even then you need to prove a causal link.

Two dogs from the same litter are the same weight and eat the same food and sleep in the same place. One has a black eye patch, the other doesn't. One is hit and killed by a car when crossing the road. All factors except the eye patch are the same, and yet you cannot link the death to the presence or not of the eye patch, can you?

Vivian on 7/9/2012 at 09:05

Hey, hang on a minute. You use correlation to test hypotheses of causation. Lack of correlation does go a long way to disproving causation. The opposite is not strictly true unless you have a solid hypothesis of causation, but correlation is certainly used to justify putative causative relationships if you have that plausible mechanism. In this case, there is a pretty obvious causative mechanism (guns allow people to shoot people, therefore more people with more guns will = more people getting more shot) but that is not supported by LarryGs analysis of the data. Could mean either the analysis is flawed, the data is flawed, or the causative hypothesis is false, and that's where we get into academic bitching, but his idea is solid.

In your example you can't disprove the hypothesis that the eyepatch was a causative factor in the dogs death. Common sense comes in a bit obvs, but technically that would still be a valid hypothesis until you had more data from dogs without eyepatches being hit by cats in similar situations and could prove a lack of correlation between eyepatchs and being hit by a car.

DDL on 7/9/2012 at 09:09

It was a pretty terrible graph anyway (don't use line plots for independent countries sorted by different criteria, for instance. Also, don't label the x-axis with arbitrary numbers when it's actually a list of countries).

It's a fun dataset, though. If you take a smattering of western countries, and sort them by firearm ownership and normalise them all to the highest value (so I don't have to go around re-plotting all the different data ranges), you can get some amusing charts.

(http://s11.postimage.org/8ojaaiuwh/Comedy_Gunstats_1.jpg) Gunstats 1

(http://s10.postimage.org/bg9wn14on/Comedy_Gunstats_2.jpg) Gunstats 2

Though if you do it as a percentage of homicides due to firearms, the correlation isn't really there: seems italy and switzerland really like them some gun murders, even though they don't have many guns (or indeed, that many people).

And plotting homicide rates against gun ownership rates gives a graph that almost looks like a correlation but is really just two datapoints: 'america' and 'everyone else'.

(http://s11.postimage.org/w0q81yjn5/Comedy_Gunstats_3.jpg) Gunstats 3

(can you guess which point is the US? :))

SubJeff on 7/9/2012 at 09:20

DDL, your images appear broken.

Vivian - we already know that there is no correlation between number of guns/pop and number of gun deaths. I accept that correlation is a useful tool in establishing causation but it's not an instant answer because you need that mechanism. I don't agree that your mechanism - "guns allow people to shoot people, therefore more people with more guns will = more people getting more shot" - is good enough because we have examples of the opposite, both ways, in other countries.

Thirith on 7/9/2012 at 09:20

Quote Posted by DDL

Though if you do it as a percentage of homicides due to firearms, the correlation isn't really there: seems italy and switzerland really like them some gun murders, even though they don't have many guns (or indeed, that many people).

Minor correction: while Switzerland may have low gun ownership numbers, the majority of Swiss males between 18 and 40 have an automatic rifle at home, given to them for their military service. They're not supposed to have bullets for those guns, but apparently it's relatively easy to smuggle out some ammo when you do your annual or biannual military refresher course. (Can't speak about any of this from first-hand experience, as I only became Swiss at the age of 30, and at that point I no longer had to do the compulsory military service.)

Vivian on 7/9/2012 at 09:21

As a hypothesis for testing, what's wrong with it? It's the basic assumption under analysis, isn't it?

Al_B on 7/9/2012 at 09:22

Quote Posted by Subjective Effect

Unless you have erased all other forms of confounding you cannot even begin to suggest it. You have to have ALL factors equivalent, and even then you need to prove a causal link.

Of course - which is why I stated that all other factors were equal. Your example about dogs is simply due to the sample set size. If a million dogs have a black eye patch and a million dogs don't but for some unknown reason a very high percentage of dogs with the eye patch get killed by cars compared with the ones without the patch then I'd also suggest there's some causation factor at work.

Chimpy Chompy on 7/9/2012 at 09:31

It's been a long time since A-level statistics (which I hated. Seriously, worst part of maths) so I can't do Larry's analysis. But the original data has the %ages of murders done with guns. So I thought I'd convert to total murders and churn out some scatter plots.

Upper plot is the whole world and excel's basic linear line of best fit has only a very gentle negative slope.

The lower one is just western europe and other wealthy nations (US, Canada, Auz, NZ, Japan).

Inline Image:

http://img268.imageshack.us/img268/263/chimpydoesgunnumbers.png

[edit]labels a bit clearer now

SubJeff on 7/9/2012 at 09:53

Quote Posted by Al_B

If a million dogs have a black eye patch and a million dogs don't but for some unknown reason a very high percentage of dogs with the eye patch get killed by cars compared with the ones without the patch then I'd also suggest there's some causation factor at work.

Certainly. But is the causation the fact of having an eye patch in and of itself (which would clearly seem ridiculous) or something else related to it? This could be anything from having an eye patch being linked to a genetic abnormality with hearing to the host nation having some weird luck/superstition thing with eye patches meaning the owners "sacrifice" them to the Gods Of The Road.

Vivan - it's a fine hypothesis for testing, I just don't think that there is anything in it.