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I was reading an article on the RSS website where they discussed some top statistics of 2017. One of them was an apparently viral tweet from Kim Kardashian that compares deaths from lawn mower accidents and falling out of bed with terror related acts. The link for this article is here.
I've seen this type of comparison many times on the news; their main point was that we don't need to be afraid of terrorist attacks because when you look at the data, the probability of being killed by a terrorist is so much lower than being killed by a lawn mower (in this case).
However, I feel like this comparison is not correct. I'm not a statistician, and my knowledge of probability is very shaky, but there must be another way of making this comparison.

I would like to know if there is indeed a more accurate way of comparing these things.

For example, a death from a lawn mower is most likely an accident. There are many additional factors about each event that we don't know about. Such as, was the person drunk at the time, was the machine modified etc. Also, for so many people who do not have lawns, this is almost a non-risk.

However a terrorist related event is very random, it's intentional, the aim is to kill as many as possible in a single time period and there is a whole international effort to prevent these events. I'm sure there are not many people out there whose job it is to prevent deaths from lawn mower accidents.
So taking some of these factors into account, it seems that there should be a better way to compare these events.

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    $\begingroup$ If you live in a condo or apartment in the city and like to compete in marathons and other mass races, then lawn mower statistics is irrelevant to you, while terrorist threat is relevant. Also, following that logic we shouldn't worry about Ebola. We're not going to get sick, some folks in remote places will, so who cares? Let them deal with it. Right? $\endgroup$ – Aksakal Jan 25 '18 at 3:29
  • $\begingroup$ I'm not sure what is your point in the comment? If Ebola is not active in my region, then I would not worry about. I would still care, but that's not the point of the question. My question is more about how one would compare such events as death from a lawn mower accident with deaths from terrorist attack. If these type of comparisons should not be made, then is there a technical/statistical reason why not? $\endgroup$ – jmich738 Jan 25 '18 at 3:48
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    $\begingroup$ many reasons. if you look at the argument made in these comparisons it's usually: death rate from terrorism is low -> the threat is low -> don't worry about it. the flaw in the argument is what economists call endogeneity. I could argue that the death rate is low precisely because we worry a great deal about terrorism and actively fight it. so the threat is actually quite significant, but because we fight it the death toll is low lately in US. However, 3000 dead and 6000 wounded in 9/11 should remind us of what may happen if we stop worrying about the threat $\endgroup$ – Aksakal Jan 25 '18 at 4:09
  • $\begingroup$ Thank you for that. This gives me a topic to read up on and have a more robust foundation for my argument. $\endgroup$ – jmich738 Jan 25 '18 at 4:45
  • $\begingroup$ Notice that same arguments apply to terrorism, e.g. if you live in the rural area or suburbs and do not visit city centers then the risk for you is also small etc. But even if you compared the lawn mover owners that live in the cities, then you’d probably find that they have greater risk of dying because of lawn mover accident rather then terrorism. Same as you’re more likely to die in car crash then airplane crash, but people talk more about plane crashes. $\endgroup$ – Tim Jan 25 '18 at 16:04
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The RSS comment only holds if you put all the humans from the same country they pick these numbers from and consider them all equally exposed to the same risks (they look at it as a risk for a population). You can use these numbers to implement strategies to reduce mortality in this population (for example, invest more on preventing lawn mower deaths). This is what governments (should) do (taking into account previous funding and how this funding translates into survival rate) when they decide of the budget they want to allocate to road mortality, suicide or cancer prevention.

People that do not mow the lawn and do not walk nearby land mowers have more chances to get killed in terrorist attacks than by mowing the lawn if they behave exactly like everyone else for the rest, since their probability of getting killed by a lawnmower is 0 (you look at it as a risk for a particular group of individuals within your population). This is the numbers you should use if you want to stay alive longer (for example, if you are a base jumper you should probably stop base jumping) because the general population statistics will poorly describe the risks you are exposed to as an individual.

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