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Can any statisticians comment why total population is taken into account when only a portion actually participates in said activities?

ch4s3 10y ago
I think it's so that you can more easily compare things apples to apples.
- gwern 10y ago
  I think it's just hard to estimate. How many visits-to-the-beach go into that shark attack number? It'd be useful to know the per-visit risk for the same reason it'd be useful to know the per-mile risk for driving, but is harder to estimate: "It’s important to be aware, however, that being based on population-level data, the micromort is not a measure of your personal risk. For example, the risk calculation for fatal shark attacks is based on the average risk across the whole population. So it effectively estimates a risk based on the assumption that all Australians swim in the deep ocean a similar number of times per year. But if you live in Alice Springs, you would not expect your risk of being killed by a shark to be the same as for a surfer who lives on the coast. Similarly, if you only wade in water up to your knees and don’t swim in deep water, your personal risks would be different."
- jpttsn 10y ago
  Which sort of amounts to treating oranges as apples in the case. I always find it super silly when people apply population data to themselves. There's always much better data to go on if you know a bit about the individual.
ramblenode 10y ago
As others have said, possibly to make very disparate events comparable across a population, like the risk of skydiving vs. a shark attack. Unfortunately, this results in an almost useless measure for any particular individual when the probability of being in a risk group is small. Here is a breakdown of the risk for a random person in the US dying from skydiving in 2012 [0]: (1 death / 100,000 jumps) x (3 million jumps / 350,000 jumpers) x (350,000 jumpers / 313 million people) The last two terms give us the prior P(jump) ~= 0.01 and the first is the conditional probability P(death | jump) ~= 0.0001. The non-skydiver's risk factor is, of course, zero while the skydiver's risk is about 100x greater than that of the average person (who doesn't actually exist). As you can see, the population measure isn't very informative for either group. [0] http://adventure.howstuffworks.com/skydiving8.htm http://adventure.howstuffworks.com/skydiving8.htm
laughfactory 10y ago
As a statistician once told me: "the odds of running into a grizzly bear are miniscule, but if you're the one who runs into it, they're 100%." So it's important to remember that when evaluating odds and probability. Many things are unlikely to occur, but they do occur to some. I realize this is only tangential to your question, but wanted to put it out there.
- k__ 10y ago
  Fair enough. But wouldn't it make sense to group people who are risk aware together? Like 90% of a population will live risk free lifes, and only 10% have high risk. I mean, depending how risk friendly 10% of the population are, they could screw up the result and then it seems all people of that population are crazier than most of them really are...
imh 10y ago
Lots of answers about apples-to-applesness, and such, but from a very practical viewpoint, the "said activities" part of "participating in said activities" is hard to define and measure. Should you condition on swimming, swimming in the ocean, swimming in the ocean in california, swimming in the ocean in the Santa Cruz area, or swimming in the ocean at Año Nuevo (or even some part of that beach)? However you decide to break it down, do you even have that data? In stats, lots of questions begin and end with "do you have data on that?"

ch4s3 10y ago

I think it's so that you can more easily compare things apples to apples.

gwern 10y ago
I think it's just hard to estimate. How many visits-to-the-beach go into that shark attack number? It'd be useful to know the per-visit risk for the same reason it'd be useful to know the per-mile risk for driving, but is harder to estimate: "It’s important to be aware, however, that being based on population-level data, the micromort is not a measure of your personal risk. For example, the risk calculation for fatal shark attacks is based on the average risk across the whole population. So it effectively estimates a risk based on the assumption that all Australians swim in the deep ocean a similar number of times per year. But if you live in Alice Springs, you would not expect your risk of being killed by a shark to be the same as for a surfer who lives on the coast. Similarly, if you only wade in water up to your knees and don’t swim in deep water, your personal risks would be different."
jpttsn 10y ago
Which sort of amounts to treating oranges as apples in the case. I always find it super silly when people apply population data to themselves. There's always much better data to go on if you know a bit about the individual.

ramblenode 10y ago

As others have said, possibly to make very disparate events comparable across a population, like the risk of skydiving vs. a shark attack. Unfortunately, this results in an almost useless measure for any particular individual when the probability of being in a risk group is small. Here is a breakdown of the risk for a random person in the US dying from skydiving in 2012 [0]: (1 death / 100,000 jumps) x (3 million jumps / 350,000 jumpers) x (350,000 jumpers / 313 million people) The last two terms give us the prior P(jump) ~= 0.01 and the first is the conditional probability P(death | jump) ~= 0.0001. The non-skydiver's risk factor is, of course, zero while the skydiver's risk is about 100x greater than that of the average person (who doesn't actually exist). As you can see, the population measure isn't very informative for either group. [0] http://adventure.howstuffworks.com/skydiving8.htm http://adventure.howstuffworks.com/skydiving8.htm

laughfactory 10y ago

As a statistician once told me: "the odds of running into a grizzly bear are miniscule, but if you're the one who runs into it, they're 100%." So it's important to remember that when evaluating odds and probability. Many things are unlikely to occur, but they do occur to some. I realize this is only tangential to your question, but wanted to put it out there.

k__ 10y ago
Fair enough. But wouldn't it make sense to group people who are risk aware together? Like 90% of a population will live risk free lifes, and only 10% have high risk. I mean, depending how risk friendly 10% of the population are, they could screw up the result and then it seems all people of that population are crazier than most of them really are...

imh 10y ago

Lots of answers about apples-to-applesness, and such, but from a very practical viewpoint, the "said activities" part of "participating in said activities" is hard to define and measure. Should you condition on swimming, swimming in the ocean, swimming in the ocean in california, swimming in the ocean in the Santa Cruz area, or swimming in the ocean at Año Nuevo (or even some part of that beach)? However you decide to break it down, do you even have that data? In stats, lots of questions begin and end with "do you have data on that?"