Argthtjtr

To me "1 in 80 deaths..." is by far the clearer statement. The denominator in your "1 in 80" is the set of all death events and that statement makes it explicit.

There's ambiguity in the "1 in 80 people..." formulation. You really mean "1 in 80 people who dies..." but the statement can just as easily be interpreted as "1 in 80 people now alive..." or similar.

I'm all for being explicit about the reference set in probability or frequency assertions like this. If you're talking about the proportion of deaths, then say "deaths" not "people".

First of all, my first intuitive thought was: "S2 can only be the same as S1 if the traffic death rate stays constant, possibly over decades" - which certainly wouldn't have been a good assumption in the last so many decades. This already hints that one difficulty lies with implicit/unspoken temporal assumptions.

I'd say your statements have the form

1 in $x$ $population$ experience $event$.

In S1, the population are deaths, and the implied temporal specification is at present or "in a suitably large [to have sufficent case numbers] but not too wide time frame [to have approximately constant car accident characteristics] around the present"

In S2, the population are people. And others seem to read this not as "dying people" but as "living people" (which after all, is what people more frequently/longer do).
If you read the population as living people, clearly, not one of every 80 people living now dies "now" of a car accident. So that is read as "when they are dying [possibly decades from now], the cause of death is car accident".

Take home message: always be careful to spell out who your population are and the denominator of fractions in general. (Gerd Gigerenzer has papers about not spelling out the denominator being a major cause of confusion, particularly in statistics and risk communication).

It depends on whether you are describing or predicting.

"1 in 80 people will die in a car accident" is a prediction. Of all the people alive today, some time within their remaining lifetime, one in 80 will die that way.

"1 in 80 deaths are caused by a car accident" is a description. Of all the people who died in a given period (e.g. the time span of a supporting study), 1 in 80 of them did indeed die in a car accident.

Note that the time window here is ambiguous. One sentence implies that the deaths have already occurred; the other implies they will occur some day. One sentence implies that your baseline population is people who have died (and who were alive before that); the other implies a baseline population of people who are alive today (and will die eventually).

These are actually different statements entirely, and only one of them is probably supported by your source data.

On a side note, the ambiguity arises from a mismatch between the state of being a person (which happens continuously) and the event of dying (which happens at a point in time). Whenever you combine things in this way you get something that is similarly ambiguous. You can instantly resolve the ambiguity by using two events instead of one state and one event; for example, "Of each 80 people who are born, 1 dies in a car accident."

The two statements are different because of sampling bias, because car accidents are more likely to occur when people are young.

Let's make this more concrete by positing an unrealistic scenario.

Consider the two statements:

• One half of all deaths are caused by a car accident.


• One half of all people alive today will die in a car accident.

We will show that these two statements are not the same.

Let's simplify things greatly and suppose that everybody born will either
die of a heart attack at age 80 or a car accident at age 40. Further, let's suppose that the first statement above holds, and that we're in a steady state population, so deaths balance births. Then there will be three populations of humans, all equally large.

• People under 40 who will die of a car accident.


• People under 40 who will die of a heart attack.


• People over 40 who will die of a heart attack.

These three populations have to be equally large, because the rate of people dying in car accidents (from the first population above) and the rate of people dying in heart attacks (from the third population above) are equal.

Why are they equal? The number of people who die in car accidents each year is $1/40$ of the number of people in the first population, and the number of people who die by heart attacks is $1/40$ of the number of people in the third population, so the two populations have to have equal size. Further, the second population is the same size as the third (because the third population is the second, 40 years later).

So in this case, only one third of all people alive today will die in a car accident, so the two statements are not the same.

In real life, my impression is that car accidents occur at a significantly younger age than most other causes of death. If this is the case, there will be a substantial difference between the numbers in your statement one and two.

If you modified the second statement to

• One half of all people born will die in a car accident,

then under the assumption of a steady state population, the two statements would be equivalent. But of course, in the real world we don't have a steady state population, and a similar (although more complicated) argument shows that for a growing, or shrinking, population, sampling bias still makes these two statements different.

Is my default interpretation indeed equivalent to Statement One?

No.

Let's say we have 800 people. 400 died: 5 from a car crash, the other 395 forgot to breathe. S1 is now true: 5/400=1/80. S2 is false: 5/800!=1/80.

The problem is that technically S2 is ambiguous because it doesn't specify how many deaths there were in total, while S1 does. Alternately, S1 has one more piece of information (total deaths) and one less piece of information (total people). Taken at face value, they describe different ratios.

Is unusual or reckless for this to be my default interpretation?

I actually disagree with your interpretation, but I think it doesn't matter. Likely, context would make it obvious what is meant.

• On the one hand, obviously all people die, thus it is implicit that total people = total deaths. So if you are discussing rates of death in general, your default interpretation applies.


• On the other, if you are discussing a limited data set in which it is not a given that everybody dies, my interpretation above is more accurate. But it seems not hard for the reader to overlook this.

You might ask where you could possibly encounter people who don't die. For one, we could be working with a statistical dataset that only tracks people for 5 years, so the one ones still alive at the end of the study must be ignored, as it's not known what they will die from. Alternatively, the cause of death may be unknown, in which case you can't really assign it to cars or not cars.

If you do think S1 and S2 different, such that to state the second when one means the first is misleading/incorrect, could you please provide a fully-qualified revision of S2 that is equivalent?

"One in 80 people who die, does so as a result of a car accident." which amounts to rephrasing S1.

I would agree that your interpretation of the second statement is consistent with the first statement. I would also agree that it's a perfectly reasonable interpretation of the second statement. That being said, the second statement is much more ambiguous.

The second statement can also be interpreted as:

• Given a sample of individuals in a recent car accident, 1/80 died.


• Given a population sample at large, 1/80 will die because of factors related to a car accident, some of them being the accidents themselves, but some others being suicide, injuries, medical malpractice, vigilante justice, etc.


• Extrapolating current safety trends indicates that 1/80 people alive today will die because of a car accident.

The second and third interpretations above might be close enough for lay audiences, but the first one is pretty substantially different.

The basic difference is that the two statements refer to different populations of humans, and different time frames.

"One in 80 deaths is caused by a car accident" presumably refers to the proportion of deaths in some fairly limited time period (say one year). Since the proportion of the total population using cars, and the safety record of the cars, have both changed significantly over time, the statement doesn't make any sense unless you state what time interval it refers to. (As a ridiculous example, it would clearly have been completely wrong for the year 1919, considering the level of car ownership and use in the total population at that time). Note, the "proportion of the total population using cars" in the above is actually a mistake - it should be "the proportion of people who will die in the near future using cars" and that is going to be skewed by the fact that young and old people have different probabilities of dying from non-accident-related causes, and also have different amounts of car use.

"One in 80 people dies as a result of a car accident" presumably refers to all humans who are currently alive in some region, and their eventual cause of death at some unknown future time. Since the prevalence and safety of car travel will almost certainly change within their lifetimes (say within the next 100 years, for today's new-born infants) this is a very different statement from the first one.

A1) Assuming everyone dies, and assuming the context of a sufficiently small period of time around that which the measurements were taken, yes, your interpretation of S2 matches S1.

A2) Yes, your interpretation of S2 is reckless. S2 can be interpreted as "1 in 80 people involved in car accidents die" which is obviously not equivalent to S1. Therefore using S2 could cause confusion.

Your interpretation of 1 in 80 is reasonable, though, and the other interpretation (1 in any 80) is very unusual. "1 in N of U is P" is a very common shorthand for "given a predicate, P, and N random samples, x, from universe U, the expected number of samples such that P(x) is true approximately equals 1".

A3) Out if all people, 1 in 80 dies as a result of a car accident.

Yes, it is wrong, and neither phrasing seems sufficient to consistently convey your desired meaning

Speaking as a layperson, if your target is laypeople, I would definitely recommend posting over at https://english.stackexchange.com/, rather than here - your question took me a few reads to unentangle what S1 & S2 intuitively mean to me vs. what you meant to say.

For the record, my interpretations of each statement:

• (S1) - per 80 deaths, 1 death by car accident




• (S2) - per 80 people in a car accident, 1 death

To convey your meaning, I would likely use a modified S2: "One in 80 people will die in a car accident."

This still contains some ambiguity, but keeps a similar brevity.