- Statement One (S1): "One in 80 deaths is caused by a car accident."
- Statement Two (S2): "One in 80 people dies as a result of a car accident."
Now, I personally don't see very much difference at all between these two statements. When writing, I would consider them interchangeable to a lay audience. However, I've been challenged on this by two people now, and am looking for some additional perspective.
My default interpretation of S2 is, "Of 80 people drawn uniformly at random from the population of humans, we would expect one of them to die as a result of a car accident"- and I do consider this qualified statement equivalent to S1.
My questions are as follows:
Q1) Is my default interpretation indeed equivalent to Statement One?
Q2) Is unusual or reckless for this to be my default interpretation?
Q3) 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?
Let's put aside the obvious quibble that S1 does not specifically refer to human deaths and assume that that is understood in context. Let us also put aside any discussion of the veracity of the claim itself: it is meant to be illustrative.
As best I can tell, the disagreements I've heard so far seem to center around defaulting to different interpretations of the first and second statement.
For the first, my challengers seem to interpret it as as 1/80 * num_deaths = number of deaths caused by car accidents, but for some reason, default to a different interpretation of the second along the lines of, "if you have any set of 80 people, one of them will die in a car accident" (which is obviously not an equivalent claim). I would think that given their interpretation of S1, their default for S2 would be to read it as (1/80 * num_dead_people = number of people who died in a car accident == number of deaths caused by car accident). I'm not sure why the discrepancy in interpretation (their default for S2 is a much stronger assumption), or if they have some innate statistical sense that I'm in fact lacking.