| Okay... let’s try this way. Assume we know a) the total number of miles driven in a year by sober humans and b) the number of traffic fatalities by sober humans over a year. (The year part isn’t actually important for this, it could be for all time as far as this is concerned — what is important is the miles). Your observations are the number of miles. Time doesn’t play into this, but you could do the same calculation by hours driven or number of trips, if you have that data. Hours driven and mileage driven are going to be pretty well related, so let’s just use that. Let’s say this rate is 1 fatality every 100 million miles. Your question is now: given that we’ve observed one fatality in 3 million miles driven for Uber — is the rate for Uber worse than the rate for humans? (Null hypothesis is that the rates are the same). Another way of saying this is - given the rate of one fatality per 100m miles, what is the likelihood that we’d see one fatality in 3m miles? If you want to estimate the number of fatalities that will happen over the next X million miles driven, you’d use the Poisson distribution, because this is a rare event over a long time span (or mile-span in this case). Plug in the rate, the number of miles, and you can get a pvalue for each fatality count: none, 1 fatality, 2 fatalities, etc...). Given this rate (1/100m), you can also calculate the likelihood that there would be 1 fatality in 3 million miles. Turns out, it’s not that likely — suggesting that the fatality rate for Uber is higher than humans [0]. It doesn’t say what the rate is exactly, just that it is likely to be higher. Now it’s possible that the Uber rate is the same as humans, just not all that likely. https://news.ycombinator.com/item?id=16684764 |