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> This is misleading if all you're saying is that both Jane and Jill get paid less than 90k. But nobody is saying that. That is a totally normal statement to m

> This is misleading if all you're saying is that both Jane and Jill get paid less than 90k. But nobody is saying that. That is a totally normal statement to make. E.g. 90k > (20k + 30k) It works just as well for the murder rate per 100k residents: 39.80 > (23.14 + 7.01 + 3.39) Detroit > (Chicago + LA + NYC)

jstanley 6y ago
Are you saying that if Chicago,LA,NYC have death rates of 23.14,7.01,3.39 per 100k, then the combined death rate of Chicago, LA, and NYC is 23.14 + 7.01 + 3.39 = 33.54 per 100k? If that's what you're saying, then you're wrong, because the combined death rate of 3 cities would be the number of deaths across 3 cities divided by the number of people across 3 cities. It would not be the number of deaths per 100k in each city added together! If that's not what you're saying, then I don't understand how it can be meaningful to compare those figures.
- hobofan 6y ago
  "Combined" is AFAIK not well defined. You are taking it as the (weighted) average, while I'm taking it as the sum. As which of the two you take it is obviously very context dependent. If someone would ask you what the combined output of two factories per hour is, would you tell them the average? I think it's a very meaningful comparison, as it highlights that there is a severely increased risk of dying of murder in Detroit. To put the same in a different framing: You could live one year in Chicago, one year in LA, one year in NYC and run a lower risk of being murdered than if you were living in Detroit for just one year. Of course this is just one small piece in the overall puzzle of mortality statistics, and might not have a big impact even at elevated levels, but that's a different topic. Such "combined number of second, third, ... places" (= sum) figures are good at quickly highlighting that there must be something out of the ordinary happening, because a smallish deviation of a few percent can not be expressed as a sum of e.g. second and third place. There are of course some other problems with this method of comparing figures (e.g. bias - as a foreigner, I would have assumed a much higher murder rate for NYC), but there is nothing inherently wrong with comparing numbers this way.
  - jstanley 6y ago
    The comparison with time is totally bogus because the amount of time does not change as you add more cities/factories. If someone asked you the combined output of two factories per worker, would you tell them the sum?! If the first factory produces 1 item per hour and the second factory produces 1 item per hour, then combined they are producing 2 items per hour. Agreed. If the first factory produces 5 items with 1 worker and the second factory produces 5 items with 1 worker, then combined they're producing 5 items per worker, not 10 items per worker!
    - hobofan 6y ago
      > The comparison with time is totally bogus because the amount of time does not change as you add more cities/factories. But it does (when we are summing over the time axis)! We always had time built into the unit (deaths/100k people/year), so of course it makes sense to look at it in the context of time by applying specific values for them. > If someone asked you the combined output of two factories per worker, would you tell them the sum?! With that specific vague query, I'd probably ask a follow up question, as I assume that the person asking the question doesn't exactly know how to interpret the number, which is often the case if someone asks for "combined" and "per" in the same sentence. I've helped people build enough BI dashboards to spot when people try to avoid thinking about the data implications behind the operations they think they want to do, and "combine" is one of the top keywords for that. > If the first factory produces 5 items with 1 worker and the second factory produces 5 items with 1 worker, then combined they're producing 5 items per worker, not 10 items per worker! Factory 1 is producing 5 items/worker/hour, just as factory 2 is, so "combined" they are producing 10 items/hour, which is just as valid as your statement. As long as you are mindful with the units and the context, either way is fine.

jstanley 6y ago

Are you saying that if Chicago,LA,NYC have death rates of 23.14,7.01,3.39 per 100k, then the combined death rate of Chicago, LA, and NYC is 23.14 + 7.01 + 3.39 = 33.54 per 100k? If that's what you're saying, then you're wrong, because the combined death rate of 3 cities would be the number of deaths across 3 cities divided by the number of people across 3 cities. It would not be the number of deaths per 100k in each city added together! If that's not what you're saying, then I don't understand how it can be meaningful to compare those figures.

hobofan 6y ago
"Combined" is AFAIK not well defined. You are taking it as the (weighted) average, while I'm taking it as the sum. As which of the two you take it is obviously very context dependent. If someone would ask you what the combined output of two factories per hour is, would you tell them the average? I think it's a very meaningful comparison, as it highlights that there is a severely increased risk of dying of murder in Detroit. To put the same in a different framing: You could live one year in Chicago, one year in LA, one year in NYC and run a lower risk of being murdered than if you were living in Detroit for just one year. Of course this is just one small piece in the overall puzzle of mortality statistics, and might not have a big impact even at elevated levels, but that's a different topic. Such "combined number of second, third, ... places" (= sum) figures are good at quickly highlighting that there must be something out of the ordinary happening, because a smallish deviation of a few percent can not be expressed as a sum of e.g. second and third place. There are of course some other problems with this method of comparing figures (e.g. bias - as a foreigner, I would have assumed a much higher murder rate for NYC), but there is nothing inherently wrong with comparing numbers this way.
- jstanley 6y ago
  The comparison with time is totally bogus because the amount of time does not change as you add more cities/factories. If someone asked you the combined output of two factories per worker, would you tell them the sum?! If the first factory produces 1 item per hour and the second factory produces 1 item per hour, then combined they are producing 2 items per hour. Agreed. If the first factory produces 5 items with 1 worker and the second factory produces 5 items with 1 worker, then combined they're producing 5 items per worker, not 10 items per worker!
  - hobofan 6y ago
    > The comparison with time is totally bogus because the amount of time does not change as you add more cities/factories. But it does (when we are summing over the time axis)! We always had time built into the unit (deaths/100k people/year), so of course it makes sense to look at it in the context of time by applying specific values for them. > If someone asked you the combined output of two factories per worker, would you tell them the sum?! With that specific vague query, I'd probably ask a follow up question, as I assume that the person asking the question doesn't exactly know how to interpret the number, which is often the case if someone asks for "combined" and "per" in the same sentence. I've helped people build enough BI dashboards to spot when people try to avoid thinking about the data implications behind the operations they think they want to do, and "combine" is one of the top keywords for that. > If the first factory produces 5 items with 1 worker and the second factory produces 5 items with 1 worker, then combined they're producing 5 items per worker, not 10 items per worker! Factory 1 is producing 5 items/worker/hour, just as factory 2 is, so "combined" they are producing 10 items/hour, which is just as valid as your statement. As long as you are mindful with the units and the context, either way is fine.