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Isn't that at odds with the article? Quoting, "The reason is that there are (of course) more students in the larger classes, and so you oversample large classe

by taeric 2y ago

Isn't that at odds with the article? Quoting, "The reason is that there are (of course) more students in the larger classes, and so you oversample large classes when computing the average experience of students." This leans on the experiences of the students, which necessarily leans on the population. (Granted, this is more clearly a different question/scenario.) I'll try and play with the simulation some. And to be clear, I don't disagree with your statements. I just feel these are still different questions/statements. How long I expect to wait at a given trip/stop is not the same as how long I expect I have waited at that stop over the days.

marcosdumay 2y ago
My comment paraphrases what the article says. You seem to be expecting something different from the inspection paradox, but all it says is that the waiting time will be higher than half of the interval between buses. And it only applies when the time between buses is random.
- taeric 2y ago
  One of the things I've found far more often than makes sense, is that many paraphrases also change the statement they are paraphrasing. The article goes out of its way to call out that sampling the average experience of students. This was obviously different in class sizes. Since there are more students than there are classes, it makes sense that the average size of classes that a student attends is different than the average size of classes offered. It isn't that people are giving you two different answers, they are answering two different questions. Also, the article specifically says the waiting time paradox makes a stronger claim that the average will tend specifically to 2N. "But the waiting time paradox makes a stronger claim than this: when the average span between arrivals is N minutes, the average span experienced by riders is 2N minutes. Could this possibly be true?" I'm trying to explore/understand how that works out.
  - marcosdumay 2y ago
    Oh, right. I was focused on the progression, I didn't notice you were talking about a factor of 2 that I forgot there.

by taeric 2y ago

marcosdumay 2y ago

My comment paraphrases what the article says. You seem to be expecting something different from the inspection paradox, but all it says is that the waiting time will be higher than half of the interval between buses. And it only applies when the time between buses is random.

taeric 2y ago
One of the things I've found far more often than makes sense, is that many paraphrases also change the statement they are paraphrasing. The article goes out of its way to call out that sampling the average experience of students. This was obviously different in class sizes. Since there are more students than there are classes, it makes sense that the average size of classes that a student attends is different than the average size of classes offered. It isn't that people are giving you two different answers, they are answering two different questions. Also, the article specifically says the waiting time paradox makes a stronger claim that the average will tend specifically to 2N. "But the waiting time paradox makes a stronger claim than this: when the average span between arrivals is N minutes, the average span experienced by riders is 2N minutes. Could this possibly be true?" I'm trying to explore/understand how that works out.
- marcosdumay 2y ago
  Oh, right. I was focused on the progression, I didn't notice you were talking about a factor of 2 that I forgot there.