If I have 39% of students at a school that exhibit a specific, objective, measurable behavior, can I extrapolate this and say that any student at that school has a 39% chance of exhibiting that behavior?
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$\begingroup$ If you are a Bayesian, your rationale is correct. $\endgroup$– RPzCommented Jun 25, 2015 at 17:35
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$\begingroup$ Thank you! I didn't know what Bayesian was, but now I do! $\endgroup$– KenCommented Jun 25, 2015 at 17:42
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$\begingroup$ I don't understand what this has to do with a Bayesian interpretation of probability. Could you explain? $\endgroup$– whuber ♦Commented Jun 25, 2015 at 17:56
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$\begingroup$ @rpz Can you explain your answer please? I can think of a number of ways the rationale could be incorrect for a Bayesian (and also ways it might be correct without being Bayesian); what assumptions are you making here for this to be correct if one is a Bayesian? $\endgroup$– Glen_bCommented Jun 25, 2015 at 17:57
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2 Answers
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Let's say that the measurable behavior is gender. In other words, 39% of students at a school are female. If you picked out a student, let's call her Jill, would you say Jill has a 39% of being female? No! She has a 100% probability of being female. However, if someone told you, "I'm going to pick a student out - what's the probability that they're female?" you ought to say 39%.
Another example, if someone told you they were going to pick out a student who has shoulder length hair - what is the probability that they are female? Your answer should likely be higher than 39% (since a large proportion of those with shoulder length hair are female).
In other words, knowing absolutely nothing about the randomly selected student, they have a 39% of being female. But if you knew some other information, the probability changes.
answered Jun 25, 2015 at 17:24
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There is a 39% chance that a student selected at random from the entire population of students at that school exhibits the behavior.
Your wording/extrapolation is very slightly incorrect.
