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I have human perceptual data measured in a continuous scale. I am however not sure that the underlying variable being measures is in reality continuous, in fact I believe it might be a discrete scale.

For example, I ask people how fragile they perceive an object to be, with 0 being not at all, and 100 the most fragile. It is unlikely that people are perfectly capable of making this judgement, since there are only so many just noticeable differences for fragility. Instead, they'll likely distinguish between a few levels of fragility.

I do however not know how many discrete options there should be.

I was wondering if there was some form of analysis magic to find out an optimal or *estimated *number of discrete options that is a better reflection of the 'true underlying' variable being measured.

If this question is completely offtopic for this board, please tell me where I could better ask this question.

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    $\begingroup$ This is optimal binning task. If you have an external criterion variable to guide the discretization than one kind of methods should be used. If you don't have then other kind of methods should be used. $\endgroup$ – ttnphns Dec 18 '18 at 10:30
  • $\begingroup$ @ttnphns Can you elaborate on this external criterion variable? Or a source on optimal binning tasks? I'm only finding too-high level explanations $\endgroup$ – Mitchell van Zuylen Dec 18 '18 at 10:52

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