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(Please note that this is all hypothetical at this point and the data specifics should not matter that much).

Let's say I have a dataset where participants took a certain amount of time to complete a task (x-axis below). These participants naturally separated into two rough groups: those who took about 4 seconds and those who took about 11 seconds. If I want to label participants as either "slow" or "fast", how could I reasonably do this? What is this sort of binning called? What papers should I start with reading? etc.

For the purpose of this question, assume the grouping is meaningful and I have a good idea of what caused it.

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    $\begingroup$ I don't think this is anything to do with binning as usually understood. If it's sufficient to detect the modes and the antimode between them, a graph like that you've drawn is a good method. $\endgroup$
    – Nick Cox
    Commented Jan 15 at 17:58
  • $\begingroup$ But if I want to label data as belonging to one group or the other, what is the best way to create a cut-off? I assume doing it by eye is insufficient and there must be some modelling technique that can do do? $\endgroup$
    – grace.cutler
    Commented Jan 15 at 18:03
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    $\begingroup$ Why assume that doing by eye is insufficient? A better approach would need a direct specification of the generating process. If you don't have one, then use the data directly. Any way, what is the gain from verbal labels? $\endgroup$
    – Nick Cox
    Commented Jan 15 at 18:16
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    $\begingroup$ Are you perhaps asking about how to cluster univariate data? $\endgroup$
    – whuber ♦
    Commented Jan 15 at 20:49
  • $\begingroup$ Clustering is all too likely to make a small group out of the rightmost tail, not what is wanted here. Working with log time or 1 / time might improve matters. $\endgroup$
    – Nick Cox
    Commented Jan 16 at 1:32

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