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Which measures of diversity are used where? When I search for diversity indicators I find the Simpson and Shannon index, but these are both for categorical data. If I have data with some structure (e.g. age), where I can actually define a distance between population members, which diversity measures could I use?

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    $\begingroup$ With a continuous variable we usually talk about variability, scale, dispersion or spread. So: standard deviation, interquartile range, median absolute deviation from the median, Gini's mean difference, or whatever suits the data and the problem. $\endgroup$
    – Nick Cox
    Commented Jan 26, 2021 at 12:26
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    $\begingroup$ The nature of the problem of one drives the selection of the measure of goodness. What is the nature of your problem? How do you think you would tell if the measure of diversity was doing its job? If we were going to compare pseudo sigma Versus entropy, what sorts of things in the problem you were solving would tell us which one would serve better than the other? A bootstrapping-based measure might tell you something about what you should expect from a blind and perfectly equal process. $\endgroup$
    – EngrStudent
    Commented Jan 26, 2021 at 12:47
  • $\begingroup$ Yes, I am also thinking about taking the variance or something like the mean squared distance between members. I would like to know what people in sociology actually use. It seems there are some pretty standard measures for diversity when it comes to categorical data (Simpson or Shannon=Entropy), but I did not find any literature on non-categorical data. It seems I am missing the right code words. I think dispersion was the word I was looking for @NickCox. Thanks $\endgroup$
    – Lochend
    Commented Jan 26, 2021 at 12:52
  • $\begingroup$ It seemslike you want a measure of diversity taking into account the metric structure of a variable like age Maybe have a look at stats.stackexchange.com/questions/483535/… $\endgroup$
    – kjetil b halvorsen ♦
    Commented Nov 11, 2022 at 21:10

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