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Is it possible to calculate a diversity index (Simpson's or eventually Shannon's index) from ordinal data?

As in, we surveyed 50 transects and recorded several species' "abundance" in 4 categories (e.g., 0, from 1 to 5 individuals, from 6 to 10 individuals, from 11 to 20 etc; it's not the case though, but a mere example).

Is it possible to apply a diversity index to these data?

kjetil b halvorsen
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GManono
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    Your data recording method coarsens the data. Worse, the bins are not even disjoint. Which bin does an observation of 5 individuals go into? You still have categories you can use for calculation. Your sites and your transects can be compared with each other, which is probably your main goal any way. – Nick Cox Sep 05 '21 at 08:42
  • The bins were an example, just so you get the idea without getting into further details. – GManono Sep 05 '21 at 15:43
  • I would use social catregories like race & ethnicity, sexual orientation, or religious affiliation as an example: really highlights a motivational use of such measures. Aside: "diversity" with respect to what standard? Uniform distribution (all categories equally represented), or to some population's distribution (e.g., the most recent U.S. Census for some American locality)? – Alexis Sep 05 '21 at 16:30
  • @Alexis My bad, I meant "semi quantitative" data. We basically have a set of 80 species which we were looking for during each transect. The transect being underwater, we had limited time and decided to estimate the species abundance instead of counting each individuals (e.g. 0 : the species is absent, 1: few individuals are present, 3: more than 20, and 4: more than 50). It is therefore possible to evaluate the transects' "richness" but I don't know if it's possible to estimate shannon's (or simpson's) biodiversity index, as the formula takes the number of individuals into account. – GManono Sep 05 '21 at 17:06
  • Have you checked this thread?https://www.researchgate.net/post/calculating_diversity_from_rank-score_data – panda Sep 05 '21 at 17:45
  • Ah! You mean ordinal data. :) – Alexis Sep 05 '21 at 17:57
  • Your zero has the same meaning as anybody else's. Otherwise it seems to me that your codes 1 2 3 can be used to calculate analogs but not approximations of any index you care to name. There is probably literature on this as ordinal schemes used to be (e.g.) popular (even standard) with plant ecologists. But if you're not counting individuals or measuring cover or abundance you can't get close to Simpson or Shannon. There are real ecologists here; you need their attention. – Nick Cox Sep 05 '21 at 18:09
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    Ah yes, that's it! My bad, I must have badly translated what I meant. Thank you @Panda and @Alexis! – GManono Sep 07 '21 at 04:25
  • Yes, see https://stats.stackexchange.com/questions/44783/measuring-divisiveness-in-film-scores/581407#581407 @Alexis – kjetil b halvorsen Jul 12 '22 at 02:51

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