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I am trying to interpret results for a question asking "which has the most variable abundances" so, I found the coefficient of variation in abundance of all species. Does it make sense to have values of, e.g. 1692.62851? Does that just mean there is a lot of variation?

Here is the code I used:

tapply(ReefFish$count, ReefFish$commonname, function(x) 100*sd(x)/mean(x))

And here is an example of what the results look like:

      Abbott's moray eel           Acanthurus species                Achilles tang 
              1380.81680                   1259.28627                    273.58431 
           Agile chromis               Apogon species           Apogonidae species 
               219.78818                   1743.84983                   1337.90434 
        Arc-eye hawkfish             Banded angelfish                 Banded moray 
               128.28607                    339.85437                   2395.82971 
           Belted wrasse              Bicolor anthias                  Bird wrasse 
               163.22654                   1465.00481                    144.66134 
           Biting blenny            Black triggerfish         Blackbar triggerfish 
               368.99585                    199.68766                    840.54370
Alison
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  • Who is asking and why are they asking? From this being count data we would expect a rather strong correlation between variance and mean abundance. – Roland Sep 15 '21 at 08:39
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    I'd check worrying cases graphically. For abundances that might be zero or at very least very low on occasion, or even often, and very high on occasion, a scale like square root, cube root or log(1 + count) can help. Plot each taxon as both distribution and time series. – Nick Cox Sep 15 '21 at 08:46
  • I just am not very familiar with coefficient of variation. I understand what it means and the concept but not exactly how to interpret the values. Do the examples I listed just mean that they all have a lot of variation from the mean? Which was expected. And say the largest value would just be the species with the most variation? – Alison Sep 15 '21 at 08:49
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    It's a measure of relative variation. Again, the best way to interpret it is to relate different results to different graphs. Look at other threads with the same tag https://stats.stackexchange.com/questions/118497/how-to-interpret-the-coefficient-of-variation – Nick Cox Sep 15 '21 at 09:02
  • A secondary point is that citing more than 3 or 4 significant figures is pointless. – Nick Cox Sep 15 '21 at 09:04
  • I mostly get it but am still kind of confused. I guess does that mean there isn't anything wrong with my code and that those values are accurate? As long as I compare them to each other to interpret them? – Alison Sep 15 '21 at 09:15
  • I am not commenting on your code -- I don't use R routinely -- but on the face of it the code is correct, The questions for anybody's code are whether the code ignores missing values. I am not a biologist but I have often used coefficient of variation and even more often not used it as being not very helpful. That's not mean to be cryptic because in the thread cited a few comments above I discussed the CV at some length. If the CV makes sense, it means you should just be thinking on logarithmic scale. – Nick Cox Sep 15 '21 at 09:23
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    With all interpretation questions here there is a statistical side and a substantive side. If you are a fisheries biologist the interpretation is up to you. If you are learning, fine and the test is to show the data to a fisheries biologist, be prepared for lots of questions, e.g. when and where and how counted. Then the comments should be of the flavour, "Sure, because of this thing about the species or this thing about the environment" or whatever. Or "That's crazy". – Nick Cox Sep 15 '21 at 09:28
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    Please see https://stats.meta.stackexchange.com/questions/3175/top-k-list-of-reasons-to-close-a-question-immediately/4554#4554 on why "How do I interpret this?" can be hard to answer. – Nick Cox Sep 15 '21 at 09:28

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