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For this data, I am looking at the relationship between bee population (1000s of bees) and area of genetically modified crops (km2).

I have generated a scatter graph using this data:

https://i.imgur.com/1xnpSBN.png

Question:

What is the most appropriate correlation method to use here?

In my opinion, there does not seem to be a monotonic relationship between the data. Therefore, is this data parametric, therefore follows a normal distribution? Therefore, out of three types of correlation (Pearson, Spearman, Kendall), is Pearson the most appropriate method to use for this data?

Maybe I am incorrect in my assumptions. Perhaps you can help?

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    $\begingroup$ There does not seem to be any correlation between the variables, nonetheless the data is very linear so Pearson's coefficient is OK. $\endgroup$ – user2974951 Oct 15 '18 at 11:31
  • $\begingroup$ Hi. How did you come to that conclusion looking at the graph? Please explain so I understand. Thank you. $\endgroup$ – Erstwhistle Oct 15 '18 at 11:32
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    $\begingroup$ Pearson correlation doesn't assume normality (unless you want to conduct inference - p-values, ... - using certain methods), it's just a measure of linear relationship. A flat line seems like a good fit to your data. X has different values, y just seems to be fluctuating about a flat line. At low, medium and high x, the average y appears to be just about the same. So if you have a dead flat linear relationship, Pearson correlation is adequate for quantifying it, you should get a correlation close to zero. $\endgroup$ – Heteroskedastic Jim Oct 15 '18 at 11:47
  • $\begingroup$ To confirm, if I used Spearman or Kendall, that would be incorrect? Also, what type of variable is bees and area of genetically modified crop? Interval, Ratio, Ordinal or Nominal? $\endgroup$ – Erstwhistle Oct 15 '18 at 11:50
  • $\begingroup$ No, they would both be correct, however since these two measures are non-parametric they are less correct than Pearson's, in the sense that they have lesser power. As for the data, show us a sample of it, but it looks like both are numeric / ratio. $\endgroup$ – user2974951 Oct 15 '18 at 11:58
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First, this sentence

Therefore, is this data parametric, therefore follows a normal distribution?

doesn't make much sense. Data can't be parametric or nonparametric, only models can. And, since the data have two variables, it's not clear what you mean by "follows a normal distribution" do you mean multivariate normality?

Second, looking at the lot, it looks pretty monotonic to me. You have a flat line with one outlier in the top right. So, what type of correlation you want depends on how you want to treat that outlier.

Pearson's regression will give that point a lot of weight. For most purposes, that's going to give an inaccurate view of the relationship. Either Kendall's or Spearman's will give it less weight.

But a bigger question is whether you want any measure of correlation. That is, will any single number give a reasonable description of your data? I think the answer is "no".

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  • $\begingroup$ Hello. I think Kendall is most appropriate in this situation because it is not affected by outliers as much as the other types of correlation. Do you agree? Also, to test for significance, should I choose a one or two way test? Thank you Peter. $\endgroup$ – Erstwhistle Oct 15 '18 at 12:18

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