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I'm not quite sure what statistical test I should be conducting for my dataset. I am aiming to find the correlation between two variables (concentration of copper vs concentration of chlorophyll). My original graph used the averages of my data (chlorophyll concentration) with standard deviation at each copper concentration, but I was told that every data point had to be used when calculating a PMCC, as opposed to just averages... This new graph looks incorrect to me though. (Images attached below)

ORIGINAL GRAPH:

enter image description here

NEW GRAPH WITH ALL DATA (rough):

enter image description here

Additionally, I am aware that my data is non-linear. However, the "anomalous" point at 5 mg/L can be scientifically explained, so I have opted to keep it in my graph. Does this mean I should be using Spearman's Rank instead? I am not really sure what that test is used for but would it tell me the degree of correlation between the two variables and would I use my averaged values or the whole dataset?

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  • $\begingroup$ What is a "PMCC"? And what property of the Cu-Chl association are you hoping to describe with your correlation coefficient, given that the association appears to be nonlinear? $\endgroup$
    – whuber ♦
    Commented Aug 22, 2023 at 15:03
  • $\begingroup$ PMCC presumably means product-moment correlation coefficient, a.k.a. Pearson correlation. $\endgroup$
    – Nick Cox
    Commented Aug 22, 2023 at 15:14
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    $\begingroup$ If you think the maximum at 5 mg/l is genuine, and the other subsets too, then you have a humped relationship and neither Pearson nor Spearman correlation is going to be helpful. Only some relevant science will help much, as the implication is that some humped curve is appropriate. $\endgroup$
    – Nick Cox
    Commented Aug 22, 2023 at 15:17
  • $\begingroup$ Are certain different data points connected, for example by belonging to the same individual? Standard tests of correlation (and even nonlinear relationship) will assume independence of observations. Does it make sense to assume this here? $\endgroup$
    – Christian Hennig
    Commented Aug 22, 2023 at 23:14
  • $\begingroup$ Are you actually interested in whether there is any systematic relationship between the two variables, or are you interested whether, by and large, chl becomes larger with larger copper? $\endgroup$
    – Christian Hennig
    Commented Aug 22, 2023 at 23:16

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Whoever told you to use all the data is correct.

Neither Spearman nor Pearson will deal well with these data. Both are for linear relationships, it's just that one is on the raw data and the other on the ranks. But your relationship isn't linear.

Since you say the nonlinearity can be explained, you should model it. You could use loess or some other smooth line.

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    $\begingroup$ Perfect linearity on the ranks implies monotonicity in the data. All linear relationships are monotonic but not all monotonic relationships are linear. Because there are repeated measurements for each level of copper concentration I also don't think that the out-of-the-textbook procedures for Spearman and Pearson are ideal here. $\endgroup$
    – Galen
    Commented Aug 22, 2023 at 15:27
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    $\begingroup$ "Since you say the nonlinearity can be explained, you should model it." (+1) $\endgroup$
    – Galen
    Commented Aug 22, 2023 at 15:30

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