I'm looking for a correlation between 2 parameters, neither of which is normally distributed. Hence from my (very limited) understanding of statistics, I should be running a Spearman correlation or log-transforming before running Pearson's. Both of these tests are not significant. However, the Pearson's correlation on untransformed data is strongly significant and the scatterplot looks like a trend does exist:
After some googling I know that the scatterplot resembles this scenario of significant outliers: so the Pearson's correlation might not be valid, but I am confident that the stray points are not random noise because using alternative surrogate parameters for the y-axis (fib4) that are measured in completely different ways gives the exact same result. It looks like something is going on but I don't even know how to articulate it- like there is a positive linear? correlation that only holds at the positive extreme values. I would really appreciate it if someone can set me on the right path. Thanks kindly in advance.
The opposite situation (significant Spearman, non-significant Pearson's) has been asked before and the answer was that Spearman is more robust to scattering by outliers as it only uses rank vs actual values, which makes sense. I also know that using values makes Pearson's more powerful which could explain the situation, but it doesn't seem a valid test anyway.
Addit: log-transformed Pearson's correlation is also significant, but isn't robust to removal of just 1 point. For anyone with the same question I believe the conclusion is that these inconsistencies reflect a weak (at best) relationship.