I'm looking at correlation for a large number of vectors, and many (about 3000) of these pairwise comparisons appear to have a significant correlation even after Bonferroni correction. Plotting these vectors tells a different story, though. A few look like this:

[![scatter plot showing a clear negative correlation][1]][1]

but the vast majority are clearly spurious correlations arising from a few outliers, with plots that look like this:

[![a cluster of points at the bottom left, with a few scattered outliers along the left edge and top right of the plot][2]][2]

I want to filter down to just the vectors which seem genuinely associated, but it's not realistic to go through 3000 plots. Are there statistics I can calculate for each pair of vectors that will help me distinguish between the first and second cases above?


  [1]: https://i.sstatic.net/Uk5vD.png
  [2]: https://i.sstatic.net/eciHt.png