>However, one is not permitted to cherry-pick data, so the "outliers" have to be left in.
I respect why you think this, but I don't agree. Identifying points on the graph which don't fit with the pattern of the rest of the data is a reasonable way to identify outliers. Even if you choose not to exclude those, there's a greater problem:
Correlation is not robust if it depends on 2 or 3 points being in just the right place. And, robustness is one of the things you really ought to check for if you calculate Pearson's r. If you get different results with outliers in and out, that's a problem for your results.
In my opinion, any significant result here is just statistical noise.
I agree that the statistics on this association are pretty lousy, even with the outliers in. However, one would preferably find an specific reason to exclude outliers, rather than rely on intuition.
I respect why you think this, but I don't agree. Identifying points on the graph which don't fit with the pattern of the rest of the data is a reasonable way to identify outliers. Even if you choose not to exclude those, there's a greater problem:
Correlation is not robust if it depends on 2 or 3 points being in just the right place. And, robustness is one of the things you really ought to check for if you calculate Pearson's r. If you get different results with outliers in and out, that's a problem for your results.
In my opinion, any significant result here is just statistical noise.
See Wikipedia for further discussion: https://en.wikipedia.org/wiki/Pearson_product-moment_correla...