So the default value for the poor_map_value_threshold is 1, which I assume is 1 sigma. So if the electron density for a putative water is less than 1 sigma in the 2mFo-DFc map OR if the calculated correlation coefficient is less than the poor_cc_threshold value (default 0.7), then the water is removed, right?

yes.

For my own education, what would be the best way of calculating the correlation coefficient values for all the waters or ligands in a given model? What I want to do is get a sense for the relationship between electron density and correlation coefficient values for waters in my structure to understand how “strict” the default poor_cc_threshold value is and whether/how much I might want to raise it.

You can use

phenix.model_vs_data model.pdb data.mtz --comprehensive

and that will list map CC for all atoms or per residue,

OR

use

phenix.real_space_correlation

if you need more fine-tuning.

I have to run now - otherwise I miss my flight to London -:)

All the best!
Pavel.