For the purpose of developing methods in crystallography it is necessary to have some means of assessing the quality of electron density maps produced, for example, by MAD phasing. The common procedure is to make a direct comparison of the phased map with the electron density map of the refined structure. This can be done through measurements of the average phase discrepancy, , between the two maps and/or through the calculation of a direct map correlation coefficient of the form
This expression has been shown by Lunin et al  to be exactly equivalent to
and is thus the weighted average of the phase differences between the two maps. Perfect agreement where the phase errors are all zero gives and a set of random phase results in a correlation coefficient which tends to zero. It is almost impossible to say without doubt whether an electron density map would have been interpretable in ab initio structure determination. Map interpretation, although automated to a level where regions of extended protein main chain may be identified, is still somewhat subjective.
It has been suggested  that map correlation coefficients greater than 0.5 indicate a map which could readily be interpreted, although values as low as 0.4 may still lead to structure determination.