When we adjust beliefs in stages, the expected sizes of the respective adjustments are additive in the sense that
However, the observed sizes of the adjustments are not additive. We have
The size of each adjustment is the variance of the corresponding bearing. Therefore
so that
Thus, while
the observed value of this covariance
may be taken to expresses the degree of support/conflict between the two collections of evidence in determining the revision of beliefs. As a summary, we define the path correlation to be
If this correlation is near 1 then the two collections of data are
complementary in that their combined effect in changing our beliefs is greater
than the sum of the individual effect of each collection. If the path
correlation is near -1 then the two collections are giving contradictory
messages which give smaller overall changes in belief, in combination, than we
would expect from the individual adjustments with D and 
.