Because finding the statistical uncertainty in a transfer function data point, as a function of its coherence and how many averages were taken, comes up just about every few years (e.g. the last time I saw it was in the LLO eLOG), here it is quoted in the aLOG for the next generation: 

Relative uncertainty in transfer function magnitude: 
 
d|TF|           1 - C  
----- = sqrt ( ------- ) 
 |TF|           2 C N  
 
where C is the coherence, and N is the number of averages.

Absolute uncertainty in transfer function phase:
 
                  1 - C  
d <(TF) = sqrt ( ------- )   [rad]
                  2 C N   
 
where C is the coherence, and N is the number of averages, and is in units of radians.

Ref: Bendat and Piersol, "Random Data" 2nd Ed, p317.