Standard deviation of the error per km of levelling line

This makes sense because the longer the line, the more likely it is that systematic errors will accumulate to significant magnitudes.

Double peg method give accuracy between each level shift. 

You may approach the accuracy issue as a leveling network adjustment problem using least squares solution. Then you will end up with several statistical parameters to qualify your results such as the variance component and the residual per each estimated point in your leveling network.