  We discuss a statistical analysis of Aharonov-Bohm conductance oscillations
measured in a two-dimensional ring, in the presence of Rashba spin-orbit
interaction. Measurements performed at different values of gate voltage are
used to calculate the ensemble-averaged modulus of the Fourier spectrum and, at
each frequency, the standard deviation associated to the average. This allows
us to prove the statistical significance of a splitting that we observe in the
h/e peak of the averaged spectrum. Our work illustrates in detail the role of
sample specific effects on the frequency spectrum of Aharonov-Bohm conductance
oscillations and it demonstrates how fine structures of a different physical
origin can be discriminated from sample specific features.
