  Quantum Hall interferometers have been used to probe fractional charge, and
more recently, fractional statistics of quasiparticles. Theoretical predictions
have been made regarding the effect of electrostatic coupling on interferometer
behavior and observation of anyonic phases. Here we present measurements of a
small Fabry-Perot interferometer in which these electrostatic coupling
constants can be determined experimentally, facilitating quantitative
comparison with theory. At the $\nu = 1/3$ fractional quantum Hall state, this
device exhibits Aharonov-Bohm interference near the center of the conductance
plateau interrupted by a few discrete phase jumps, and $\Phi_0$ oscillations at
higher and lower magnetic fields, consistent with theoretical predictions for
detection of anyonic statistics. We estimate the electrostatic parameters $K_I$
and $K_{IL}$ by two methods: by the ratio of oscillation periods in
compressible versus incompressible regions, and from finite-bias conductance
measurements, and these two methods yield consistent results. We find that the
extracted $K_I$ and $K_{IL}$ can account for the deviation of the values of the
discrete phase jumps from the theoretically predicted anyonic phase $\theta _a
= 2\pi /3$. In the integer quantum Hall regime, we find that the experimental
values of $K_I$ and $K_{IL}$ can account for the the observed Aharonov-Bohm and
Coulomb dominated behavior of different edge states.
