  In a frequency range where a microwave resonator simulates a chaotic quantum
billiard, we have measured moduli and phases of reflection and transmission
amplitudes in the regimes of both isolated and of weakly overlapping resonances
and for resonators with and without time-reversal invariance. Statistical
measures for S-matrix fluctuations were determined from the data and compared
with extant and/or newly derived theoretical results obtained from the
random-matrix approach to quantum chaotic scattering. The latter contained a
small number of fit parameters. The large data sets taken made it possible to
test the theoretical expressions with unprecedented accuracy. The theory is
confirmed by both, a goodness-of-fit-test and the agreement of predicted values
for those statistical measures that were not used for the fits, with the data.
