  The quasiparticles (QPs) or quasiholes (QHs) of fractional quantum Hall
states have been predicted to obey fractional braid statistics, which refers to
the Berry phase (in addition to the usual Aharonov-Bohm phase) associated with
an exchange of two QPs or two QHs, or equivalently, to half of the phase
associated with a QP / QH going around another. Certain phase slips in
interference experiments in the fractional quantum Hall regime have been
interpreted as arising from the statistics associated with a QP moving along
the edge of the sample around another QP in the interior. A conceptual
difficulty with this interpretation is that the edge, being compressible, does
not support a QP or a QH with a sharply quantized fractional charge or
fractional statistics. We analyze the experiment in terms of composite fermions
(CFs) obeying integral braid statistics and suggest that the observed phase
slips can be naturally understood as a measure of the relative braid statistics
of a CF in the ground state at the edge and a fractionally charged QP / QH in
the interior; in contrast to fractionally charged excitations, the CFs are
known to remain sharply defined even in compressible regions such as the edge
or the CF Fermi liquid state at half filled Landau level. We further propose
that transport through a closed $\textit{tunneling}$ loop confined entirely in
the bulk can, in principle, allow an unambiguous measurement of the relative
braid statistics of a fractionally charged QP / QH braiding around another
fractionally charged QP / QH. Optimal parameters for this experimental geometry
are determined from quantitative calculations.
