Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.fractional quantum Hall effect | 5/2 fractional quantum Hall state | edge-current tunneling | quantum point contact | non-Abelian statistics A mong the roughly 100 known fractional quantum Hall (FQH) states, the filling factor ν = 5/2 state is special. It is an evendenominator state with elementary excitations that may have nonAbelian statistics (1-10). If the ground state is non-Abelian, it would be insensitive to environmental decoherence (11) and would therefore be useful for fault-tolerant topological quantum computation. Because of this potential application, much theoretical effort has focused on the 5/2 state, and a variety of wave functions have been proposed (1-3, 5-7, 12-15). There have also been several experiments on the 5/2 state, with more of them supporting non-Abelian than Abelian statistics (16,17). All of the proposed wave functions for the 5/2 state have an effective charge e* of the quasiparticles that is a quarter of the elementary charge e, and this effective charge has been confirmed experimentally (18-21). However, the wave function of the 5/2 state is still under discussion.The proposed wave functions of the 5/2 state can be distinguished by the strength of the interaction between quasiparticles, described by a coupling constant g. This coupling constant can be obtained from experiments using weak-tunneling theory (22). The FQH effect emerges in a highly interacting 2D electron gas (2DEG) at high magnetic field and ultralow temperature. The FQH states have gapless conducting edge currents at the boundaries of the 2DEG, in which fractionally charged quasiparticles carry the current. If the counter-propagating edge currents of a FQH state are brought close enough together in a quantum point contact (QPC), back-scattering is induced. In the weak-tunneling regime, the rate of quasiparticle tunneling depend...