It is believed that a Quark-Gluon Plasma (QGP), a deconfined state of quarks and gluons, existed microseconds after the Big Bang, when the universe was at a temperature of approximately 150 to 200 MeV. It is predicted that a hadron-quark phase transition, which is the same transition as happened at the very beginning of the universe but in the reverse direction, occurs in heavy-ion collisions at ultrarelativistic energies. For the purpose of producing such an excited state of matter in the laboratory, the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory has been constructed and is presently taking data. What we expect to get from RHIC is a better understanding of the universe and of matter at the nuclear and subnuclear level.

In non-central heavy-ion collisions, the initial spatial deformation due to geometry and the pressure developed early in the collision causes azimuthal momentum-space anisotropy, which is correlated with the reaction plane. Measurements of this correlation, known as anisotropic transverse flow, can help us understand processes such as thermalization, creation of the quark-gluon plasma, phase transitions, etc. Elliptic flow is characterized by the second harmonic coefficient v₂ of an azimuthal Fourier decomposition of the momentum distribution, and has been observed and extensively studied in Au + Au collisions from subrelativistic energies on up to RHIC. At RHIC energies, elliptic flow is inferred to be a relative enhancement of emission in the plane of the reaction, and provides information about the early-time thermalization achieved in the collisions.

Generally speaking, large values of flow are considered signatures of hydrodynamic behavior, while smaller flow signals can have alternative explanations. Furthermore, there are several possible sources of azimuthal correlations which are unrelated to the reaction plane ("non-flow effects") — examples include correlations caused by resonance decays, dijets, Bose-Einstein effects, Coulomb interactions, momentum conservation, etc. Conventional flow analyses are based on correlations between particle pairs and are sensitive to both flow and non-flow effects. A generalization from pair correlation analyses to quadruplet correlation analyses has the potential to remove non-flow effects, and becomes more important in collisions at RHIC energy, where non-flow effects are expected to contribute significantly to the correlation between particle pairs. This dissertation studies elliptic flow in Au + Au collisions at RHIC, and fully corrects the results for all classes of non-flow effects as well as corrects for various analysis artifacts which can distort or obscure the physics interpretation of the measurements.