  Correlation measurements with respect to the spectator and participant planes
in relativistic heavy ion collisions were proposed to extract the chiral
magnetic effect (CME) from background dominated azimuthal correlators. This
paper investigates the effects of two- and three-particle nonflow correlations
on the extracted CME signal fraction, $f_{\text{CME}}$. It is found, guided by
a multiphase transport (AMPT) model and the heavy ion jet interaction generator
(HIJING) together with experimental data, that the nonflow effects amount to
approximately $(4\pm5)$% and $(-5\pm3)$% without and with pseudorapidity gaps,
respectively, in 20-50% centrality Au+Au collisions at $\sqrt{s_{\text{NN}}}=
200 \text{ GeV}$.
