Conditionally averaged random potential fluctuations are an important quantity for analyzing turbulent electrostatic plasma fluctuations. Experimentally, this averaging can be readily performed by sampling the fluctuations only when a certain condition is fulfilled at a reference position. Alternatively, for time stationary and homogeneous turbulence, analytical expressions, involving higher order correlation functions R(n)(r, t) = < phi-n(zeta, tau)-phi-(r + zeta, t + tau) >, can be derived for the conditional averages. These expressions have the form of series expansions, which have to be truncated for practical applications. The convergence properties of these series are not known, except in the limit of Gaussian statistics. By applying the analysis to numerically simulated ion acoustic turbulence, we demonstrate that by keeping two or three terms in these series an acceptable approximation is obtained even in cases deviating significantly from Gaussian statistics.