On using distributional analysis techniques for determining the onset of the influence of experimental variables

Much of the investigation of eye-movement control in visual cognition has focused on the influence of experimental variables on mean fixation durations. In the present paper we explored the convergence between two distributional analysis techniques that were recently introduced in this domain. First, Staub, White, Drieghe, Hollway and Rayner, (2010) proposed fitting the ex-Gaussian distribution to individual participants' data in order to ascertain whether a variable has a rapid or a slow influence on fixation durations. Second, the Divergence Point Analysis (DPA) procedure was introduced by Reingold, Reichle, Glaholt and Sheridan (2012, Reingold & Sheridan, 2014) in order to determine more precisely the earliest discernible impact of a variable on the distribution of fixation durations by contrasting survival curves across two experimental conditions and determining the point at which the two curves begin to diverge. In the present paper we introduced a new version of the DPA procedure which is based on ex-Gaussian fitting. We evaluated this procedure by re-analysing data obtained in previous empirical investigations as well as by conducting a simulation study. We demonstrated that the new ex-Gaussian DPA technique produced estimates that were consistent with estimates produced by prior versions of DPA procedure, and in the present simulation, the ex-Gaussian DPA procedure produced somewhat more accurate individual participant divergence point estimates. Based on the present findings we also suggest guidelines for best practices in the use of DPA techniques.