A fundamental challenge in RT research is how to aggregate data across participants who may differ substantially in overall speed. Simply averaging means or medians discards the rich information contained in RT distributions. Vincentizing solves this by averaging the quantiles of individual distributions, producing a group-level distribution that preserves the shape characteristics of the individual distributions.
The Vincentizing Procedure
The procedure works as follows: (1) for each participant, compute the quantiles of their RT distribution at specified percentile points (e.g., the 0.1, 0.2, ..., 0.9 quantiles); (2) average these quantiles across participants at each percentile point; (3) the resulting set of averaged quantiles defines the group Vincent distribution.
Q̄(p) = (1/N) × Σᵢ₌₁ᴺ Qᵢ(p)
where Qᵢ(p) is the p-th quantile of participant i's RT distribution
A key mathematical property is that if all individual distributions belong to the same parametric family, the Vincent average often belongs to that family as well. For example, the Vincent average of ex-Gaussian distributions is itself ex-Gaussian — this is known as the Vincent averaging closure property. This property does not hold for all distribution families, but it does hold for the normal, ex-Gaussian, and Gumbel distributions.
Advantages Over Mean Averaging
When researchers average raw RT means, fast and slow participants contribute equally, and the resulting average can misrepresent the shape of the underlying distributions. Vincentizing preserves distributional features: if every participant shows a prominent right tail, the Vincent average will show it too. This is critical for evaluating models that make predictions about the entire RT distribution, not just the mean.
Roger Ratcliff (1979) revived and formalized the Vincentizing method in his landmark paper introducing the diffusion model for two-choice RT. He demonstrated that Vincentizing produces group distributions that can be meaningfully compared to model predictions, a practice that became standard in the RT modeling literature. The method is now an essential tool in any RT researcher's toolkit.
Quantile-Probability Plots
Vincentized quantiles are commonly displayed in quantile-probability (QP) plots, where the x-axis shows response probability (accuracy) and the y-axis shows RT quantiles for correct and error responses. These plots simultaneously display speed and accuracy information across the entire RT distribution, providing a rich target for model fitting. The DDM and other sequential sampling models are routinely evaluated against QP plots constructed from Vincentized data.
Vincentizing has been extended to handle unequal numbers of observations per participant (weighted Vincentizing) and has been compared to alternatives such as fitting parametric models to each participant and then averaging the parameters. Both approaches have merits, but Vincentizing remains the most widely used nonparametric method.