Combining reaction-time distributions to conserve shape

To improve the estimate of the shape of a reaction-time distribution, it is sometimes desirable to combine several samples, drawn from different sessions or different subjects. How should these samples be combined? This paper provides an evaluation of four combination methods, two that are currently in use (the bin-means histogram, often called "Vincentizing", and quantile averaging) and two that are new (linear-transform pooling and shape averaging). The evaluation makes use of a modern method for describing the shape of a distribution, based on L-moments, rather than the traditional method, based on central moments. Also provided is an introduction to shape descriptors based on L-moments, whose advantages over central moments-less biased and less sensitive to outliers-are demonstrated. Whether traditional or modern shape descriptions are employed, the combination methods currently in use, especially bin-means histograms, based on averaged bin means, prove to be substantially inferior to the new methods. Averaged bin-means themselves are less deficient when estimating differences between distribution shapes, as in delta plots, but are nonetheless inferior to linear-transform pooling.