Reaction times - including saccadic latencies - vary unpredictably from trial to trial to a surprising extent. Their distributions are typically skewed, with a long tail in the direction of longer latencies.

However, it turns out that a very simple transformation - thinking in terms of reciprocal latency instead of latency itself - has the effect of making reaction time distributions not only symmetrical, but Gaussian. A distribution in which the reciprocal of the random variable obeys a Gaussian or normal distribution may be called a Recinormal distribution. In the following figure, the reaction time data are plotted on a reciprocal scale. To preserve the convention of longer reaction times to the right, the scale is mirrored so that infinite time (whose reciprocal is zero) is at the right, and the distance from this origin is proportional to (1/T), where T is the latency.

Raw histograms such as these, though very commonly used, are not very satisfactory from a mathematical point of view: their vertical scale is in effect arbitrary, and the overall shape depends markedly on bin-size. Cumulative histograms have the virtue of being normalised (they necessarily run from 0 to 1) and are essentially continuous functions; they also make it much easier to plot several data sets in one diagram, for comparison. The same data is plotted here as a cumulative rather than raw or frequency histogram, again using a reciprocal scale.

Finally, we can see at once whether such a distribution is in fact Gaussian, by using a probability scale (probit scale) for the probability axis. This scale stretches progressively away from 50%, in such a way that a cumulative plot of a Gaussian results in a straight line. The intersection of this line with the 50% line represents the median, and the slope is directly related to the standard deviation. Such a plot can be called a Reciprobit plot. Here you can download a .CDR file of reciprobit graph paper that you can try plotting your own data on.

The idea that the reciprocal of reaction time is a fundamental variable arises naturally from models in which reaction time is due to some process proceeding at a certain rate to completion. If variability of latency is due to variability of this rate, then we would expect the reciprocal of reaction time to be distributed in the same way as the underlying rate. More specifically, we can imagine a process in which a decision signal rises linearly at a rate r from an initial level S0 to a fixed threshold ST at which movement is initiated. If r varies randomly from trial to trial with a Gaussian distribution, then a recinormal distribution of reaction times will be generated.

This is the essence of the LATER model.

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