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
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
Carpenter, R. H. S., and Williams, M. L. L. (1995). Neural computation
of log likelihood in the control of saccadic eye movements. Nature,
Carpenter R H S, (1981). Oculomotor Procrastination, In Eye
Movements: Cognition and Visual Perception, D. F. Fisher, R. A.
Monty, & J. W. Senders (Ed), (pp. 237-246). Hillsdale: Lawrence Erlbaum.
Carpenter R H S, (1988). Movements of the Eyes (2nd ed.). London:
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