  Most psychophysical experiments discard half the data collected.
Specifically, experiments discard reaction time data, and use binary responses
(e.g. yes/no) to measure performance. Here, Shannon's information theory is
used to define Shannon competence $s'$, which depends on the mutual information
between stimulus strength (e.g. luminance) and a combination of reaction times
and binary responses. Mutual information is the entropy of the joint
distribution of responses minus the residual entropy after a model has been
fitted to these responses. Here, this model is instantiated as a proportional
rate diffusion model, with the additional innovation that the full covariance
structure of responses is taken into account. Results suggest information
associated with reaction times is independent of (i.e. additional to)
information associated with binary responses, and that reaction time and binary
responses together provide substantially more than the sum of their individual
contributions (i.e. they act synergistically). Consequently, the additional
information supplied by reaction times suggests that using combined reaction
time and binary responses requires fewer stimulus presentations, without loss
of precision in psychophysical parameters. Finally, because s' takes account of
both reaction time and binary responses, (and in contrast to d') $s'$ is immune
to speed-accuracy trade-offs, which vary between observers and experimental
designs.
