When measuring thresholds, careful selection of stimulus amplitude can
increase efficiency by increasing the precision of psychometric fit parameters
(e.g., decreasing the fit parameter error bars). To find efficient adaptive
algorithms for psychometric threshold (“sigma”) estimation, we
combined analytic approaches, Monte Carlo simulations and human experiments for
a one-interval, binary forced-choice, direction-recognition task. To our
knowledge, this is the first time analytic results have been combined and
compared with either simulation or human results. Human performance was
consistent with theory and not significantly different from simulation
predictions. Our analytic approach provides a bound on efficiency, which we
compared against the efficiency of standard staircase algorithms, a modified
staircase algorithm with asymmetric step sizes, and a maximum likelihood
estimation (MLE) procedure. Simulation results suggest that optimal efficiency
at determining threshold is provided by the MLE procedure targeting a fraction
correct level of 0.92, an asymmetric 4-down, 1-up (4D1U) staircase targeting
between 0.86 and 0.92 or a standard 6D1U staircase. Psychometric test
efficiency, computed by comparing simulation and analytic results, was between
41%–58% for 50 trials for these three algorithms,
reaching up to 84% for 200 trials. These approaches were
13%–21% more efficient than the commonly-used 3D1U
symmetric staircase. We also applied recent advances to reduce accuracy errors
using a bias-reduced fitting approach. Taken together, the results lend
confidence that the assumptions underlying each approach are reasonable, and
that human threshold forced-choice decision-making is modeled well by
detection-theory models and mimics simulations based on detection theory
models.