Abstract
Staircase procedures are commonly used to measure the threshold stimulus level corresponding to a specific probability of response. The primary benefit of staircases is that they require only that the probability of response changes monotonically with stimulus level. Weighted staircases can target an arbitrary probability of response by adjusting the ratio of ascending and descending step sizes. Threshold is typically estimated from the mean of reversals. However, the mean of reversals is asymptotically biased away from the targeted probability for weighted staircases, making them unusable in practice. A correction was proposed that eliminates the bias by shifting the mean of reversals to the stimulus level at the targeted probability of response. The correction assumes that the probability of response is symmetric with respect to rotation around 0.5. Simulations were used to evaluate the effectiveness of the correction for a range of procedural parameters including typical guess and lapse rates that violate the symmetry assumption. Results showed that corrected thresholds reduced bias in all cases, and effectively eliminated bias over a range of step sizes in all but the most asymmetric conditions. The correction should always be used when thresholds are reported from the mean of reversals in weighted staircase procedures.
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