UDTRUnderwater Demolition Team Replacement (US Navy)
UDTRUp and Down Transformed Response Rule
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Figure 13 shows means and standard deviations of estimates of [gamma], [lambda], [theta], and [sigma] (left to right) as a function of N for 1-1 (upper part), 1-4 (center part), and 4-1 (lower part) UDTR staircases; Figure 14 does the same for 4x (upper part) and 1/4 x (lower part) UDWR staircases.
The ideal plan would have the usability indices of single-presentation MOCS (top panel in Figure 10a), but the estimates of [gamma] and [lambda] should have the properties attained with UDWR staircases using large steps (darker circles in the first column in the lower part and in the second column in the upper part of Figure 14), the estimates of [theta] should have the properties attained with conventional MOCS or 1-1 UDTR staircases (third column in Figure 12 and in the upper part of Figure 13), and the estimates of [sigma] should have the properties attained with 4x UDWR staircases (fourth column in the upper part of Figure 14).
only 1-1, 1-2, and 2-1 UDTR staircases render smaller variability for [??] than comparable conventional MOCS, but 1-3, 1-4, 3-1, and 4-1 UDTR staircases render larger variability.
UDTR and UDWR staircases yield OLS underestimates of [lambda], and OLS estimates of [theta] and [sigma] that are similar to their ML counterparts.
With the remaining plans (conventional MOCS, UDTR staircases and UDWR staircases), usability was slightly inferior than under OLS or ML estimation.
In 2AFC detection tasks, the strategy of interweaving two staircases with offset lattices and base step sizes [DELTA] = [sigma]/2, [sigma]/3, [sigma]/4, and [sigma]/5 was evaluated for all UDTR, UDWR, and UDTWR staircases considered in Section 4.
In 1-d UDTR staircases, 100% usability was attained regardless of relative step size only when d = 4 and after 900 trials; in [k.sup.x] UDWR staircases, 100% usability could not be achieved when k = 2 or [DELTA] = [sigma]/2 but otherwise it was attained in 700 trials regardless of relative step size; finally, in 1-d UDTWR staircases, 100% usability was attained irrespective of relative step size with 700 trials provided d [greater than or equal to] 2.
The same interweaving strategy was evaluated with yes-no and 2AFC discrimination tasks using base step sizes [DELTA] = [sigma]/2, [sigma]/3, [sigma]/4, and [sigma]/5 for all UDTR and UDWR staircases in Sections 5 and 6.1.
Also, dual UDWR designs (lower part of Figure 18) outperform dual UDTR designs (upper and center parts of Figure 18), providing unbiased estimates of all parameters regardless of step size when N [greater than or equal to] 300 trials.
To look into this issue more closely, we carried out a simulation for one of Kaernbach's conditions, namely, 10,000 replicates of 1-1 UDTR staircases starting on threshold, [DELTA] = [sigma]/11 (comparable to the step sizes used by Kaernbach), 48-120 yes-no trials (Kaernbach used 10-100), and a logistic [PSI] (Kaernbach used a cumulative Gaussian) with [lambda] = [gamma] = 0, [theta] = -1.5, and [sigma] = 1; and we also simulated MOCS set up as always in this paper, running for the same numbers of trials, and using L = 12 so as to render the same sampling lattice as the adaptive staircase.
Adaptive Staircase With Up-Down Transformed Rules (UDTRS)