The latter comprises a total of six variants of conventional MOCS, one variant of single-presentation MOCS, one of QUEST, 27 variants of UDTR staircases arising from the factorial combination of three rules and nine step sizes (63 variants in the case of yes-no tasks, because of the use of four additional rules), 27 variants of UDWR staircases (54 for yes-no tasks), and 36 variants of UDTWR staircases (none for yes-no tasks).
under UDTWR staircases and also under kx UDWR staircases, [[DELTA].sup.-] < [[DELTA].sup.+], whereas under 1/k x UDWR staircases, [[DELTA].sup.-] > [[DELTA].sup.+].
Between UDTR staircases (left column of Figure 5, excluding the top panel) and UDWR staircases (center column of Figure 5), the latter appear preferable in the 4x version, yielding 100% usability with 700 trials when [DELTA] [greater than or equal to] [sigma]/5.
Figure 6 shows separate usability indices for the estimation of [lambda] and [sigma] (0 could be estimated 100% of the times in all conditions) as a function of N for QUEST, single-presentation MOCS, and all variants of conventional MOCS (first panel in Figures 6a and 6b) as well as for the best variants of UDTR, UDWR, and UDTWR staircases in terms of overall usability (second to fourth panels in Figures 6a and 6b).
Distributions of estimates for our 27 variants of UDTR, 27 of UDWR, and 36 of UDTWR staircases were similar to those displayed in the bottom three rows of Figures 4a and 4b.
In our study, spacing in conventional MOCS with L levels was [sigma]/(L - 1) whereas spacing in UDTR and UDWR staircases varied between [sigma]/10 and [sigma]/2.
(1985) does not hold for ML estimation: The variability of ML estimates of 9 from UDTR staircases is always smaller than that arising from comparable MOCS (center panel in the top row of Figure 9), as is the variability from UDWR staircases using fine spacing (lighter symbols in the center panel in the center row).
The remaining plans comprise 63 variants of UDTR staircases (1-1, 1-2, 1-3, 1-4, 2-1, 3-1, and 4-1 rules each with nine base spacings) and 54 variants of UDWR staircases (2x, 3x, 4x, 1/2 x, - 1/3, and 1/4 x rules each with nine base spacings).
Yet, different broad types of either UDTR or UDWR staircases seem well suited to estimating each of these two parameters.
Thus, 1-d and u-1 UDTR staircases merely differ in that their patterns of usability for [gamma] and [lambda] are interchanged, but they both yield the same patterns for [sigma] and overall (compare the third and fourth rows in Figure 10); kx and 1/k x UDWR staircases differ in the same respects (compare the bottom two rows in Figure 10).
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.