Psychophysical Methods109converge onto the region around the threshold. In this they
resemble the method of limits. But adaptive methods do not
suffer from hysteresis, which is characteristic of the method
of limits.
For example, Näsänen, Ojanpää, and Kojo (2001) used a
staircase procedure(Wetherill & Levitt, 1965) to study the
effect of stimulus contrast on observers’ability to find a letter
in an array of numerals (Figure 4.16). The display was first
presented at a duration of 4 s. After three consecutive correct
responses, its duration was reduced by a factor of 1.26
(log1.260.1), and after each incorrect response the dura-
tion was increased by the same factor. As a result, the dura-
tion was halved in three steps (4, 3.17, 2.52, 2.00,...,
0.10,..., s), or doubled (4, 5, 6.4, 8,..., s). When the se-
quence reversed from ascending to descending (because
ofconsecutive correct responses) or from descending to as-
cending (because of an error), a reversalwas recorded. The
procedure was stopped after eight reversals. The length of the
procedure ranged from 30 to 74 trials. Since the durations
were on a logarithmic scale, the threshold was computed by
taking the geometric mean of the eight reversal durations.
What does this staircase procedure estimate? It estimates
the array duration for which the observer can correctly iden-
tify the letter among the digits 79% of the time (pc = .79).
Let us see why. Suppose that we are presenting the array at an
observer’s threshold duration. At this level, the procedure has
the same chance of (a) going down after three correct re-
sponses as it has of (b) going up after one error. So pc^3 =
1 – pc=.5, which gives pc=^3 .5.79 (for further study:
Hartmann, 1998; Macmillan & Creelman, 1991).
Näsänen et al. (2001) varied the contrast of the letters and
the size of the array. The measure of contrast they used is
called the Michelson contrast: c=LLmmaaxxLLmmiinn, where Lmaxis
the maximum luminance (in this case the background lumi-
nance), and Lminis the minimum luminance (the luminance of
the letters). In the notation of Figure 4.14, L 0 +mL 0 =Lmax
andL 0 – mL 0 =Lmin. Figure 4.17 shows that search time de-
creased when set size was decreased and when contrast was
increased. Using an eye tracker, the authors also found that
the number of fixations and their durations decreased with in-
creasing contrast, from which they concluded that “visual
span, that is, the area from which information can be col-
lected in one fixation, increases with increasing contrast”
(Näsänen et al., 2001, p. 1817).10090807060500.00 0.02 0.04 0.06 0.08 0.10 0.12
Temporal Frequency [Hz]Percent correct responsesObs: JB – SOA: 150 msLog-odds correct responses
01230.0541.380.052Figure 4.15 The psychometric function for one condition of the experi-
ment and one observer: proportion of correct responses (percentage) as a
function of grating-motion velocity. Top:The curve fitted to the data is a
Weibull function. Bottom:The proportion of correct responses is trans-
formed into log-odds, resulting in a function that is approximately linear.
(A graph much like the one in the top panel was kindly provided by José
Barraza, personal communication, July 26, 2001.)
3 1 3 5 9 0 1 1 5 8
9 6 0 2 5 4 3 9 6 6
4 9 5 0 9 9 2 5 4 7
6 0 7 5 2 0 0 5 9 8
1 8 5 0 1 8 7 1 3 0
9 4 3 3 4 5 6 9 0 8
1 9 2 1 0 6 5 3 B 6
1 4 9 7 6 8 9 3 8 8
5 2 3 3 8 7 7 9 9 9
8 1 6 5 1 0 5 3 4 7AB
CD
HE
KN
RS
UV
XZ
Stop
ResumeFigure 4.16The largest search array (10×10 characters) used by
Näsänen et al. (2001). The observer was to find a letter in this array and
respond by clicking on the appropriate field in the two columns on the left.
Source:From “Effect of stimulus contrast on performance and eye move-
ments in visual search,” by R. Näsänen, H. Ojanpää, and I. Kojo, 2001,
Vision Research, 41,Figure 1. Copyright 2001 by Elsevier Science Ltd.
Reprinted with permission.