Sequential dependencies and regression in psychophysical judgments

A quantitative analysis of sequential effects with numeric stimuli

“…Ward (1973Ward ( , 1979 and others have found such tendencies in magnitude estimation and in cross-modality matching (e.g., Baird et aI., 1980;Green et al, 1980). A further by-product is reported by Cross (1973), who notes that sequence effects can lead to the underestimation of the exponents of psychophysical power functions.…”

Magnitude estimation and sensory matching

“…In fact, the 6-<iB shift is relatively modest in size, presumably because each plotted point entails averaging responses to a given stimulus following various SPLs from the other subset. Even greater shifts are evident if one examines responses to a given stimulus following every possible prior stimulus individually, as Cross (1973), for instance, has done. Marks et al (1986), following the work of Ward (1982), noted that sequential processes-in particular, the assimilation of each response to the response made to the prior stimulus-could account, in principle, for a sizable portion (about 50%) of the bias they observed in cross-10 2 "7" ""'------------------.... modal matches.…”

“…In general, sequential effects tend to contain two main components-contrast between the current response and the previous stimulus, but assimilation of the current response to the previous response (e.g., Jesteadt, Luce, & Green, 1977;Lockhead & King, 1983;Ward, 1982). Hence, a stimulus will tend to "mismatch" itself each time it follows a different prior stimulus or response, as Cross (1973, Figure I), Lockhead and King (1983, Figure 2), and Ward (1973, Figure 2) have shown; overall, sequential effects tend to be largely assimilative, in that responses to current stimuli resemble responses to immediately prior stimuli.…”

On bias in magnitude scaling and some conjectures of Stevens

“…Generalizations of these models have been considered in the psychophysical literature, particularly in research concerned with sequential effects, where various dynamic extensions have been considered. For example, the psychophysical function (Equation 2) has been generalized to allow for possible stimulus context effects (e.g., Cross, 1973;DeCarlo & Cross, 1990), whereas the judgmental model of Equation 3 has been generalized to allow for effects of changes in the proportionality constant over trials, due to the use of different reference points (e.g., DeCarlo, 1990DeCarlo, , 1994DeCarlo, , 2003DeCarlo & Cross, 1990). Although the model of bias presented below can easily be incorporated into dynamic models, dynamic generalizations are not the focus here (and they do not change the main results presented below).…”