DEPTH OF SEQUENTIAL DEPENDENCIES IN PSYCHOPHYSICAL JUDGMENT

In a first experiment, subjects had to rate the size of squares. We found that the depth of sequential dependencies depended on the judgment task. Whereas for magnitude estimation only the immediately preceding stimulus-response event was included in the judgment process, events up to two trials back were incorporated for category judgment. In a second experiment, squares of two categories differing in color were presented. Under these conditions, category-specific sequential effects were found. Sequential dependencies were stronger when the current stimulus and the preceding stimulus belonged to the same category. More specifically, the depth of sequential effects was affected by the categories of previous stimuli. For category judgment, when the stimuli one and two trials back did not share the category with the current stimulus but the stimulus three trials back did, the event three trials back affected the judgment. However, if the stimuli one and two trials back belonged to the same category as the current stimulus, the event three trial back exerted no influence. The results are discussed in a framework in which preceding events play the role of referents. There is some evidence indicating that not only the immediately preceding stimulus-response pair affects the judgment of the current stimulus, but also events more than one trial back. For instance, analyzing response errors in absolute judgment, Ward and Lockhead (1971) found that sequential effects extended to at least five trials back. On the other hand, Jesteadt, Luce and Green (1977) concluded from regression analyses of magnitude estimations that sequential dependencies were limited to the immediately preceding event. What is the reason for the different results concerning the depth of sequential effects? Possibly, the depth depends on the judgment task. Whereas Lockhead and Ward referred to an experiment on absolute judgment, Jestead, Luce and Green focused on experiments on magnitude estimation. The present study is meant to examine whether the depth of sequential dependencies is really affected by the task. Experiment 1 Method Subjects had to judge the size of squares that varied from 50 mm to 83 mm in steps of 3 mm. Subjects performed in one of two judgment tasks: category judgment on a 5-category scale and magnitude estimation. One session consisted of three blocks lasting about 10 minutes each. There were 200 trials per block. Measurement of sequential dependencies To determine the depth of sequential dependencies, it may be determined up to which lag g partial correlations between current responses r(t) and preceding responses r(t-g) as well as between r(t) and preceding stimuli s(t-g) are significant. In the present experiment, partial correlations between r(t) and r(t-g) and between r(t) and s(t-g) turned up to be significant up to g = 8. Does this mean that stimulus-response events up to 8 trials back may be included in the judgment process? To answer this question, we have t o take into account that pseudosequentia l effects may appear as artifacts. Gregson (1976) and Haubensak (1992 ) have pointed out that judgment s average d over subjects show sequential dependencie s even if individual data do not when some individuals tend to judge the stimuli generall y high and others tend to judge genera lly low. Such pseudosequen tial effects may even appea r in analyzing individual data average d over an exper iment if systemati c response shifts occur in the course of the experiment . Therefore, ar tifacts produced by averaging th e data mus t be eliminated in deter mining the dept h of sequential dependencies. There are two ways to disentangl e sequential effects and pseudosequen tial effects. 1) We can estimate the magnitude of pseudosequen tial effect and compar e them with the values obtained in an experiment . As long as the empirical values are greater than those calculated for pseudoeffects, we can assume that the corresponding stimulus-response events are actually included in the judgment process. We made the fo llowing steps . First, individual mean judgment s were calculated for each stimulus within each of the three block s of the experiment separately . Second, to produce stimulus-response series without sequential effects, these mean judgment s were used as scale values in a computer program based on a Thurstonelike model . This was done for each individual and for each block of the experiment . Third, the series from the three block s were combined for each individual to calculat e partial correlations between r(t) and r(t-g) that are due to drifts of the judgment scale. Then the calculated pseudoeff ects were compare d with the empirical fi ndings. 2) A second way t o eliminate artifacts produced by averaging dat was proposed by Schifferstein and Kuiper (1997). One can correct for differences in scale usage by calculating standardi zed response s which are brought back to a mean of 0 and a standard deviation of 1. Following this procedure, we deter mined mean m and standard devia tion σ of the responses r and calculated standardized response s rs = (r – m)/σ for each subj ect and each part of a session separately . Then, thes e standardized response s were used to analyze sequential dependencies. Results Empirical correlations and correlations calculated from the simulation of pseudosequen tial effects are represente d in Figures 1and 2. Mean values average d over the subjects are shown. The curves differ for category judgment and magnitude estimation. Figure 1. Empirical partial correlations between the current respons e and preceding responses of the lag g and calculated pseudoeffects for categor y judgment 0 0.05 0.1 0.15 0.2 0.25 0.3