A test of a two-stage model of magnitude judgment

It has been suggested that the power law J = aⁿ, describing the relationship between numerical magnitude judgments and physical magnitudes, confounds a sensory or input function with an output function flawing to do with O’s use of numbers. Judged magnitudes of differences between stimuli offer some opportunity for separating these functions. We obtained magnitude judgments of differences between paired weights, as well as magnitude judgments of the weights making up the pairs. From the former we calculated simultaneously an input exponent and an output exponent, working upon Attneave’s assumption that both transformations are describable as power functions. The inferred input and output functions, in combination, closely predict the judgments of individual weights by the same Os. Although pooled data (geometric means of judgments) conform fairly well to a linear output function, individual data do not; i.e., individual Os deviate quite significantly fromlinearity and from one another in their use of numbers. Individual values of the inferred sensory exponent, k, show significantly better uniformity over Os than do values of the phenotypica! magnitude exponent previously found to describe interval judgments of weight.     

An application of a dynamic model of judgment to magnitude production

A dynamic model of judgment, together with a model of stimulus context effects, is applied to magnitude production (MP) and magnitude estimation (ME) experiments. Participants' responses in MP were correlated across trials, as is typically found for ME. The magnitudeof the autocorrelation, however, was small, which suggests that participants in MP tend to rely more heavily on a long-term frame of reference. Second, a stimulus context effect found for ME did not appear for MP, most likely because of the different nature of the task (i.e., intermediate values of the stimulus were heard while the participant produced a response). A fit of an earlier regression model, on the other hand, suggests that the number presented on the previous trial in MP has a large contrastive effect on the current response.The present model offers a different view of this result, in that it shows that a negative coefficient for the earlier model is consistent with a positive judgmental effect. The regression effect noted by Stevens and Greenbaum (1966), which is a value of the estimated ME exponent that is smaller than the inverse of the estimated MP exponent, was also found; it i s shown that the effect did not arise from bias in estimation.     

Comparative judgment of numerosity and numerical magnitude: attention preempts automaticity

It is commonly believed that humans are unable to ignore the meanings of numerical symbols, even when these meanings are irrelevant to the task at hand. In 5 experiments, the authors tested the notion of automatic activation of numerical magnitude by asking participants to compare, while timed, pairs of numerical arrays on either numerosity or numerical value. Garner and Stroop effects were used to gauge the degree of interactive processing. The results showed that both effects were sensitive to the discriminability of values along the constituent dimensions, to the number of stimulus values used, and to practice and motivation. Notably, Stroop and Garner effects were eliminated under several conditions. These findings are incompatible with claims of obligatory activation of meaning in numerical processing, and they cast doubt on theories positing automatic processing of semantic information for alphanumerical symbols.     

Nested models of relative judgment: Applications to a similarity averaging model

A theoretical analysis of the Eisler and Ekman (1959) model of similarity judgments for unidimensional continua is presented, based on a general model of relative judgment. This general model assumes that judgments are mediated by perceived relations of pairs of stimuli, that there exists a transformation of the judgmental response that is a function of the sensory ratio of the two stimuli, and that response bias operates in a multiplicative manner. Three structural conditions are presented, each imposing constraints on the structure of observed judgments. The structural conditions define threenested models of relative judgment, with the second a weakened version of the first, and the third a weakened version of the second. The special virtue of the general model is that it is applicable to a variety of judgmental tasks (e.g., ratio estimation, similarity, pair comparison), the key being derivation of theresponse transformation conforming to the structural conditions. The structural conditions thus constitute necessary conditions for several different judgmental models. The theory was first applied with success to ratio estimation judgments (Fagot, 1978), and this paper applies the general model to the Eisler and Ekman similarity “averaging” model. Empirical tests were carried out on published data for pitch, darkness, visual area, and heaviness judgments. Although the strong form of the model presented by Eisler and Ekman was rejected, weakened versions were generally supported by the data. These results were similar to those obtained for ratio estimation (Fagot, 1978), and are interpreted to be very promising for the general model of relative judgment.     

A two-stage model of visual search

A two-stage visual search model is described. Four experiments show that in a VM paradigm sequential presentation of the display leads to increases in accuracy and decreases in latency. Slower presentation rates allow for faster transfer of the target from iconic to short-term memory. When target and background items are dissimilar, transfer to short-term memory need not take place and decisions can be made on the basis of the Stage 1 analysis. These results are taken as confirming evidence for the proposed model.     

The sausage machine: A new two-stage parsing model

It is proposed that the human sentence parsing device assigns phrase structure to word strings in two steps. The first stage parser assigns lexical and phrasal nodes to substrings of roughly six words. The second stage parser then adds higher nodes to link these phrasal packages together into a complete phrase marker.This model of the parser is compared with ATN models, and with the two-stage models of Kimball (1973) and Fodor, Bever and Garrett (1974). Our assumption that the units which are shunted from the first stage to the second stage are defined by their length, rather than by their syntactic type, explains the effects of constituent length on perceptual complexity in center embedded sentences and in sentences of the kind that fall under Kimball's principle of Right Association. The particular division of labor between the two parsing units allows us to explain, without appeal to any ad hoc parsing strategies, why the parser makes certain ‘shortsighted’ errors even though, in general, it is able to make intelligent use of all the information that is available to it.     

On the discrepant results in synchrony judgment and temporal-order judgment tasks: a quantitative model

Research on the perception of temporal order uses either temporal-order judgment (TOJ) tasks or synchrony judgment (SJ) tasks, in both of which two stimuli are presented with some temporal delay and observers must judge the order of presentation. Results generally differ across tasks, raising concerns about whether they measure the same processes. We present a model including sensory and decisional parameters that places these tasks in a common framework that allows studying their implications on observed performance. TOJ tasks imply specific decisional components that explain the discrepancy of results obtained with TOJ and SJ tasks. The model is also tested against published data on audiovisual temporal-order judgments, and the fit is satisfactory, although model parameters are more accurately estimated with SJ tasks. Measures of latent point of subjective simultaneity and latent sensitivity are defined that are invariant across tasks by isolating the sensory parameters governing observed performance, whereas decisional parameters vary across tasks and account for observed differences across them. Our analyses concur with other evidence advising against the use of TOJ tasks in research on perception of temporal order.     

Determinants of linear judgment: a meta-analysis of lens model studies

The mathematical representation of E. Brunswik's (1952) lens model has been used extensively to study human judgment and provides a unique opportunity to conduct a meta-analysis of studies that covers roughly 5 decades. Specifically, the authors analyzed statistics of the "lens model equation" (L. R. Tucker, 1964) associated with 249 different task environments obtained from 86 articles. On average, fairly high levels of judgmental achievement were found, and people were seen to be capable of achieving similar levels of cognitive performance in noisy and predictable environments. Further, the effects of task characteristics that influence judgment (numbers and types of cues, inter-cue redundancy, function forms and cue weights in the ecology, laboratory versus field studies, and experience with the task) were identified and estimated. A detailed analysis of learning studies revealed that the most effective form of feedback was information about the task. The authors also analyzed empirically under what conditions the application of bootstrapping--or replacing judges by their linear models--is advantageous. Finally, the authors note shortcomings of the kinds of studies conducted to date, limitations in the lens model methodology, and possibilities for future research.     

The team role test: development and validation of a team role knowledge situational judgment test

The main objectives in this research were to introduce the concept of team role knowledge and to investigate its potential usefulness for team member selection. In Study 1, the authors developed a situational judgment test, called the Team Role Test, to measure knowledge of 10 roles relevant to the team context. The criterion-related validity of this measure was examined in 2 additional studies. In a sample of academic project teams (N = 93), team role knowledge predicted team member role performance (r = .34). Role knowledge also provided incremental validity beyond mental ability and the Big Five personality factors in the prediction of role performance. The results of Study 2 revealed that the predictive validity of role knowledge generalizes to team members in a work setting (N = 82, r = .30). The implications of the results for selection in team environments are discussed.     

A two-stage detection model applied to skilled visual search by radiologists

Harvard Medical School and Peter Bent Brigham Hospital, Boston, Massachusetts 02115 The model treats the detection of targets in a visual search task as a concatenation of two serial detection stages. Preattentive visual mechanisms in the initial stage function as a filter, selecting specific features of a visual pattern for the observer’s explicit attention and final cognitive evaluation. The model uses bivariate normal distributions to represent the decision variables for the two serial stages, assuming different parameters for the target and nontarget features in a test set. The model is applied to the detection performance of radiologists interpreting chest x-rays under various conditions of search. It accounts for the substantial improvement in radiologists’ ability to distinguish between target and nontarget test features when they had to search the x-ray images, compared to their performance without visual search. A change in the ROC curve between two different search tasks could be interpreted as a shift in the selection cutoff used by the preattentive filter.     

Tests of a two-stage model of visual matching

Predictions from a model of visual matching were tested in two experiments. The model consists of a wholistic comparison process followed by an element-by-element comparison process. All stimuli are processed by the first stage but only those that permit a decision based on a wholistic comparison produce responses. When discrimination is difficult and a decision cannot be reached by a wholistic comparison, the second stage of processing is initiated. Degree of discriminability and stimulus duration (100 and 1000 msec.) were varied in both experiments. In Exp. 1, the stimulus elements were arranged in a square configuration to facilitate a wholistic comparison. As predicted, the hard-different stimuli took longer to match than the same or easy-different stimuli. The hard-different stimuli presented for 1000 msec. took longer to match than those presented for 100 msec. There was no difference in accuracy between responses to hard-different pairs at the two durations. In Exp. 2, the stimulus elements were arranged in a horizontal row and placed one above the other to facilitate element-by-element comparison. As predicted, these stimuli produced slower and more accurate responses for same and hard-different stimulus pairs only when they were exposed for 1000 msec. Responses to easy-different stimulus pairs were made quickly and accurately.     

Relative judgment: A phenomenon and a theory

An experiment is described in which it was demonstrated that relative judgments of the more probable of two statements are quicker if the statements are both probable rather than improbable. For judgments of the less probable, the reverse result was obtained. This phenomenon is discussed in relation to various theories of judgment and choice. A theory is presented which assumes that judgment involves a relation between a stimulus and a word and follows Thurstone’s notion that stimuli differ in their discrirninal dispersions. This new theory is shown to be consistent with recent results in psycholinguistics.     

Judgments of average magnitude: Analyses in terms of the functional measurement and two-stage models

Subjects made magnitude estimates of the average loudness of pairs of 1,000-Hz tones varying in sound pressure. A test of fit of an averaging model employing an analysis of variance suggested that the judgments were internally consistent. However, estimates of the parameters of a two-stage model based on the assumption that power transformations were imposed in both input and output implied a nonlinear output function, inconsistent with the averaging model. Additional analyses employing a nonmetric scaling solution also suggested that output was nonlinear, indicating that this implication was not an artifact of the strong assumptions of the two-stage model. Large differences were found among the output functions of individual subjects, and it was suggested that these may have inflated the error term in the analysis of variance, reducing its power to detect violations of the additive model. Similar analyses were performed on data from judgments of average grayness collected by Weiss (1972).     

Variations in the magnitude of attentional capture: Testing a two-process model

Although large variations in the magnitude of attentional capture have been evidenced across a wide range of studies and paradigms (see Burnham, 2007, for a review), the nature of these variations is unclear. In the present study, we used a modified spatial cuing task to address two related issues. In the first experiment, we explored the hypothesis that the magnitude of attentional capture varies systematically as a function of cue-target similarity. Targets of a particular color were preceded by uninformative peripheral cues carrying varying percentages of the target color. As was predicted, the magnitude of attentional capture varied directly with the similarity between cue and target. In the second experiment, we explored whether these similarity effects reflect a mixture of trials on which attention is fully captured and trials on which attention is not captured at all (i.e., a two-process model). A mixture analysis conducted on obtained reaction time distributions proved inconsistent with a two-process model.