Unitary classification in a comparison task.

Sequential effects were used to diagnose whether elements in a two-object comparison task are represented as a perceptual unit or separately. The presence of sequential effects and absence of influences of individual elements on the subsequent trial in a successive comparison task favor the hypothesis that the elements in a pair are represented as a unit, and that a response is made to the perceptual unit. The patterns of response times on same and different trials differed in several ways; these suggested that the quality of the representations of same and different trials may differ.     

Components of geometric analogy solution

Geometric analogy solution was investigated as a function of systematic variations in the information structure of individual items. Latency data from the verification of true and false items indicated that individuals decompose figural patterns in a way that represents a sequential determination of the various elements that need to be isolated. They also appear to identify and evaluate the transformations applied to elements in a way that represents a sequential determination of the separate or successive transformations that fully specify an item rule. Analysis and evaluation of transformations took more time than element analysis and was the primary source of errors. The combined effects of element and transformation processing violated a simple additive model and the best fitting functions suggested that nonadditive increases in solution latency and error rates were due to working memory limitations associated with the representation and manipulation of item features at high levels of rule complexity. Correlational data also indicated that these factors partially account for individual differences in performance on psychometric tests. The latency and error data for true and false items are used to develop a general theoretical system that incorporates assumptions about the form of item representation, working memory factors, and processing components and strategies in analogical reasoning tasks.     

Two classes of models for magnitude estimation

One class of models assumes that presentation of a signal results in an internal representation as a random variable. Depending on whether the signal is close to or far from the preceding signal, the variance of the representation is smaller or larger. Responses are determined largely by this random variable; however, when the signal is close to the preceding one, the response is generated by modifying the representation multiplicatively by some function of the ratio of the previous response to its representation. Power and linear functions are explored. The form of the random variable is assumed to be that arising from either the timing or the counting model operating on a Poisson process. Detailed analyses are carried out successfully only for the timing model with neural sample sizes independent of intensity; however, the data require the sample to increase with intensity. The linear response function coupled with the constant sample size counting model appears somewhat viable, but detailed calculations are very difficult to carry out. The second class of models postulates a power function relation between magnitude estimates and signals intensity for which the exponent is a Gaussian distributed random variable and the unit is the product of two log normal random variables. Again we assume an attention band such that succesive stimuli that are widely separated in intensity lead to independent samples of the random variables while a variety of assumptions is explored for successive stimuli that are near each other in intensity. Although they each give rise to the qualitative features of the data, estimates of parameters are sufficiently inconsistent that we are led to reject all of the submodels studied.     

Unitary classification in a comparison task

Sequential effects were used to diagnose whether elements in a two-object-comparison-task are represented as a perceptual unit or separately. The presence of sequential effects and absence of influences of individual elements on the subsequent trial in a successive comparison task favor the hypothesis that the elements in a pair are represented as a unit, and that a response is made to the perceptual unit. The patterns of responsetimes onsame anddifferent trials differed in-several ways; these suggested that the quality of the representations ofsame anddifferent trials may differ.     

The role of sparsely distributed representations in familiarity recognition of verbal and olfactory materials

We present the generalized signal detection theory (GSDT), where familiarity is described by a sparse binomial distribution of binary node activity rather than by normal distribution of familiarity. Items are presented in a distributed representation, where each node receives either noise only, or signal and noise. An old response (i.e., a “yes” response) is made if at least one node receives signal plus noise that is larger than the activation threshold, and item variability is determined by the distribution of activated nodes as the threshold is varied. A distinct representation leads to better performance and a lower ratio of new to old item variability, than a more distributed and less distinct representations. Here we apply the GSDT to empirical data on verbal and olfactory memory and suggest that verbal memory relies on a distinct neural item representation, whereas olfactory memory has a fuzzy neural representation leading to poorer memory and inducing a larger ratio of new to old item variability.     

Effect of learning on production of duration in variable motor conditions

It has been suggested that increasing proprioceptive feedback and ensuring its consistency from trial to trial favours timing accuracy. The progressive acquisition of a timing performance with isometric and anisometric responses was investigated in conditions of 'inconsistent feedback', with two different methods: counting seconds or not. Subjects gripped the handle of a dynamometer during precisely 5 seconds in 4 randomly distributed conditions: 'Weak' or 'Strong' constant force, 'Slow' or 'Rapid' variable force. A first group produced the durations without counting and a second group counted seconds either mentally or aloud. Learning was examined in 4 successive blocks of trials. Average produced durations did not differ as a function of group, but the variability was reduced when subjects counted seconds. In both groups, the constant force conditions induced more accurate responses than the variable force conditions in the first block of trials. 'Slow' and 'Rapid' conditions were respectively associated with overestimation and under-estimation of response duration. These trends diminished progressively with learning. Both groups yielded sequential effects linked to duration and independent of condition. These data suggest that, whether subjects counted or not, learning was not based on condition-specific proprioceptive feedback. It may involve the elaboration of an internal temporal reference common to all conditions.     

Decade breaks in the mental number line? Putting the tens and units back in different bins.

Most models of number recognition agree that among other number representations there is a central semantic magnitude representation which may be conceptualized as a logarithmically compressed mental number line. Whether or not this number line is decomposed into different representations for tens and units is, however, controversial. We investigated this issue in German participants in a magnitude comparison (selection) task in which the larger of two visually presented Arabic two-digit numbers had to be selected. Most importantly, we varied unit-decade-compatibility: a number pair was defined as compatible if the decade magnitude comparison and the unit magnitude comparison of the two numbers would lead to the same response (e.g. 52 and 67) and as incompatible if this was not the case (e.g. 47 and 62). While controlling for overall numerical distance, size and other variables, we consistently found compatibility effects. A control experiment showed that this compatibility effect was not due to perceptual presentation characteristics. We conclude that the idea of one single number line representation that does not additionally assume different magnitude representations for tens and units is not sufficient to account for the data. Finally, we discuss why decade effects were not found in other experimental settings.     

Signal recognition models compared for random and Markov presentation sequences

Models of two-category signal recognition are compared to data from a variety of experimental conditions. For recognition, one of two signals (S₁, S₂) which vary slightly on some simple physical dimension is presented on each trial, and 0 is to identify (I₁, I₂ ) which signal was presented. In general, Os show a decrease in both Pr(I₁ /S₂) and Pr(I₂/S₁) for either greater Pr(S₂) or, sequentially, for greater S₂ recency. These effects are described as probability and sequential contrast, respectively. The memory state model (MS) describes a three-state threshold process with responses determined by a simple first-order Markov process which depends on the sensory state and response on the immediately preceding trial. The memory trace regression model (MTR) assumes that O compares the observed signal event with the memory trace of the previous signal event. When the difference is large, the sign of the difference determines the response; when it is small, the response depends on the preceding response. The memory trace is assumed to regress toward the mean signal value. Both models accurately predict the observed bias changes as a function of signal probabilities and of the subsequence of events on the previous trial. The response axioms of the MTR model are modified to predict the results for individual Os for Markov chains of signal events. The response axioms of the MS model are modified to predict responding when information is given to O concerning signal probabilities. Although both models do well under all conditions, the MS model uses fewer parameters and correctly predicts the direction of higher order sequential dependencies.     

He said,she said: Episodic retrieval induces conflict adaptation in an auditory Stroop task

People respond more slowly if an irrelevant feature of a target stimulus is incompatible with the relevant feature or the correct response. Such compatibility effects are often reduced in trials following an incompatible trial, which has been taken to reflect increased cognitive control. This pattern holds only if two trials share some similarities, however, suggesting that it may be modulated by the episodic context. To look into this possibility, we had participants respond to high- or low-pitched tones by saying “high” or “low,” respectively, and ignore the simultaneously presented auditory word “high” or “low.” As expected, performance was impaired if the heard word was incompatible with the required response, and this Stroop-like effect was reduced after incompatible trials. This sequential modulation was observed, however, only if the voice in the two successive trials was the same, whereas no modulation was obtained when the speaker changed. The results suggest that sequential modulations are due to the automatic retrieval of episodic event representations that integrate stimuli, actions, and situational and task-specific control information, so that later reactivation of some elements of a given representation tends to retrieve the other elements as well.     

The bow and sequential effects in absolute identification

The bow and sequential effects in absolute identification are investigated in this paper by following two strategies: (1) Experiments are performed in which sequential dependencies in signal presentations are manipulated, and 12) analyses are conducted (some of which are largely free of model-specific assumptions) which bear directly on the question of the origin of the sequential effects. The main result of the study is that absolute identification performance is greatly improved in a design in which each signal lies close to the preceding signal presented, even though the entire range of signals used is the same as in a random presentation design. This finding is consistent with the attention-band model of Luce, Green, and Weber (1976) and rejects hypotheses that suggest that the variability in the signal representation in absolute identification is a function solely of the range of signals being used. However, nonparametric analyses of sequential response errors show that a plausible assumption concerning the trial by-trial movement of the attention band provides an incomplete explanation of Seluential effects in absolute identification. These results are far better explained in terms of systematic shifts of category boundaries in a Thurstonian model, as suggested by Purks, Callahan, Braida, and Durlach (1980). Experiments are also performed which suggest that memory decay is not the major factor accounting for the bow effect in absolute identification.     

Autocorrelation of choice-reaction times.

A choice-reaction (CR) task requires that the subject estimate, raking the warning signal or his response on the preceding trial as a reference point, the time when the reaction stimulus is due, so that he can begin deciding on his response at an appropriate time. This paper presents a model for the reproduction of temporal intervals, with particular emphasis on the sequential statistics of a series of such reproductions. When this model is concatenated with the sequential probability ratio test model for 2CRT, it provides a quantitative account of the pattern of autocorrelation found in a series of RTs. There is no corresponding autocorrelation in the incidence of errors, however, because after an error the subject systematically adjusts the epoch at which he begins sampling as a precaution against a further error. These post-error adjustments can readily be incorporated into the model. The ideas presented enable several different CR phenomena to be related, and they have implications for the relation between speed and accuracy, for the form of empirical distributions of RTs, and for the effects of temporal uncertainty.     

Hierarchical structure in perceptual representation

A theoretical framework for perceptual representation is presented which proposes that information is coded in hierarchical networks of nonverbal propositions. The hierarchical structure of the representations implies selective organization: Some subsets of a figure will be encoded as integral, structural units of that figure, while others will not. A context-sensitive metric for the “goodness” of a part within a figure is developed, corresponding to the probability that the subset will be encoded as a structural unit. Converging evidence supporting this position is presented from four different tasks using simple, straight-line figures. The tasks studied are (a) dividing figures into “natural” parts, (b) rating the “goodness” of parts within figures, (c) timed verification of parts within figures, and (d) timed mental synthesis of spatially separated parts into unitary figures. The results are discussed in terms of the proposed theory of representation, the processes that operate on those representations, and the general implications of the data for perceptual theories.     

Cardiac orienting responses of 6- and 16-week-old infants

Since previous data suggested that the magnitude of orienting evidenced by cardiac deceleration increased over the first 16 weeks of life, 6- and 16-week-old infants were compared on various characteristics of orienting: habituation, dishabituation, and magnitude of deceleration to stimulus offset as well as to stimulus onset. Neither the change in stimulus following habituation trials nor the stimulus offset produced a large enough response to confidently evaluate age differences suggested by the data. Stimulus onset elicited a pronounced deceleration which for the two age groups was of equivalent magnitude on initial trials and declined similarly with stimulus repetition. It was suggested that similarity of the two age groups on these parameters was due to control of state within a narrow alert range, and that, in general, younger infants are less likely than older infants to show orienting when conditions for orienting are marginal.     

Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect

Number magnitude and number parity representation are fundamental number representations. However, the representation of parity is much less understood than that of magnitude: Therefore, we investigated it by examining the (new) Linguistic Markedness of Response Codes (MARC) effect: Responses are facilitated if stimuli and response codes both have the same (congruent) linguistic markedness (even-right, odd-left) while incongruent conditions (even-left, odd-right) lead to interference. We examined systematically the MARC (for parity) and the Spatial Numerical Association of Response Codes (SNARC; for magnitude) effect for different number notations (positive Arabic, negative Arabic, number words) and with different methods of data analysis. In a parity judgement task, the SNARCeffect indicating a magnitude representation was replicated for all notations except for negative numerals. The MARCeffect was found for number words in all analyses, but less consistently for the other notations. In contrast, a correlational analysis of the reaction time (RT) data, as suggested by Sternberg (1969) using a nonmetric multi-dimensional scaling (MDS) procedure, produced a clear association of parity and response code for all notations (MARCeffect), but little evidence of the SNARCeffect. We discuss the extent to which these notation-specific MARC and SNARC effects constrain current models of number processing and elaborate on the possible functional locus of the MARC effect.     

Thurstone's discriminal processes fifty years later

Four issues are discussed concerning Thurstone's discriminal processes: the distributions governing the representation, the nature of the response decision rules, the relation of the mean representation to physical characteristics of the stimulus, and factors affecting the variance of the representation. A neural schema underlying the representation is proposed which involves samples in time of pulse trains on individual neural fibers, estimators of parameters of the several pulse trains, samples of neural fibers, and an aggregation of the estimates over the sample. The resulting aggregated estimate is the Thurstonian representation. Two estimators of pulse rate, which is monotonic with signal intensity, are timing and counting ratios and two methods of aggregation are averaging and maximizing. These lead to very different predictions in a speed-accuracy experiment; data indicate that both estimators are available and the aggregation is by averaging. Magnitude estimation data are then used both to illustrate an unusual response rule and to study the psychophysical law. In addition, the pattern of variability and correlation of magnitude estimates on successive trials is interpreted in terms of the sample size over which the aggregation takes place. Neural sample size is equated with selective attention, and is an important factor affecting the variability of the representation. It accounts for the magical number seven phenomenon in absolute identification and predicts the impact of nonuniform distributions of intensities on the absolute identification of two frequencies. 1977 Psychometric Society Presidential Address. This work was supported in part by a grant of the National Science Foundation to Harvard University. I wish to express my appreciation to S. Burbeck, D. M. Green, M. Shaw, and B. Wandell for their useful comments on an earlier draft of this paper.     

Congruency sequence effect without feature integration and contingency learning

The magnitude of congruency effects, such as the flanker-compatibility effects, has been found to vary as a function of the congruency of the previous trial. Some studies have suggested that this congruency sequence effect is attributable to stimulus and/or response priming, and/or contingency learning, whereas other studies have suggested that the control process triggered by conflict modulates the congruency effect. The present study examined whether sequential modulation can occur without stimulus and response repetitions and contingency learning. Participants were asked to perform two color flanker-compatibility tasks alternately in a trial-by-trial manner, with four fingers of one hand in Experiment 1 and with the index and middle fingers of two hands in Experiment 2, to avoid stimulus and response repetitions and contingency learning. A significant congruency sequence effect was obtained between the congruencies of the two tasks in Experiment 1 but not in Experiment 2. These results provide evidence for the idea that the sequential modulation is, at least in part, an outcome of the top-down control process triggered by conflict, which is specific to response mode.     

Timing and the control of variation

Two rat experiments shed light on how variation in behavior is regulated. Experiment 1 used the peak procedure. On most trials, the 1st bar press more than 40 s after signal onset ended the signal and produced food. Other trials lasted much longer and ended without food. On those trials, the variability of bar-press duration increased greatly after the 1st response more than 40 s after signal onset. In Experiment 2, which asked whether the increase was due to the omission of expected reward or the decrease in reward expectation, reward expectation had a strong effect on response duration, whereas omission of expected reward had little effect. In both experiments, response rate and response duration changed independently, suggesting that they reflect different parts of the underlying mechanism. In Experiment 1, response durations implied that timing of the signal was more accurate than the rate-vs.-time function might suggest. Experiment 2 suggested that lowering reward expectation increases variation in response form.     

On the ability to inhibit simple and choice reaction time responses: a model and a method

This article reports four experiments on the ability to inhibit responses in simple and choice reaction time (RT) tasks. Subjects responding to visually presented letters were occasionally presented with a stop signal (a tone) that told them not to respond on that trial. The major dependent variables were (a) the probability of inhibiting a response when the signal occurred, (b) mean and standard deviation (SD) of RT on no-signal trials, (c) mean RT on trials on which the signal occurred but subjects failed to inhibit, and (d) estimated RT to the stop signal. A model was proposed to estimated RT to the stop signal and to account for the relations among the variables. Its main assumption is that the RT process and the stopping process race, and response inhibition depends on which process finishes first. The model allows us to account for differences in response inhibition between tasks in terms of transformations of stop-signal delay that represent the relative finishing times of the RT process and the stopping process. The transformations specified by the model were successful in group data and in data from individual subjects, regardless of how delays were selected. The experiments also compared different methods of selecting stop-signal delays to equate the probability of inhibition in the two tasks.     

Dynamic adjustment of temporal preparation: Shifting warning signal modality attenuates the sequential foreperiod effect

We examined sequential effects in the variable foreperiod (FP) paradigm, which refer to the finding that responses to an imperative signal (IS) are fast when a short FP trial is repeated but slow when it is preceded by a long FP trial. The effect has been attributed to a trace-conditioning mechanism in which individuals learn the temporal relationship between a warning signal (WS) and the IS in a trial-by-trial manner. An important assumption is that the WS in a current trial (i.e., trial FP_n) acts as a conditioned stimulus, such that it automatically triggers the conditioned response at the exact critical moment that was imperative in the previous trial (i.e., trial FP_n−1). According to this assumption, a shift from one WS modality in trial FP_n−1 to another modality in trial FP_n is expected to eliminate or at least reduce the sequential FP effect. This prediction was tested in three experiments that included a random variation of WS modality and FP length within blocks of trials. In agreement with the prediction, a shift in WS modality attenuated the asymmetry of the sequential FP effect.