Varieties of Binocular Interaction in Human Vision

Binocular processing was investigated using a quantitative, process-oriented metatheory of response times. The analyses are not confined to particular distributional assumptions or specific models. Upper and lower performance boundaries for probability summation in parallel processing are defined and compared with observed distributions of reaction times using a variety of dichoptic stimuli. Performance that exceeds the upper bound strongly suggests faciliatory convergence between the two eyes (binocular channel summation). Performance below the lower bound suggests that inputs to the two eyes are processed serially. The results indicate that binocular channel summation in subjects with normal stereo vision requires targets of the same luminance polarity (paired increments or decrements) in corresponding retinal locations. When corresponding retinal locations are stimulated with opposing luminance polarities (increment to one eye, decrement to the other), performance is consistent with probability summation, indicating that parallel ON and OFF pathways remain segregated at least to the level of binocular fusion. Further analyses of data from a stereo-blind observer suggests serial processing of binocular inputs.     

The optimum decision rules in thesame-different paradigm

In this paper we derive the optimum (likelihood-ratio) decision statistic for asame-different paradigm. The likelihood ratio is dependent on the degree of correlation between the two observations on each trial. For the two extreme cases in which the observations are either independent or highly correlated, the optimum decision rule is identical to each of two previously suggested decision rules. For these two cases, the receiver-operating characteristic (ROC) curves are calculated. Finally, an experimental procedure is suggested for assessing the decision rule actually used by the observer in asame-different task.     

Robust versus optimal strategies for two-alternative forced choice tasks

It has been proposed that animals and humans might choose a speed-accuracy tradeoff that maximizes reward rate. For this utility function the simple drift-diffusion model of two-alternative forced-choice tasks predicts a parameter-free optimal performance curve that relates normalized decision times to error rates under varying task conditions. However, behavioral data indicate that only ≈30% of subjects achieve optimality, and here we investigate the possibility that, in allowing for uncertainties, subjects might exercise robust strategies instead of optimal ones. We consider two strategies in which robustness is achieved by relinquishing performance: maximin and robust-satisficing. The former supposes maximization of guaranteed performance under a presumed level of uncertainty; the latter assumes that subjects require a critical performance level and maximize the level of uncertainty under which it can be guaranteed. These strategies respectively yield performance curves parameterized by a presumed uncertainty level and required performance. Maximin performance curves for uncertainties in response-to-stimulus interval match data for the lower-scoring 70% of subjects well, and are more likely to explain it than robust-satisficing or alternative optimal performance curves that emphasize accuracy. For uncertainties in signal-to-noise ratio, neither maximin nor robust-satisficing performance curves adequately describe the data. We discuss implications for decisions under uncertainties, and suggest further behavioral assays.     

Decision making under internal uncertainty: the case of multiple-choice tests with different scoring rules

This paper assesses framing effects on decision making with internal uncertainty, i.e., partial knowledge, by focusing on examinees' behavior in multiple-choice (MC) tests with different scoring rules. In two experiments participants answered a general-knowledge MC test that consisted of 34 solvable and 6 unsolvable items. Experiment 1 studied two scoring rules involving Positive (only gains) and Negative (only losses) scores. Although answering all items was the dominating strategy for both rules, the results revealed a greater tendency to answer under the Negative scoring rule. These results are in line with the predictions derived from Prospect Theory (PT) [Econometrica 47 (1979) 263]. The second experiment studied two scoring rules, which allowed respondents to exhibit partial knowledge. Under the Inclusion-scoring rule the respondents mark all answers that could be correct, and under the Exclusion-scoring rule they exclude all answers that might be incorrect. As predicted by PT, respondents took more risks under the Inclusion rule than under the Exclusion rule. The results illustrate that the basic process that underlies choice behavior under internal uncertainty and especially the effect of framing is similar to the process of choice under external uncertainty and can be described quite accurately by PT.     

Understanding the limits of self‐control: Positive affect moderates the impact of task switching on consecutive self‐control performance

Performing consecutive self‐control tasks typically leads to deterioration in self‐control performance. This effect can be explained within the strength model of self‐control or within a cognitive control perspective. Both theoretical frameworks differ in their predictions with regard to the impact of affect and task characteristics on self‐control deterioration within a two‐task paradigm. Whereas the strength model predicts decrements in self‐control performance whenever both tasks require a limited resource, under a cognitive control perspective, decrements should only occur when people switch to a different response conflict in the second task. Moreover, only the cognitive control model predicts an interaction between task switching and positive affect. In the present research, we investigated this interaction within a two‐task paradigm and found evidence that favored a cognitive control interpretation of the results. Positive affect only benefitted consecutive self‐control performance if response conflicts in the two tasks were different (resisting sweets followed by a Stroop task). If they were the same (two consecutive Stroop tasks), positive affect impaired self‐control performance. These effects were partially replicated in the second study that also examined negative affect, which did not affect self‐control performance. We conclude that drawing on cognitive control models could add substantially to research on self‐control. Copyright © 2013 John Wiley & Sons, Ltd.     

Judgement under uncertainty and conjunction fallacy inhibition training

Intuitive predictions and judgements under uncertainty are often mediated by judgemental heuristics that sometimes lead to biases. Our micro-developmental study suggests that a presumption of rationality is justified for adult subjects, in so far as their systematic judgemental biases appear to be due to a specific executive-inhibition failure in working memory, and not necessarily to a lack of understanding of the fundamental principles of probability. This hypothesis was tested using an experimental procedure in which 60 adult subjects were trained to inhibit the classical conjunction bias on a frequency judgement task derived from Tversky and Kahneman's work. Pre- and post-test performance was assessed via a probability judgement task. The data indicated a training effect, suggesting that subjects traditionally labelled as “irrational” with respect to the classical rules of inductive reasoning are in fact “inefficient inhibitors”. These findings are discussed in terms of a polymorphous view of rationality.     

Generality of the summation effect in human causal learning

Considerable research has examined the contrasting predictions of the elemental and configural association theories proposed by Rescorla and Wagner (1972) and Pearce (1987), respectively. One simple method to distinguish between these approaches is the summation test, in which the associative strength attributed to a novel compound of two separately trained cues is examined. Under common assumptions, the configural view predicts that the strength of the compound will approximate to the average strength of its components, whereas the elemental approach predicts that the strength of the compound will be greater than the strength of either component. Different studies have produced mixed outcomes. In studies of human causal learning, Collins and Shanks (2006) suggested that the observation of summation is encouraged by training, in which different stimuli are associated with different submaximal outcomes, and by testing, in which the alternative outcomes can be scaled. The reported experiments further pursued this reasoning. In Experiment 1, summation was more substantial when the participants were trained with outcomes identified as submaximal than when trained with simple categorical (presence/absence) outcomes. Experiments 2 and 3 demonstrated that summation can also be obtained with categorical outcomes during training, if the participants are encouraged by instruction or the character of training to rate the separately trained components with submaximal ratings. The results are interpreted in terms of apparent performance constraints in evaluations of the contrasting theoretical predictions concerning summation.     

Binocular interactions in suprathreshold contrast perception

Suprathreshold binocular contrast interactions were studied psychophysically. A split-screen CRT display was used to present separate sine-wave gratings to the observer’s left and right eyes. The method of constant stimuli and a modified method of adjustment were used to find sets of binoculartest patterns that matched a given binocularstandard. Test patterns consisted of the simultaneous presentation of sine-wave gratings that differed in contrast to the left and right eyes. Standard patterns consisted of identical sine-wave gratings presented to the two eyes, and had the same spatial frequency as the test patterns. Binocular contrast matching functions were obtained for several standard contrasts at 1 and 8 c/deg. Binocular matching functions were obtained for luminance increments as well. The binocular contrast matching functions departed from a simple binocular averaging rule, and behaved as if the eye receiving the higher contrast disproportionately dominated the binocular contrast percept. Departures from the binocular averaging rule were slightly greater for higher standard contrasts. Spatial frequency had little effect, and the luminance increment matching functions also departed from the binocular averaging rule. There was evidence for a contrast version of Fechner’s paradox and for substantial individual differences in a form of ocular dominance. In a further experiment, additivity of suprathreshold binocular contrast summation was examined by testing the double-cancellation condition. We found no systematic violations of additivity at 1 and 8 c/deg. Models of suprathreshold binocular contrast summation were examined.     

The variance reaction time model

The variance reaction time model (VRTM) is proposed to account for various recognition data on reaction time, the mirror effect, receiver-operating-characteristic (ROC) curves, etc. The model is based on simple and plausible assumptions within a neural network: VRTM is a two layer neural network where one layer represents items and one layer represents contexts. The recognition decision is based on a random walk of nodes activated at recognition. VRTM suggests theoretical constraints on the distributions of nodes activated at recognition and the noise in the random walk. The variability in the net inputs to nodes depends on the item frequency (the number of times that the item has been encoded) and the list length. The essential mechanism that accounts for the empirical data is a non-linear activation function. The mean activation threshold in the non-linear activation function is placed to achieve efficient discriminability between new and old items and there is variability in the activation threshold. VRTM predicts the mirror effect for low and high frequency words, a strength based mirror effect between conditions but not within one condition, appropriate ROC-curves for old/new and high/low frequency items, and list-length effects. Furthermore, it predicts appropriate means and distributions of reaction times for old/new, correct/incorrect, and high/low frequency items as well as speed/accuracy tradeoffs. VRTM has an explicit mathematical solution, it is simulated in a neural network, and it is fitted to a number of datasets.     

Predicting emotional concomitants of learned helplessness: The role of motivational orientation

Previous theoretical and empirical analyses indicate that an extrinsic motivational orientation, i.e., performing activities to please others or concern with criticism, predicts the cognitive and behavioral deficits associated with learned helplessness. Conversely, intrinsically motivated students, who perform activities for the inherent pleasure of mastery over challenge, have been shown to be virtually resilient to successive failure experiences and even show a facilitation effect. However, research has not yet addressed the extent to which motivational orientation predicts the emotional deficits associated with helplessness—namely, depression and a maladaptive attributional style. Furthermore, no research has examined the relative predictability of these variables to investigate subjects' feelings after an experimental manipulation of failure. The present research found support for the proposition that an extrinsic motivational orientation predicts depression and the Expanded Attributional Style Questionnaire. More importantly, our findings demonstrated that an extrinsic motivational orientation was a more reliable predictor of subjects' feelings after a failure manipulation than either depression or a maladaptive attributional style. These findings are discussed in light of intervention strategies to attenuate the development of an extrinsic motivational orientation in students.     

Learning conceptual rules: III. Processes contributing to rule difficulty

Eight unique bidimensional conceptual rule forms were compared in a rule learning paradigm. It was predicted that rule difficulty order and error distributions across stimulus class defined by a truth table would be a function of Ss' preexperimental experience predominantly with conjunctive concepts. The hypothesis stated specifically that loci of difficulty with rules derive from: (a) assignment of TT stimuli (those with both relevant attributes) to the negative category; (b) assignment of FF stimuli (those with neither relevant attributes) to the positive category; (c) assignment of TT and FF stimuli to the same category. The main effects of rule and truth table class and the interaction of rule and truth table class were statistically significant. The results confirm all predictions about rule order and error distributions.     

Statistical significance tests for binormal ROC curves

Statistical significance tests are derived and evaluated for measuring apparent differences between an obtained and an expected binormal ROC curve, between two independent binormal ROC curves, and among groups of independent binormal ROC curves. A binormal ROC curve is described by two parameters which represent the spread of the means and the ratio of the standard deviations of the two underlying Gaussian decision variable distributions. To test the significance of apparent differences between or among ROC curves, approximate χ² statistics for each of the three tests were constructed from maximum likelihood estimates of the two parameters defining the binormal ROC curve. The performance of each test statistic was evaluated by simulating five-category rating scale data with equal numbers of noise and signal-plus-noise trials (set at 50, 250, and 500) for each of three typical ROC curves. For the significance test involving only one ROC curve, rating scale data were generated from the chance diagonal of the ROC space also. Although test performance was found to be somewhat dependent on the number of trials and on the location of the ROC curve in the ROC space, comparisons of the obtained and expected fractions of (falsely) significant results at various α levels showed the proposed statistical significance tests to be reliable under practical experimental conditions.     

Dichotic, diotic, and monaural summation of loudness: a comprehensive analysis of composition and psychophysical functions

In a series of six experiments, the method of magnitude estimation, constrained by a multivariate model, was used to assess the rules that govern the summation of the loudness of two-tone complexes. This methodology enabled us to specify the amounts of summation and simultaneously to construct the corresponding loudness scales. The components had different frequency separations and in the different experiments were presented (1) dichotically, a different frequency to each ear; (2) diotically, to both ears; and (3) monaurally. Results replicated and in some conditions extended known features of multiple signal processing by the auditory system. Thus, qualitatively different rules of loudness integration appeared. For monaural and diotic modes of stimulation, overall loudness depended on total sound energy within the critical band, but on the simple sum of component loudnesses beyond the critical band. For dichotic presentations, a fully additive rule of loudness summation appeared, regardless of frequency spacing. For the latter (but not the former), loudness summation was perfect, with the underlying loudness scales closely approximating Stevens's sone scale.     

Interpreting cross-sectional data on stages of change

Abstract

The vast majority of studies investigating stage theories of health behaviour such as the transtheoretical model have used a cross-sectional research design. Participants are classified into stages and compared on theoretically relevant variables. This paper discusses the proper interpretation of cross-sectional data on stages of change. Linear patterns are not consistent with the stage model assumption that different causal factors are important at different stages but discontinuity patterns (patterns that do not show consistent increments or decrements across stages) can be diagnostic of a stage model. Researchers who use cross-sectional designs should specify predictions concerning the patterns to be expected under a stage model and under possible rival models, and interpret their data accordingly. Wherever possible, they should conduct prospective longitudinal and experimental studies which enable stronger inferences to be drawn.     

Extending Statistics of Extremes to Distributions Varying in Position and Scale and the Implications for Race Models

Race models are characterized by the largest or smallest of samples from n distributions. The asymptotic theory of extremes has demonstrated that for identically distributed, independent, and lower-bounded random variables, whose left tail approximates a power function, the distribution of the minimum tends toward a Weibull distribution as n increases. In this article, we remove the restriction of identically distributed random variables by letting the lower bound or the scale of the random variables be random variables themselves. We prove that the Weibull distribution is still the asymptotic distribution of the minimum and relate its parameters to the parameters of the input distributions. We discuss the potential use of such findings in models of psychological processes.     

A Model of Students' Decimal Computation Procedures

A model that describes the construction and execution of decimal computation procedures is presented. Our hypothesis is that students compute by relying solely on syntax-based rules; semantic knowledge has no effect on performance. To test the claim, a model is developed in which computation procedures are viewed as chains of component symbol manipulation rules. The model assumes that students acquire through instruction the individual rules that achieve subgoals in the computation process. The task for the procedural system is to select rules that satisfy each subgoal in sequence. The model specifies the rules of the system and identifies the syntactic features of the task that affect the selection of individual rules at each decision point. It then predicts the relative difficulty of decimal computation items and predicts the procedural flaw that will occur most frequently on each item. Written test and interview data are presented to test the predictions. Concluding comments discuss the nature of students' computation procedures, compare the model with other models of computation performance, and outline how the model might inform instruction.     

Type 2 tasks in the theory of signal detectability: Discrimination between correct and incorrect decisions

It has been known for over 40 years that there are two fundamentally different kinds of detection tasks in the theory of signal detectability. The Type 1 task is to distinguish between events defined independently of the observer; the Type 2 task is to distinguish between one’s own correct and incorrect decisions about those Type 1 events. For the Type 1 task, the behavior of the detector can be summarized by the traditional receiver operating characteristic (ROC) curve. This curve can be compared with a theoretical ROC curve, which can be generated from overlapping probability functions conditional on the Type 1 events on an appropriate decision axis. We show how to derive the probability functions underlying Type 2 decisions from those for the Type 1 task. ROC curves and the usual measures of performance are readily obtained from those Type 2 functions, and some relationships among various Type 1 and Type 2 performance measures are presented. We discuss the relationshiPbetween Type 1 and Type 2 confidence ratings and caution against the practice of presenting transformed Type 2 ratings as empirical Type 1 ratings.     

Acquisition of decision making criteria: reward rate ultimately beats accuracy

Speed-accuracy trade-offs strongly influence the rate of reward that can be earned in many decision-making tasks. Previous reports suggest that human participants often adopt suboptimal speed-accuracy trade-offs in single session, two-alternative forced-choice tasks. We investigated whether humans acquired optimal speed-accuracy trade-offs when extensively trained with multiple signal qualities. When performance was characterized in terms of decision time and accuracy, our participants eventually performed nearly optimally in the case of higher signal qualities. Rather than adopting decision criteria that were individually optimal for each signal quality, participants adopted a single threshold that was nearly optimal for most signal qualities. However, setting a single threshold for different coherence conditions resulted in only negligible decrements in the maximum possible reward rate. Finally, we tested two hypotheses regarding the possible sources of suboptimal performance: (1) favoring accuracy over reward rate and (2) misestimating the reward rate due to timing uncertainty. Our findings provide support for both hypotheses, but also for the hypothesis that participants can learn to approach optimality. We find specifically that an accuracy bias dominates early performance, but diminishes greatly with practice. The residual discrepancy between optimal and observed performance can be explained by an adaptive response to uncertainty in time estimation.     

Comparison of implicit and explicit learning processes in a probabilistic task

This experiment compared the performance with explicit (rule-application and rule-discovery) and implicit (nonrule-instructed) learning approaches on the performance of a probabilistic video game task requiring fine motor control. The task required visual tracking of a small ball of light and "catching" it by means of joystick manipulation. A general pattern of improvement with practice occurred for all conditions. All conditions showed use of predictive relations among stimulus events. However, task performance of the rule-application and rule-discovery conditions were inferior to the nonrule-instructed implicit condition, particularly during the early phases of rule acquisition and application. This pattern strongly suggests substantial performance costs associated with attempting to discover or apply probabilistic rules. Decrements are likely due to increased cognitive demands associated with attempting to remember and strategically apply provided probability rules or attempting to discover and apply potentially important and useful probability information from a complex visual display.     

Factors affecting the slope of empirical ROC curves: Comparison of binary and rating responses

Receiver operating characteristics (ROC curves) were obtained at six signal-to-noise ratios, with two response procedures, in each of three detection paradigms. In all three paradigms-one-interval and two-interval simple detection, and two-interval pedestal-a binary response produced ROC curves with slopes near unity at all signal levels, and a category-rating response led to ROC curves whose slopes decreased with increasing signal strength. This result is thought to be attributable to the varying a priori probability of signal presentation associated with our binary response procedure. The index of detectability taken from the negative diagonal of the ROC space was found to be invariant despite the differences in slope.