Independence and separability of volume and mass in the size-weight illusion

Numerous size-weight illusion models were classified in the present article according to general recognition theory (Ashby & Townsend, 1986), wherein the illusion results from a lack of perceptual separability, perceptual independence, decisional separability, or a combination of the three. These options were tested in two experiments in which a feature-complete factorial design and multidimensional signal detection analysis were used (Kadlec & Townsend, 1992a, 1992b). With haptic touch alone, the illusion was associated with a lack of perceptual and decisional separability. When the participant viewed the stimulus in his or her hand, the illusion was associated only with a lack of decisional separability. Visual input appeared to improve the discrimination of mass, leaving only the response bias due to expectation.     

Further considerations of a general d′ in multidimensional space

Thomas (Psychonom. Bull. Rev. 6 (1999) 224) proposed a generalization of d′,d_g′ for multidimensional distributions and demonstrated that it is not equivalent to Euclidean distance as had been assumed in some previous studies. In this note, it is further shown not to be a metric in the general sense as it fails the triangle inequality. Also, a rigorous proof is offered of the claim (found in Thomas, Psychonom. Bull. Rev. 6 (1999) 224) that in order for the definition of d_g′ to correspond to the quantity that is estimated from data in the traditional way (using hits and false alarms) one must assume a distance classifier (proved in the case of equal covariance matrices). If one assumes optimal responding instead, then the estimated d′ corresponds to (the square root of) Mahalanobis distance. This latter observation clears up an apparent paradox between the fact that d_g′ is not a metric and Ashby and Perrin's (Psychol. Rev. 95 (1988) 124) statement relating the weighted Euclidean scaling model and a signal detection model of similarity that would yield a distance classifier.     

Indecision on decisional separability

The theoretical framework of General Recognition Theory (GRT; Ashby & Townsend, Psychological Review, 93, 154-179, 1986) coupled with the empirical analysis tools of Multidimensional Signal Detection Analysis (MSDA; Kadlec & Townsend, Multidimensional models of perception and recognition, pp. 181-228, 1992) have become one important method for assessing dimensional interactions in perceptual decision-making. In this article, we critically examine MSDA and characterize cases where it is unable to discriminate two kinds of dimensional interactions: perceptual separability and decisional separability. We performed simulations with known instances of violations of perceptual or decisional separability, applied MSDA to the data generated by these simulations, and evaluated MSDA on its ability to accurately characterize the perceptual versus decisional source of these simulated dimensional interactions. Critical cases of violations of perceptual separability are often mischaracterized by MSDA as violations of decisional separability.     

Single-letter recognition as a function of exposure duration

The time course of visual letter recognition was investigated in a single-stimulus identification experiment. On each trial, a randomly chosen stimulus letter was presented at 1 of 12 equiprobable positions that were equally spaced around the circumference of an imaginary circle centered on fixation. Exposure duration was varied from 10 to 200 ms, and the letter was followed by a pattern mask. The subject's task was to report the identity of the stimulus letter but refrain from guessing. For the briefest exposures, correct reports never occurred. For longer exposures, the function relating the probability p of recognizing the letter to the duration t of the stimulus exposure was well approximated by an exponential distribution function: p(t) = 1 − exp[−v·(t−t ₀)], where v is the rate of processing and t ₀ is the minimum effective exposure duration. The generality of this finding may be limited to cases in which stimuli are highly discriminable and response criteria are conservative. Extensions to Poisson counter or random walk models are considered for cases in which stimuli are confusable. Received: 1 July 1997 / Accepted: 2 July 1998     

General recognition theory extended to include response times: Predictions for a class of parallel systems

General Recognition Theory (GRT; Ashby & Townsend, 1986) is a multidimensional theory of classification. Originally developed to study various types of perceptual independence, it has also been widely employed in diverse cognitive venues, such as categorization. The initial theory and applications have been static, that is, lacking a time variable and focusing on patterns of responses, such as confusion matrices. Ashby proposed a parallel, dynamic stochastic version of GRT with application to perceptual independence based on discrete linear systems theory with imposed noise (Ashby, 1989). The current study again focuses on cognitive/perceptual independence within an identification classification paradigm. We extend stochastic GRT and its implicated methodology for cognitive/perceptual independence, to an entire class of parallel systems. This goal is met in a distribution-free manner and includes all linear and non-linear systems satisfying very general conditions. A number of theorems are proven concerning stochastic forms of independence. However, the theorems all assume the stochastic version of decisional separability. A vital task remains to investigate the consequences of failures of stochastic decisional separability.     

Variance ofd′ for thesame-different method

Variance estimates ofd′ are derived toward thesame-different method based on Taylor-series expansion with one and two variables. The variance estimates can be used for statistical comparison ofd′s obtained from various discrimination paradigms. Formulas and tables for estimating variance ofd′ for the method are provided. One S-PLUS program, which can produce bothd′ and variance ofd′, is also provided.     

Independence and separability in the perception of complex nonspeech sounds

All sounds are multidimensional, yet the relationships among auditory dimensions have been studied only infrequently. General recognition theory (GRT; Ashby & Townsend, 1986) is a multidimensional generalization of signal detection theory and, as such, provides powerful tools well suited to the study of the relationships among perceptual dimensions. However, previous uses of GRT have been limited in serious ways. We present methods designed to overcome these limitations, and we use these methods to apply GRT to investigations of the relationships among auditory perceptual dimensions that previous work suggests are independent (frequency, duration) or not (fundamental frequency [ f0], spectral shape). Results from Experiment 1 confirm that frequency and duration do not interact decisionally, and they extend this finding with evidence of perceptual independence. Results from Experiment 2 show that f0 and spectral shape tend to interact perceptually, decisionally, or both, and that perceptual interactions occur within, but not between, stimuli (i.e., the interactions suggest correlated noise across processing channels corresponding to perceptually separable dimensions). The results are discussed in relation to lower level sensory modeling and higher level cognitive and linguistic issues.     

Perceptual learning in contrast detection: presence and cost of shifts in response criteria

Contemporary theoretical accounts of perceptual learning typically assume that observers are either unbiased or stably biased across the course of learning. However, standard methods for estimating thresholds, as they are typically used, do not allow this assumption to be tested. We present an approach that allows for this test specific to perceptual learning for contrast detection. We show that reliable decreases in detection thresholds and increases in hit rates are not uniformly accompanied by reliable increases in sensitivity (d′), but are regularly accompanied by reliable liberal shifts in response criteria (c). In addition, we estimate the extent to which sensitivity could have increased in the absence of these liberal shifts. The results pose a challenge to the assumption that perceptual learning has limited or no impact on response criteria.     

Levels of experienced dimensionality in children and adults

This work presents a new conceptualization of the contrast between holistic and differentiated perception of multidimensional stimuli. Specifically, two hypotheses about the experiential status of dimensions within holistic perception are proposed and tested as explanations of young children's general perceptual mode and adults' integral mode. The major result is that three levels of dimensional status are realized: (1) the hypothesis of nonprimary axes characterizes adult “integral” perception of saturation and brightness relations, (2) the hypothesis of primary but not mandatory axes characterizes kindergarteners' “integral” perception of size and shade relations, and (3) the notion of mandatory axes characterizes adults' separable perception of size and shade relations. These results indicate a new interpretation of the integrality-separability distinction and the derivative developmental hypothesis. It is specifically hypothesized that the developmental history of most dimensional combinations includes these three levels.     

Categorization of visual stimuli in the honeybee Apis mellifera

Categorization refers to the classification of perceptual input into defined functional groups. We present and discuss evidence suggesting that stimulus categorization can also be found in an invertebrate, the honeybee Apis mellifera, thus underlining the generality across species of this cognitive process. Honeybees show positive transfer of appropriate responding from a trained to a novel set of visual stimuli. Such a transfer was demonstrated for specific isolated features such as symmetry or orientation, but also for assemblies (layouts) of features. Although transfer from training to novel stimuli can be achieved by stimulus generalization of the training stimuli, most of these transfer tests involved clearly distinguishable stimuli for which generalization would be reduced. Though in most cases specific experimental controls such as stimulus balance and discriminability are still required, it seems appropriate to characterize the performance of honeybees as reflecting categorization. Further experiments should address the issue of which categorization theory accounts better for the visual performances of honeybees.This contribution is part of the special issue “Animal Logics” (Watanabe and Huber 2006).     

Feature sampling in detection: implications for the measurement of perceptual independence

The article presents the feature sampling signal detection (FS-SDT) model, an extension of the multivariate signal detection (SDT) model. The FS-SDT model assumes that, because of attentional shifts, different subsets of features are sampled for different presentations of the same multidimensional stimulus. Contrary to the SDT model, the FS-SDT model enables the estimation of pure perceptual effects that are uncontaminated by strategic attention shifts. The consideration of feature sampling in detection and identification opens a new perspective on the problem of measuring, respectively, the separability and integrality of stimulus dimensions. Disregarding feature sampling as a component process in detection and identification usually results in biased estimations of perceptual independence concepts relevant for judgments of whether stimulus dimensions are processed independently.     

Multidimensional signal detection analyses (MSDA) for testing separability and independence: A Pascal program

A Pascal (Turbo 6.0) program for testing perceptual separability, decisional separability, and perceptual independence—three types of independence defined in the context of general recognition theory (GRT)—is presented. GRT is essentially a multidimensional extension of signal detectability theory (Green & Swets, 1966) and has been employed in complete-identification experimental paradigms to examine whether information processing of stimulus dimensions is perceptually and/or decisionally separable and/or perceptually independent. The definitions of these different forms of “independence” are provided, the experimental design is described, and the program, MSDA, is described and demonstrated.     

A Differential Geometric Description of the Relationships among Perceptions

We present a differential geometric method for measuring and characterizing the perceptions of an observer of a continuum of stimuli. Because the method is not based on a model of perceptual mechanisms, it can potentially be applied to a wide variety of observers and to many types of visual and auditory stimuli. The observer is asked to identify which small transformation of one stimulus is perceived to be equivalent to a small transformation of a second stimulus, differing from the first stimulus by a third small transformation. The observer's identification of a number of such transformations can be used to calculate an affine connection on the stimulus manifold. This quantity describes how the observer encodes an evolving stimulus as a perceived sequence of "reference" transformations. This type of encoding is a multidimensional generalization of Fechner's method and reduces to his psychophysical scale when the stimulus manifold is one dimensional and the reference transformation is chosen to be a just noticeable difference. The intrinsic aspects of the nature of the observer's perceptions can be characterized by the curvature and torsion tensors derived from the connection. The multidimensional analogues of psychophysical scale functions exist if and only if these quantities vanish. Differences between the affine connections of two observers characterize differences between their perceptions of the same evolving stimuli. The affine connections of two observers can also be used to map a stimulus perceived by one observer onto another stimulus, perceived in the same way by the other observer. Unlike multidimensional scaling techniques, this method does not assume that the observer has a sense of distance (a metric) or that he/she can otherwise compare stimulus pairs that are oriented along perceptually different directions in the manifold. The method was used to measure the affine connections of observers of a dot moving on different background graphics; e.g., a blank screen, a grid, or two converging lines similar to those used to create the Ponzo illusion. The results comprise quantitative measurements of the background graphic's influence on each observer's perceptions of straightness, parallelism, and distance. The measurements demonstrate differences between the perceptions of the two observers. Copyright 2000 Academic Press.     

Mutual information, perceptual independence, and holistic face perception

The concept of perceptual independence is ubiquitous in psychology. It addresses the question of whether two (or more) dimensions are perceived independently. Several authors have proposed perceptual independence (or its lack thereof) as a viable measure of holistic face perception (Loftus, Oberg, & Dillon, Psychological Review 111:835–863, 2004; Wenger & Ingvalson, Learning, Memory, and Cognition 28:872–892, 2002). According to this notion, the processing of facial features occurs in an interactive manner. Here, I examine this idea from the perspective of two theories of perceptual independence: the multivariate uncertainty analysis (MUA; Garner & Morton, Definitions, models, and experimental paradigms. Psychological Bulletin 72:233–259, 1969), and the general recognition theory (GRT; Ashby & Townsend, Psychological Review 93:154–179, 1986). The goals of the study were to (1) introduce the MUA, (2) examine various possible relations between MUA and GRT using numerical simulations, and (3) apply the MUA to two consensual markers of holistic face perception^—recognition of facial features (Farah, Wilson, Drain, & Tanaka, Psychological Review 105:482–498, 1998) and the composite face effect (Young, Hellawell, & Hay, Perception 16:747–759, 1987). The results suggest that facial holism is generated by violations of several types of perceptual independence. They highlight the important theoretical role played by converging operations in the study of holistic face perception.     

Inferential reasoning by exclusion in pigeons, dogs, and humans

The ability to reason by exclusion (which is defined as the selection of the correct alternative by logically excluding other potential alternatives; Call in Anim Cogn 9:393–403 2006) is well established in humans. Several studies have found it to be present in some nonhuman species as well, whereas it seems to be somewhat limited or even absent in others. As inconsistent methodology might have contributed to the revealed inter-species differences, we examined reasoning by exclusion in pigeons (n = 6), dogs (n = 6), students (n = 6), and children (n = 8) under almost equal experimental conditions. After being trained in a computer-controlled two-choice procedure to discriminate between four positive (S+) and four negative (S−) photographs, the subjects were tested with displays consisting of one S− and one of four novel stimuli (S′). One pigeon, half of the dogs and almost all humans preferred S′ over S−, thereby choosing either by novelty, or by avoiding S− without acquiring any knowledge about S′, or by inferring positive class membership of S′ by excluding S−. To decide among these strategies the subjects that showed a preference for S′ were then tested with displays consisting of one of the S′ and one of four novel stimuli (S′′). Although the pigeon preferentially chose the S′′ and by novelty, dogs and humans maintained their preference for S′, thereby showing evidence of reasoning by exclusion. Taken together, the results of the present study suggest that none of the pigeons, but half of the dogs and almost all humans inferred positive class membership of S′ by logically excluding S−. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Separating perceptual processes from decisional processes in identification and categorization

Four observers completed perceptual matching, identification, and categorization tasks using separable-dimension stimuli. A unified quantitative approach relating perceptual matching, identification, and categorization was proposed and tested. The approach derives from general recognition theory (Ashby & Townsend, 1986) and provides a powerful method for quantifying the separate influences of perceptual processes and decisional processes within and across tasks. Good accounts of the identification data were obtained from an initial perceptual representation derived from perceptual matching. The same perceptual representation provided a good account of the categorization data, except when selective attention to one stimulus dimension was required. Selective attention altered the perceptual representation by decreasing the perceptual variance along the attended dimension. These findings suggest that a complete understanding of identification and categorization performance requires an understanding of perceptual and decisional processes. Implications for other psychological tasks are discussed.     

Separating perceptual and decisional attention processes in the identification and categorization of integral-dimension stimuli

Four observers performed matching, identification, and categorization with stimuli that varied along the integral dimensions: brightness and saturation. General recognition theory (F. G. Ashby & J. T. Townsend, 1986) was applied to quantify the separate influences of perceptual and decisional processes within and across tasks, with a focus on separating perceptual from decisional attention processes. Good accounts of the identification data were obtained from perceptual matching representation. This perceptual representation provided a good account of the categorization data, except when decisional selective attention to 1 stimulus dimension was required. Decisional selective attention reduced the attended-dimension perceptual variance relative to the unattended-dimension perceptual variance, with a larger reduction resulting when brightness, as opposed to saturation was attended. Implications for color vision research are discussed.     

An approach to geometry of visual space with no a priori mapping functions: Multidimensional mapping according to Riemannian metrics

A method of multidimensional mapping is described which constructs a configuration of points {P_i} in a Euclidean map of Riemannian space of constant curvature (hyperbolic, Euclidean, and elliptic) from the dissimilarity matrix (d_ij). The method was applied to the distance matrix in visual space where stimulus points Q_i were either small light points in the dark or small black points in the illuminated field surrounded by white curtains and d_ij represent scaled values of perceptual distances. Configuration of points {Q_i} were at intersections of parallel or distance alleys and horopters for the subject in the horizontal plane of the eye level. In contrast to the theoretical equations for {Q_i} by Luneburg and Blank, no a priori assumption on mapping functions between {Q_i} and {P_i} is necessary in this procedure to fit theoretical curves to {P_i} in the Euclidean map. The data were accounted for better by equations in the hyperbolic plane than by ones in the Euclidean plane. Discussions are made on robustness of Euclidean representation and on how to approach geometry of visual space as a dynamic entity under more natural conditions than the traditional frameless condition for alley and horopter experiments.     

Separating perceptual processes from decisional processes in identification and categorization.

Four observers completed perceptual matching, identification, and categorization tasks using separable-dimension stimuli. A unified quantitative approach relating perceptual matching, identification, and categorization was proposed and tested. The approach derives from general recognition theory (Ashby & Townsend, 1986) and provides a powerful method for quantifying the separate influences of perceptual processes and decisional processes within and across tasks. Good accounts of the identification data were obtained from an initial perceptual representation derived from perceptual matching. The same perceptual representation provided a good account of the categorization data, except when selective attention to one stimulus dimension was required. Selective attention altered the perceptual representation by decreasing the perceptual variance along the attended dimension. These findings suggest that a complete understanding of identification and categorization performance requires an understanding of perceptual and decisional processes. Implications for other psychological tasks are discussed.     

The relationship between the objective identification threshold and priming effects does not provide a definitive boundary between conscious and unconscious perceptual processes

The Objective Threshold/Strategic Model (OT/S) proposes that strong, qualitative inferences of unconscious perception can be made if the relationship between perceptual sensitivity (typically priming effects) and stimulus visibility is nonlinear and nonmonotonic. The model proposes a nadir in priming effects at the objective identification threshold (identification d′ = 0). These predictions were tested with masked semantic priming and repetition priming of a lexical decision task. The visibility of the prime stimuli was systematically varied above and below the objective identification threshold. The obtained relationship between prime visibility and priming facilitation was nonlinear, but the results failed to confirm a nadir in priming effects at the objective identification threshold. We conclude that the objective identification threshold does not necessarily indicate the point where presumably unconscious priming effects might be inhibited by conscious cognitive processes.