Test of a response bias model of bisection

An algebraic model of bisection —a special case of Pfanzagl’s general measurement system-was tested for brightness. Nonparametric scalability, a condition derived from reflexivity, commutativity, and bisymmetry, was disconfirmed, leading to a rejection of the commutativity axiom, and necessitating the incorporation of a response bias parameter. The systematic bias in the data was substantially reduced by the introduction of the response bias parameter-interpreted as “position” bias, not hysteresis. The data are generally supportive of Pfanzagl’s bisection system, although the failure of commutativity requires the incorporation of a response bias parameter.     

The Development of the Commutativity Principle and Economical Addition Strategies

What is the relationship between the principle of commutativity and the development of addition strategies that disregard addend order? It has been proposed that the assumption (Conjecture 1) or discovery (Conjecture 2) of commutativity is a necessary condition for the invention of such advanced addition strategies. A third hypothesis suggests that children may invent labor-saving addition strategies without necessarily appreciating the commutativity principle. This study tested the three conjectures by evaluating 36 kindergartners on two types of commutativity tasks. Both tasks involved predicting whether commuted and noncommuted pairs of problems would produce the same or different answers. Commutativity was not naturally assumed by children (as proposed by Conjecture 1), but appeared to be discovered. However, contrary to Conjecture 2 and consistent with Conjecture 3, an understanding of commutativity was not evident in all those who invented labor-saving addition strategies. This study also confirmed that counting-all starting with the larger addend-a mental strategy recently discovered in a case study-was not an uncommon labor-saving device among young children.     

Perceived contrast explains asymmetries in visual-search tasks with shaded stimuli

Shaded stimuli have traditionally been used in the context of three-dimensional (3-D) shape perception. Many studies have shown a persistent asymmetry in that a circle filled with a shaded gradient that is dark at the top and bright at the bottom (top-dark circle) is much easier to locate among top-bright circles than in the opposite arrangement (a top-bright circle among top-dark circles). The immediate 3-D interpretation of top-dark and top-bright circles as hollows and protuberances, respectively, and the asymmetry just described have been explained in terms of 3-D percepts. The work described here challenges this view: the results of the first experiment show that top-dark circles are perceived as having 10% higher contrast than top-bright circles of the same physical contrast. Experiment 2 replicates classical visual-search experiments but adding a new condition where target and distractors were subjectively equated in contrast. For five of six subjects, the ubiquitous asymmetry disappears in this condition.     

A solution to a problem raised in Luce and Marley (2005)

Luce and Marley [2005. Ranked additive utility representations of gambles: Old and new axiomatizations. Journal of Risk and Uncertainty, 30, 21-62] examined various relations between mathematical forms for the utility of joint receipt ⊕ of gambles and for the utility of uncertain gambles. Their assumptions lead to a bisymmetry functional equation which, when the gambles are ranked, is defined on a restricted domain. Maksa [1999. Solution of generalized bisymmetry type equations without surjectivity. Aequationes Mathematicae, 57, 50-74] solved the general case and Kocsis [2007. A bisymmetry equation on restricted domain. Aequationes Mathematicae, 73, 280-284] presents the solution for the ranked case. The latter solution allows us to solve open problem 5 in Luce and Marley (2005) by showing that the assumptions of their Theorem 19 for an order-preserving ranked additive utility (RAU) representation U imply that U is a ranked weighted utility (RWU) representation that is additive over ⊕.     

Testing 40 Predictions From the Transtheoretical Model Again,With Confidence

Testing Theory-based Quantitative Predictions (TTQP) represents an alternative to traditional Null Hypothesis Significance Testing (NHST) procedures and is more appropriate for theory testing. The theory generates explicit effect size predictions and these effect size estimates, with related confidence intervals, are used to test the predictions. The focus of a study is shifted to a quantitative approach in contrast to the NHST dyadic decision centered on testing a prediction not based on the theory. This article describes the TTQP as an alternative approach by replicating and extending a test of 40 a priori predictions based on the Transtheoretical Model (TTM). Specific quantitative predictions were made about the magnitude of the effect size (ω²). The predictions involved movement from 1 of 3 initial stages (Precontemplation, Contemplation, and Preparation) to stage membership 12 months later. In the initial study, 36 of the 40 predictions were confirmed. The same 40 predictions are evaluated on a sample (N = 3,923) of smokers recruited from a large New England HMO for a smoking cessation study. The predictions were recalibrated based on the first study and 99% confidence intervals were employed to test the predictions. Thirty-two of the 40 predictions were confirmed. Of the 8 failures, 4 were judged to reflect a need for further recalibration, 1 was attributed to sampling fluctuation, and 3 suggested revisions of the theory are needed. The results provide overall support for the TTM. The study also illustrates some of the challenges of testing quantitative predictions.     

Kindergartners' understanding of additive commutativity within the context of word problems

Baroody and Gannon (1984) proposed that children's understanding of additive commutativity progresses through several levels of understanding based on a unary view of addition (change meaning) before developing a "true" level of understanding based on a binary conception (part-whole meaning). Resnick (1992) implied that children have both a unary and a binary conception of additive commutativity from the earliest stages of development. Fifty-three 5- and 6-year-old (M = 6-0) kindergartners' unary and binary understanding of additive commutativity was investigated using performance on tasks involving change-add-to and part-part-whole word problems, respectively. The data were inconsistent with the predictions of both models and suggest three alternate theoretical explanations. Moreover, the data indicate that success on a task involving change-add-to problems may be a more rigorous test of understanding of additive commutativity than that involving part-part-whole problems.     

Is causal induction based on causal power? Critique of Cheng (1997)

The authors empirically evaluate P. W. Cheng's (1997) power PC theory of causal induction. They reanalyze some published data taken to support the theory and show instead that the data are at variance with it. Then, they report 6 experiments in which participants evaluated the causal relationship between a fictitious chemical and DNA mutations. The power PC theory assumes that participants' estimates are based on the causal power p of a potential cause, where p is the contingency between the cause and the effect normalized by the base rate of the effect. Three of the experiments used a procedure in which causal information was presented trial by trial. For these experiments, the power PC theory was contrasted with the predictions of the probabilistic contrast model and the Rescorla-Wagner theory. For the remaining 3 experiments, a summary presentation format was employed to which only the probabilistic contrast model and the power PC theory are applicable. The power PC theory was unequivocally contradicted by the results obtained in these experiments, whereas the other 2 theories proved to be satisfactory.     

The effect of combinations of image degradations in a discrimination task

This paper explores the ways in which combinations of image degradations affect discrimination. Nine experiments are described that examine the discriminability of visual images that are degraded with three types of information reducing transformations: random punctate visual interference, lowpass spatial frequency filtering, and local area (i.e., block) averaging. The results of these experiments characterize a powerful visual ability to discriminate highly degraded stimuli unless that ability is severely challenged by relatively high levels of random visual interference. Discriminative commutativity of the orders in which the other two degradations are imposed is demonstrated. That is, the order in which the degradations are applied does not affect the final discriminative outcome. This result is in contrast to predictions from relevant mathematics and direct examination of the images produced by both orders of degradation. The commutativity is attributed to the particularly strong effect of the low-pass spatial frequency filtering degradation on the discrimination process. This study also demonstrates that combinations of degradations in a discrimination task always result in a reduction in performance, and never in the improvement that has been reported for recognition. This difference is attributed to the fact that form discrimination is mediated mainly by local features and high-frequency spatial components, whereas recognition is mediated mainly by global features and low-frequency spatial components.     

Understanding developmental reversals in false memory: Reply to Ghetti (2008) and Howe (2008)

Replies to comments on the current authors' original article. S. Ghetti (2008) and M. L. Howe (2008) presented probative ideas for future research that will deepen scientific understanding of developmental reversals on false memory and establish boundary conditions for these counterintuitive patterns. Ghetti extended the purview of current theoretical principles by formulating hypotheses about how developmental reversals are controlled by the growth of phantom recollection and by the growth of false-memory editing. Some data are available on her hypotheses about phantom recollection, which distinguish phenomenology (vague or vivid) from memory representation (verbatim or gist). Howe introduced alternative theoretical principles that can be traced to the early work of Deese and Underwood. He argued that fuzzy-trace theory is subject to 3 limitations and that his alternative conception makes 3 predictions that contrast with fuzzy-trace theory's predictions. In the current reply, it is shown that the stated limitations do not apply to fuzzy-trace theory, that previously published research runs counter to the 3 predictions, and that the core difference between the 2 approaches is that fuzzy-trace theory is an opponent-processes model whereas the alternative conception is a 1-process model. (PsycINFO Database Record (c) 2008 APA, all rights reserved).     

3-D shape perception

In this paper, we analyze and test three theories of 3-D shape perception: (1) Helmholtzian theory, which assumes that perception of the shape of an object involves reconstructing Euclidean structure of the object (up to size scaling) from the object’s retinal image after taking into account the object’s orientation relative to the observer, (2) Gibsonian theory, which assumes that shape perception involves invariants (projective or affine) computed directly from the object’s retinal image, and (3) perspective invariants theory, which assumes that shape perception involves a new kind of invariants of perspective transformation. Predictions of these three theories were tested in four experiments. In the first experiment, we showed that reliable discrimination between a perspective and nonperspective image of a random polygon is possible even when information only about the contour of the image is present. In the second experiment, we showed that discrimination performance did not benefit from the presence of a textured surface, providing information about the 3-D orientation of the polygon, and that the subjects could not reliably discriminate between the 3-D orientation of the textured surface and that of a shape. In the third experiment, we compared discrimination for solid shapes that either had flat contours (cuboids) or did not have visible flat contours (cylinders). The discrimination was very reliable in the case of cuboids but not in the case of cylinders. In the fourth experiment, we tested the effectiveness of planar motion in perception of distances and showed that the discrimination threshold was large and similar to thresholds when other cues to 3-D orientation were used. All these results support perspective invariants as a model of 3-D shape perception.     

Clinical expertise and reasoning with uncertain categories

Expert clinical psychologists, clinical psychology graduates, and nonclinical graduate students were presented with clinical and nonclinical cases in which the diagnosis or category membership of a character was uncertain; they then made feature predictions about the character. For each case, there was a diagnosis or category that was highly probable and a less likely alternative that either did (relevant condition) or did not (neutral condition) alter predictions. For clinical cases, clinical experts and graduate clinicians gave different predictions for the relevant and neutral conditions, indicating that they had considered the uncertain nature of the diagnosis in their predictions. Although they acknowledged that the diagnosis was uncertain, nonclinical students ignored the less likely diagnostic alternatives when making predictions. For the nonclinical cases, all three groups made predictions based on only the most likely category alternative. The results showed that clinical training and/or experience promote multiple-category reasoning, but that this effect is domain specific.     

3-d interpolation in object perception: evidence from an objective performance paradigm

Object perception requires interpolation processes that connect visible regions despite spatial gaps. Some research has suggested that interpolation may be a 3-D process, but objective performance data and evidence about the conditions leading to interpolation are needed. The authors developed an objective performance paradigm for testing 3-D interpolation and tested a new theory of 3-D contour interpolation, termed 3-D relatability. The theory indicates for a given edge which orientations and positions of other edges in space may be connected to it by interpolation. Results of 5 experiments showed that processing of orientation relations in 3-D relatable displays was superior to processing in 3-D nonrelatable displays and that these effects depended on object formation. 3-D interpolation and 3-D relatabilty are discussed in terms of their implications for computational and neural models of object perception, which have typically been based on 2-D-orientation-sensitive units.     

Testing n-stimuli bisymmetry

In the seventies bisection, a kind of observational averaging of two stimuli, came to be studied and empirically investigated in measurement theory and corresponding psychophysical experiments. Since 1993, Münnich, Maksa and Mokken (Aggregating evaluations of multi-attribute stimuli. 31st International Symposium on Functional Equations, Debrecen, 2000) developed the formal framework and theory for a more general type of bisection of more than two variables. A core assumption for this generalization of 2-stimuli bisection to that of n-stimuli, is that of n-variable bisymmetry. After an introduction of this concept, the validity of its assumption is tested and demonstrated with four experiments. Experiment 1 was a computer-aided task in which input modalities were different line lengths presented on computer screen. Experiments 1, 3 and 4 included field experiments of the paper and pencil type, in which numbers served as input modalities, but in different contexts.     

3-D vision and figure-ground separation by visual cortex

A neural network theory of three-dimensional (3-D) vision, called FACADE theory, is described. The theory proposes a solution of the classical figure-ground problem for biological vision. It does so by suggesting how boundary representations and surface representations are formed within a boundary contour system (BCS) and a feature contour system (FCS). The BCS and FCS interact reciprocally to form 3-D boundary and surface representations that are mutually consistent. Their interactions generate 3-D percepts wherein occluding and occluded object parts are separated, completed, and grouped. The theory clarifies how preattentive processes of 3-D perception and figure-ground separation interact reciprocally with attentive processes of spatial localization, object recognition, and visual search. A new theory of stereopsis is proposed that predicts how cells sensitive to multiple spatial frequencies, disparities, and orientations are combined by context-sensitive filtering, competition, and cooperation to form coherent BCS boundary segmentations. Several factors contribute to figure-ground pop-out, including: boundary contrast between spatially contiguous boundaries, whether due to scenic differences in luminance, color, spatial frequency, or disparity-partially ordered interactions from larger spatial scales and disparities to smaller scales and disparities; and surface filling-in restricted to regions surrounded by a connected boundary. Phenomena such as 3-D pop-out from a 2-D picture, Da Vinci stereopsis, 3-D neon color spreading, completion of partially occluded objects, and figure-ground reversals are analyzed. The BCS and FCS subsystems model aspects of how the two parvocellular cortical processing streams that join the lateral geniculate nucleus to prestriate cortical area V4 interact to generate a multiplexed representation of Form-And-Color-And-DEpth, orfacade, within area V4. Area V4 is suggested to support figure-ground separation and to interact with cortical mechanisms of spatial attention, attentive object learning, and visual search. Adaptive resonance theory (ART) mechanisms model aspects of how prestriate visual cortex interacts reciprocally with a visual object recognition system in inferotemporal (IT) cortex for purposes of attentive object learning and categorization. Object attention mechanisms of the What cortical processing stream through IT cortex are distinguished from spatial attention mechanisms of the Where cortical processing stream through parietal cortex. Parvocellular BCS and FCS signals interact with the model What stream. Parvocellular FCS and magnocellular motion BCS signals interact with the model Where stream. Reciprocal interactions between these visual, What, and Where mechanisms are used to discuss data about visual search and saccadic eye movements, including fast search of conjunctive targets, search of 3-D surfaces, selective search of like-colored targets, attentive tracking of multielement groupings, and recursive search of simultaneously presented targets.     

Local and global mechanisms of one- and two-dimensional orientation illusions

One-dimensional (1-D) orientation illusions induced on a test grating by a tilted and-surrounding 1-D inducing grating have a well-known angular function that exhibits both repulsion and attraction effects. Two-dimensional (2-D) orientation illusions are those induced on a test grating by 2-D image modulation, such as a pair of superimposed inducing gratings at different orientations, usually orthogonal (a plaid). Given the known angular functions induced by the plaid component gratings, two hypotheses were developed that predicted different plaid-induced illusion functions. Hypothesis 1 states that the 1-D component-induced effects simply add linearly; Hypothesis 2 states that there is an additional mechanism that responds to the virtual axes of mirror symmetry of the plaid and adds to the effect. The data of two experiments were consistent with the predictions from the second hypothesis but not the first. Possible neural substrates of mechanisms that extract axes of symmetry are discussed; it is suggested that such global symmetry axes may underlie the perceived orientation of complex shapes.     

Object interpolation in three dimensions

Perception of objects in ordinary scenes requires interpolation processes connecting visible areas across spatial gaps. Most research has focused on 2-D displays, and models have been based on 2-D, orientation-sensitive units. The authors present a view of interpolation processes as intrinsically 3-D and producing representations of contours and surfaces spanning all 3 spatial dimensions. The authors propose a theory of 3-D relatability that indicates for a given edge which orientations and positions of other edges in 3 dimensions may be connected to it, and they summarize the empirical evidence for 3-D relatability. The theory unifies and illuminates a number of fundamental issues in object formation, including the identity hypothesis in visual completion, the relations of contour and surface processes, and the separation of local and global processing. The authors suggest that 3-D interpolation and 3-D relatability have major implications for computational and neural models of object perception.     

Local and global mechanisms of one- and two-dimensional orientation illusions.

One-dimensional (1-D) orientation illusions induced on a test grating by a tilted and surrounding 1-D inducing grating have a well-known angular function that exhibits both repulsion and attraction effects. Two-dimensional (2-D) orientation illusions are those induced on a test grating by 2-D image modulation, such as a pair of superimposed inducing gratings at different orientations, usually orthogonal (a plaid). Given the known angular functions induced by the plaid component gratings, two hypotheses were developed that predicted different plaid-induced illusion functions. Hypothesis 1 states that the 1-D component-induced effects simply add linearly; Hypothesis 2 states that there is an additional mechanism that responds to the virtual axes of mirror symmetry of the plaid and adds to the effect. The data of two experiments were consistent with the predictions from the second hypothesis but not the first. Possible neural substrates of mechanisms that extract axes of symmetry are discussed; it is suggested that such global symmetry axes may underlie the perceived orientation of complex shapes.     

A mental model analysis of young children's conditional reasoning with meaningful premises

Mental model theory has been used to explain many differing phenomena in adult reasoning, including the extensively studied case of conditional reasoning. However, the current theory makes predictions about the development of conditional reasoning that are not consistent with data. In this article, young children's performance on conditional reasoning problems and the justifications given are analysed. A mental model account of conditional reasoning is proposed that assumes that (1) young children can reason with two models and (2) the fleshing out of conditionals involves activation of information in semantic memory that uses the minor premise as a retrieval cue.     

Spatiotemporal context influences perception of an ambiguous target in visual search

The two-stage model of amodal completion or TSM (Sekuler & Palmer, 1992), and the ambiguity theory (Rauschenberger, Peterson, Mosca, & Bruno, 2004) provide conflicting accounts of the phenomenon of amodal completion in 2-D images. TSM claims that an initial mosaic (2-D) representation gives way to a later amodally completed (3-D) representation. Furthermore, the 2-D representation is accessible only prior to formation of the 3-D representation. On the other hand, the ambiguity theory claims that the 2-D and 3-D representations develop in parallel and that preference for one of the coexisting representations over the other may be subject to the influence of spatiotemporal context provided by other elements in the visual display. Our experiments support the claim that, once formed, both representations coexist, with spatiotemporal context potentially determining which representation is perceived.