Flexibility in data interpretation: Effects of representational format

Braithwaite, D. W., & Goldstone, R. L. (2013).  Flexibility in data interpretation: Effects of representational format.  Frontiers in Psychology, 4:980, 1-16. 

Graphs and tables differentially support performance on specific tasks. For tasks requiring reading off single data points, tables are as good as or better than graphs, while for tasks involving relationships among data points, graphs often yield better performance. However, the degree to which graphs and tables support flexibility across a range of tasks is not well-understood. In two experiments, participants detected main and interaction effects in line graphs and tables of bivariate data. Graphs led to more efficient performance, but also lower flexibility, as indicated by a larger discrepancy in performance across tasks. In particular, detection of main effects of variables represented in the graph legend was facilitated relative to detection of main effects of variables represented in the x-axis. Graphs may be a preferable representational format when the desired task or analytical perspective is known in advance, but may also induce greater interpretive bias than tables, necessitating greater care in their use and design.

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Cycles and predictability in human collective behavior: An experimental generalization of Rock-Scissors-Paper

Here are some reports of our PLoS One paper on human collective behavior studying cyclic patterns in a generalization of the familiar rock-scissors-paper game.  We find situations in which groups of people grow increasingly predictable as they cycle around a set of choice options in a game similar to rock-scissors-paper but with 24 rather than 3 choices.

Social Learning Strategies in a Networked Group

Wisdom, T. N., Song, X., & Goldstone, R. L. (2013). Social Learning Strategies in a Networked Group.  Cognitive Science, 37, 1383-1425

When making decisions, humans can observe many kinds of information about others’ activities, but their effects on performance are not well understood. We investigated social learning strategies using a simple problem-solving task in which participants search a complex space, and each can view and imitate others’ solutions. Results showed that participants combined multiple sources of information to guide learning, including payoffs of peers’ solutions, popularity of solution elements among peers, similarity of peers’ solutions to their own, and relative payoffs from individual exploration. Furthermore, performance was positively associated with imitation rates at both the individual and group levels. When peers’ payoffs were hidden, popularity and similarity biases reversed, participants searched more broadly and randomly, and both quality and equity of exploration suffered. We conclude that when peers’ solutions can be effectively compared, imitation does not simply permit scrounging, but it can also facilitate propagation of good solutions for further cumulative exploration.

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See a movie of Creature League experiment in action

Integrating formal and grounded representations in combinatorics learning

Braithwaite, D. W., & Goldstone, R. L. (2013).  Integrating formal and grounded representations in combinatorics learning.  Journal of Educational Psychology, 105, 666-682.

The terms concreteness fading and progressive formalization have been used to describe instructional approaches to science and mathematics that use grounded representations to introduce concepts and later transition to more formal representations of the same concepts. There are both theoretical and empirical reasons to believe that such an approach may improve learning outcomes relative to instruction employing only grounded or only formal representations (Freudenthal, 1991; Goldstone & Son, 2005; McNeil & Fyfe, 2012; but see Kaminski, Sloutsky, & Heckler, 2008). Two experiments tested the effectiveness of this approach to instruction in the mathematical domain of combinatorics, using outcome listing and numerical calculation as examples of grounded and formal representations, respectively. The study employed a pretest-training, posttest design. Transfer performance, that is, participants’ improvement from pretest to posttest, was used to assess the effectiveness of instruction received during training. In Experiment 1, transfer performance was compared for 4 types of instruction, which differed only in the types of representation they employed: pure listing (i.e., listing only), pure formalism (i.e., numerical calculation only), list fading (i.e., listing followed by numerical calculation), and formalism first (i.e., listing introduced after numerical calculation). List fading instruction led to transfer performance on par with pure formalism instruction and higher than formalism first and pure listing instruction. In Experiment 2, an enhanced version of list fading training was again compared to pure formalism. However, no difference in transfer performance due to training was found. The results suggest that combining grounded and formal representations can be an effective approach to combinatorics instruction but is not necessarily preferable to using formal representations alone. If both grounded and formal representations are employed, the former should precede rather than follow the latter in the instructional sequence.

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Cyclic game dynamics driven by iterated reasoning

Frey, S., & Goldstone, R. L. (2013). Cyclic game dynamics driven by iterated reasoning. PLoS One, 8(2): e56416. doi:10.1371/journal.pone.0056416

Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning–what you think I think you think–will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a ‘‘hopping’’ behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.
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See a movie of actual humans (shown as Xs) playing the Mod Game.  Notice the clumping of their moves and their regular progression around the circle of choices.

Learning along with others

Goldstone, R. L., Wisdom, T. N., Roberts, M. E., & Frey, S. (2013). Learning along with others. Psychology of Learning and Motivation, 58, 1-45.

Unlike how most psychology experiments on learning operate, people learning to do a task typically do so in the context of other people learning to do the same task. In these situations, people take advantage of others’ solutions, and may modify and extend these solutions, thereby affecting the solutions available to others. We are interested in the group patterns that emerge when people can see and imitate the solutions, innovations, and choices of their peers over several rounds. In one series of experiments and computer simulations, we find that there is a systematic relation between the difficulty of a problem search space and the optimal social network for transmitting solutions. As the difficulty of finding optimal solutions in a search space increases, communication networks that preserve spatial neighborhoods perform best. Restricting people’s access to others’ solutions can help the group as a whole find good, hard-to-discover solutions. In other experiments with more complex search spaces, we find evidence for several heuristics governing individuals’ decisions to imitate: imitating prevalent options, imitating options that become increasingly prevalent, imitating high-scoring options, imitating during the early stages of a multiround search process, and imitating solutions similar to one’s own solution. Individuals who imitate tend to perform well, and more surprisingly, individuals also perform well when they are in groups with other individuals who imitate frequently. Taken together, our experiments on collective social learning reveal laboratory equivalents of prevalent social phenomena such as bandwagons, strategy convergence, inefficiencies in the collective coverage of a problem space, social dilemmas in exploration/exploitation, and reciprocal imitation.

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The structure of integral dimensions: Contrasting topological and Cartesian representations

Jones, M., & Goldstone, R. L. (2013).  The structure of integral dimensions: Contrasting topological and Cartesian representations.  Journal of Experimental Psychology: Human Perception and Performance, 39, 111-132.

Diverse evidence shows that perceptually integral dimensions, such as those composing color, are represented holistically. However, the nature of these holistic representations is poorly understood.  Extant theories, such as those founded on multidimensional scaling or general recognition theory, model integral stimulus spaces using a Cartesian coordinate system, just as with spaces defined by separable dimensions. This approach entails a rich geometrical structure that has never been questioned but may not be psychologically meaningful for integral dimensions. In particular, Cartesian models carry a notion of orthogonality of component dimensions, such that if 1 dimension is diagnostic for a classification or discrimination task, another can be selected as uniquely irrelevant. This article advances an alternative model in which integral dimensions are characterized as topological spaces. The Cartesian and topological models are tested in a series of experiments using the perceptual-learning phenomenon of dimension differentiation, whereby discrimination training with integral-dimension stimuli can induce an analytic representation of those stimuli. Under the present task design, the 2 models make contrasting predictions regarding the analytic representation that will be learned. Results consistently support the Cartesian model. These findings indicate that perceptual representations of integral dimensions are surprisingly structured, despite their holistic, unanalyzed nature.

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Similarity-dissimilarity competition in disjunctive classification tasks

Mathy, F., Haladjian, H., Laurent, E., & Goldstone, R. L. (2013).  Similarity-dissimilarity competition in disjunctive classification tasks.  Frontiers in Psychology – Cognition, 4, #26, 1-14.

Typical disjunctive artificial classification tasks require participants to sort stimuli according to rules such as “x likes cars only when black and coupe OR white and SUV.” For cate-gories like this, increasing the salience of the diagnostic dimensions has two simultaneous effects: increasing the distance between members of the same category and increas-ing the distance between members of opposite categories. Potentially, these two effects respectively hinder and facilitate classification learning, leading to competing predictions for learning. Increasing saliency may lead to members of the same category to be consid-ered less similar, while the members of separate categories might be considered more dissimilar. This implies a similarity-dissimilarity competition between two basic classifica-tion processes. When focusing on sub-category similarity, one would expect more difficult classification when members of the same category become less similar (disregarding the increase of between-category dissimilarity); however, the between-category dissimi-larity increase predicts a less difficult classification. Our categorization study suggests that participants rely more on using dissimilarities between opposite categories than finding similarities between sub-categories.We connect our results to rule- and exemplar-based classification models.The pattern of influences of within- and between-category similarities are challenging for simple single-process categorization systems based on rules or exem-plars. Instead, our results suggest that either these processes should be integrated in a hybrid model, or that category learning operates by forming clusters within each category.

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When Seeing a Dog Activates the Bark: Multisensory Generalization and Distinctiveness Effects

Brunel, L., Goldstone, R. L., Vallet, G. Riou, V., & Versace, R. (2013).  When Seeing a Dog Activates the Bark: Multisensory Generalization and Distinctiveness Effects.  Experimental Psychology, 60, 100-112.

The goal of the present study was to find evidence for a multisensory generalization effect (i.e., generalization from one sensory modality to another sensory modality). The authors used an innovative paradigm (adapted from Brunel, Labeye, Lesourd, & Versace, 2009) involving three phases: a learning phase, consisting in the categorization of geometrical shapes, which manipulated the rules of association between shapes and a sound feature, and two test phases. The first of these was designed to examine the priming effect of the geometrical shapes seen in the learning phase on target tones (i.e., priming task), while the aim of the second was to examine the probability of recognizing the previously learned geometrical shapes (i.e., recognition task). When a shape category was mostly presented with a sound during learning, all of the primes (including those not presented with a sound in the learning phase) enhanced target processing compared to a condition in which the primes were mostly seen without a sound during learning. A pattern of results consistent with this initial finding was also observed during recognition, with the participants being unable to pick out the shape seen without a sound during the learning phase. Experiment 1 revealed a multisensory generalization effect across the members of a category when the objects belonging to the same category share the same value on the shape dimension. However, a distinctiveness effect was observed when a salient feature distinguished the objects within the category (Experiment 2a vs. 2b).

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Benefits of Graphical and Symbolic Representations for Learning and Transfer of Statistical Concepts

Braithwaite, D. W, & Goldstone, R. L. (2013).  Benefits of Graphical and Symbolic Representations for Learning and Transfer of Statistical Concepts.  Proceedings of the Thirty-Fifth Annual Conference of the Cognitive Science Society.  (pp. 1928-1933).  Berlin, Germany: Cognitive Science Society.

Past research suggests that spatial configurations play an important role in graph comprehension. The present study investigates consequences of this fact for the relative utility of graphs and tables for interpreting data. Participants judged presence or absence of various statistical effects in simulated datasets presented in various formats. For the statistical effects introduced earlier in the study, performance was better with graphs than with tables, while for the effect introduced last in the study, this trend reversed. Additionally, in the later sections of the study, responses with graphs, but not tables, reflected increasing influence from the presence of stimulus features which had been relevant earlier in the study, but were no longer relevant. The findings suggest that graphs, relative to tables, may better facilitate perception of complex relationships among data points, but may also bias readers more strongly to favor some perspectives over others when interpreting data.

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How to present exemplars of several categories? Interleave during active learning and block during passive learning

Carvalho, P. F., & Goldstone, R. L. (2013).  How to present exemplars of several categories? Interleave during active learning and block during passive learning.  Proceedings of the Thirty-Fifth Annual Conference of the Cognitive Science Society.  (pp. 1982-1987).  Berlin, Germany: Cognitive Science Society.

Research on how information should be presented during inductive category learning has identified both interleaving of categories and blocking by category as beneficial for learning. Previous work suggests that this mixed evidence can be reconciled by taking into account within- and between-category similarity relations. In this paper we present a new moderating factor. One group of participants studied categories actively, either interleaved or blocked. Another group studied the same categories passively. Results from a subsequent generalization task show that active learning benefits from interleaved presentation while passive learning benefits from blocked presentation.

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Grouping by Similarity Helps Concept Learning

Weitnauer, E., Carvalho, P. F., Goldstone, R. L., & Ritter, H. (2013). Grouping by Similarity Helps Concept Learning.  Proceedings of the Thirty-Fifth Annual Conference of the Cognitive Science Society.  (pp. 3747-3752).  Berlin, Germany: Cognitive Science Society.

In inductive learning, the order in which concept instances are presented plays an important role in learning performance. Theories predict that interleaving instances of different concepts is especially beneficial if the concepts are highly similar to each other, whereas blocking instances belonging to the same concept provides an advantage for learning lowsimilarity concept structures. This leaves open the question of the relative influence of similarity on interleaved versus blocked presentation. To answer this question, we pit withinand between-category similarity effects against each other in a rich categorization task called Physical Bongard Problems. We manipulate the similarity of instances shown temporally close to each other with blocked and interleaved presentation. The results indicate a stronger effect of similarity on interleaving than on blocking. They further show a large benefit of comparing similar between-category instances on concept learning tasks where the feature dimensions are not known in advance but have to be constructed.

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An experiment on the cognitive complexity of code

Hansen, M. E., Lumsdaine, A., & Goldstone, R. L. (2013).  An experiment on the cognitive complexity of code.  Proceedings of the Thirty-Fifth Annual Conference of the Cognitive Science Society. Berlin, Germany: Cognitive Science Society.

What simple factors impact the cognitive complexity of code? We present an experiment in which participants predict the output of ten small Python programs. Even with such simple programs, we find a complex relationship between code, expertise, and correctness. We use subtle differences between program versions to demonstrate that small notational changes can have profound effects on comprehension. We catalog common errors for each program, and perform an in-depth data analysis to uncover effects on response correctness and speed.

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