D. J. K. Mewhort

The power law repealed: the case for an exponential law of practice

The power function is treated as the law relating response time to practice trials. However, the evidence for a power law is flawed, because it is based on averaged data. We report a survey that assessed the form of the practice function for individual learners and learning conditions in paradigms that have shaped theories of skill acquisition. We fit power and exponential functions to 40 sets of data representing 7,910 learning series from 475 subjects in 24 experiments. The exponential function fit better than the power function in all the unaveraged data sets. Averaging produced a bias in favor of the power function. A new practice function based on the exponential, the APEX function, fit better than a power function with an extra, preexperimental practice parameter. Clearly, the best candidate for the law of practice is the exponential or APEX function, not the generally accepted power function. The theoretical implications are discussed.

Representing word meaning and order information in a composite holographic lexicon.

The authors present a computational model that builds a holographic lexicon representing both word meaning and word order from unsupervised experience with natural language. The model uses simple convolution and superposition mechanisms (cf. B. B. Murdock, 1982) to learn distributed holographic representations for words. The structure of the resulting lexicon can account for empirical data from classic experiments studying semantic typicality, categorization, priming, and semantic constraint in sentence completions. Furthermore, order information can be retrieved from the holographic representations, allowing the model to account for limited word transitions without the need for built-in transition rules. The model demonstrates that a broad range of psychological data can be accounted for directly from the structure of lexical representations learned in this way, without the need for complexity to be built into either the processing mechanisms or the representations. The holographic representations are an appropriate knowledge representation to be used by higher order models of language comprehension, relieving the complexity required at the higher level.

Analysis of Response Time Distributions: An Example Using the Stroop Task

The shape of a response time (RT) distribution can be described by a 3-parameter model consisting of the convolution of the normal and exponential distributions, the ex-Gaussian. Analyses based on mean RT do not take the distributions shape into account and, for that reason, may obscure aspects of performance. To illustrate the point, the ex-Gaussian model was applied to data obtained from a Stroop task. Mean RT revealed strong interference but no facilitation, whereas the analysis based on the ex-Gaussian model showed both interference and facilitation. In short, analyses that do not take the shape of RT distributions into account can mislead and, therefore, should be avoided. Response time (RT) distributions typically have a positively skewed unimodal shape that contains information that cannot be derived from the distributions mean and variance. A number of studies using a variety of tasks have exploited the extra information to test models (Hacker, 1980; Hockley, 1984; Ratcliff, 1978, 1979). A distributional analysis was used, for instance, to reject the class of models for recognition memory that assumes serial processing at a constant rate: Such models predict mean RT (MRr) but do not account for the shape of the distribution in both the study-test and prememorized-list paradigms (Hockley & CorbaUis, 1982; Ratcliff& Murdock, 1976). In spite of its proven utility, however, the literature appears to treat a distributional analysis as an esoteric supplement to the traditional analysis, namely, the analysis of MRr. In this article, we argue that a distributional analysis should not be treated as a supplementary technique. Rather, we contend that RT measures should always be analyzed using a distributional analysis and that the traditional analysis of MRr risks serious misinterpretation of the data. We start by describing difficulties associated with an analysis of MRr. Next, we discuss

Identification, localization, and “iconic memory”: An evaluation of the bar-probe task

The partial report tachistoscopic task has been used to define “iconic memory,” a labile image-like precategorical visual store. Six interrelated partial report studies are reported that challenge the construct. On each trial, subjects were shown an eight-letter pseudoword (representing one of four orders of approximation to English) and a bar probe indicating which letter to report. The probe was delayed systematically, and the experiments included both mask and no-mask conditions. All three variables-familiarity of the material, masking, and delay of the probe-affected accuracy of report. Delaying the probe, for example, reduced accuracy by increasing location errors. Delaying the mask increased accuracy by reducing both location and item errors, but it did not reduce the location errors until its effect on item errors had reached asymptote. Across the stimulus array, however, masking reduced accuracy at all delays by increasing location errors. Finally, the greater accuracy associated with higher orders of approximation to English was complemented by a decrease in item errors, but the familiarity factor had no effect on location errors. Taken together, even though the task has been used to define the idea, the results indicate that the bar-probe task cannot be explained in terms of a simple iconic memory concept. Instead of a simple image-like buffer, the explanation requires a feature buffer, an “intelligent” letter identification process, and a postidentification character buffer. Iconic memory is a construct that oversimplifies the information processing system used in the bar-probe task.

Quantile maximum likelihood estimation of response time distributions

Queen’s University, Kingston, Ontario, Canada We introduce and evaluate via a Monte Carlo study a robust new estimation technique that fits distribution functions to grouped response time (RT) data, where the grouping is determined by sample quantiles. The new estimator, quantile maximum likelihood (QML), is more efficient and less biased than the best alternative estimation technique when fitting the commonly used ex-Gaussian distribution. Limitations of the Monte Carlo results are discussed and guidance provided for the practical application of the new technique. Because QML estimation can be computationally costly, we make fast open source code for fitting available that can be easily modified

Perception of Structure in Short Melodic Sequences.

Three experiments studied the perception of tone sequences having various degrees of musical structure. Ratings of perceived structure and ease of recognition in transposition were both influenced by harmonic progression (as defined by music theory), the contour (directional changes in pitch), and the excursion or repetition pattern within the sequence. The relation between the original and transposed sequence also affected ease of recognition in accordance with the number of tones shared between the two sequences. The results are described in terms of the abstraction and analysis of levels of pitch relations, an analysis conducted even by musically untrained listeners. The conceptual framework emphasizes the application of musical rules as an illustration of rules governing auditory sequences in general.

Processing spatial information and the selective-masking effect

When a mask follows tachistoscopic presentation of a letter string, the performance on the middle letters is reduced more than at the ends, the selective-masking effect. The ends-first explanation for selective masking holds that the letter string is identified from the ends to the middle. As a result, the end items escape the effects of the mask. Using a bar-probe task, we present three kinds of evidence both questioning the ends-first account and offering an alternate based on spatial-localization processes. The first experiment exposed the role of spatial localization by using words to minimize identification factors. The second obtained a comparable selective-masking effect with pseudowords; again, the pattern of errors favored the localization account. A final experiment tested predictions derived from the localization view in response to inconsistencies posed by the sequential-identification idea.

Case-sensitive letter and bigram frequency counts from large-scale English corpora

We tabulated upper- and lowercase letter frequency using several large-scale English corpora (∼183 million words in total). The results indicate that the relative frequencies for upper- and lowercase letters are not equivalent. We report a letter-naming experiment in which uppercase frequency predicted response time to uppercase letters better than did lowercase frequency. Tables of case-sensitive letter and bigram frequency are provided, including common nonalphabetic characters. Because subjects are sensitive to frequency relationships among letters, we recommend that experimenters use case-sensitive counts when constructing stimuli from letters.

Applying an exemplar model to the artificial-grammar task: Inferring grammaticality from similarity

We present three artificial-grammar experiments. The first used position constraints, and the second used sequential constraints. The third varied both the amount of training and the degree of sequential constraint. Increasing both the amount of training and the redundancy of the grammar benefited participants’ ability to infer grammatical status; nevertheless, they were unable to describe the grammar. We applied a multitrace model of memory to the task. The model used a global measure of similarity to assess the grammatical status of the probe and captured performance both in our experiments and in three classic studies from the literature. The model shows that retrieval is sensitive to structure in memory, even when individual exemplars are encoded sparsely. The work ties an understanding of performance in the artificial-grammar task to the principles used to understand performance in episodic-memory tasks.

Repetition deficit in rapid-serial-visual-presentation displays: encoding failure or retrieval failure?

The repetition deficit associated with rapid serial visual presentation (RSVP) has been explained as a repetition-induced blindness, that is, as a perceptual or encoding failure. The repetition deficit was replicated in a standard free-recall RSVP task, and it was shown that participants were able to report the lost item when they were prompted with a retrieval probe. The authors argue that both copies of the repeated items were available in memory but that they were not accessible for report. Hence, they conclude that the repetition deficit in the RSVP task reflects a retrieval failure, not a perceptual failure.