Alphabetic confusion: A test of models for individuals

An earlier article reported extensive analyses of confusion data compiled from group averages (Townsend, 1971). The present study provided for essentially the same analyses with different long-term data obtained with two individuals, the primary intent being to examine the ability of recognition and scaling models to explain data at the individual level (which the recognition models purport to describe) and to compare the confusion characteristics of the English uppercase alphabet between the two Ss and between the individual Ss and the group-averaged data. The choice and overlap models were superior to the all-or-none model in predicting the empirical confusion matrices and tended to explain the data structure in a similar manner. Multidimensional scaling analysis again supported a Euclidean metric and suggested four or five underlying stimulus dimensions. However, as before, there were no overriding intuitively appealing psychological dimensions corresponding to these, and possible reasons are discussed. The choice and overlap models appeared to fit as well or better at the individual level than at the group level and the all-or-none model to fit worse. In the present study, probability correct was fit even better by the all-or-none model than in the group study and replicated the result of being better here than the overlap and choice models. Individuals and the group were consistent in their sensory confusions as represented by similarity parameters in the choice and overlap models but differed in their response biases. A simple measure of physical similarity explained 50% of the variance of the similarity structure in the confusion data.     

独体汉字的字形相似性研究

本文以速示呈现方式获得了一系列独体汉字和字符的混淆矩阵。用Luce（1963）的选择模型特混淆矩阵分解为对称的相似矩阵和反应倾向矢量。基于相似矩阵,以聚类分析和多维量表法探索了汉字和字符的视觉特征及其表征形式,为揭示汉字视觉特征的几何特性和潜在结构,在研究方法上作了有意义的偿试、此外,本研究的结果支持了作者（1995）关于在含“十”或“口”的独体汉字中,“十”与“口”是该类汉字的突出视觉特征的结论。     

An analysis of confusion errors in naming letters under speed stress

Three subjects named six visually presented letters under two levels of speed stress. The obtained confusion matrices for each stress condition were fit by Luce’s choice theory, which provided measures of stimulus similarity and response bias. Speed stress produced proportional increases in pairwise similarity measures but had no systematic effect on response biases. In Experiment 2, the same three subjects named the same letters under two levels of stimulus quality and a constant response-time deadline. As with speed stress, degrading the stimulus produced proportional increases in pairwise similarity measures but had no systematic effect on response biases. In Experiment 3, two of the subjects participating in Experiments 1 and 2 named the six letters under conditions where the probabilities of the letters were unequal. The letters toward which the subject had been most biased in Experiments 1 and 2 were assigned low probabilities, and the letters toward which he was least biased were assigned high probabilities. The result of this manipulation was to completely reverse the ordering of the response bias parameters of the Luce choice model. It is suggested that the present methodology provides a means of validating as psychological constructs the parameters of various mathematical models of stimulus recognition.     

Multidimensional letter similarity derived from recognition errors

In order to provide a reliable measure of the similarity of uppercase English letters, a confusion matrix based on 1,200 presentations of each letter was established. To facilitate an analysis of the perceived structural characteristics, the confusion matrix was decomposed according to Luce’s choice model into a symmetrical similarity matrix and a response bias vector. The underlying structure of the similarity matrix was assessed with both a hierarchical clustering and a multidimensional scaling procedure. This data is offered to investigators of visual information processing as a valuable tool for controlling not only the overall similarity of the letters in a study, but also their similarity on individual feature dimensions.     

Word superiority over isolated letters: The neglected case of forward masking

Previous research shows that when briefly presented alphabetic stimuli are followed by pattern masks, letters in words are reported more accurately than are isolated letters (the “Word-Letter Phenomenon,” or WLP); however, when these masks are replaced by blank fields, the WLP disappears. These findings have led to the popular notion that the WLP reflects selective masking of ongoing stimulus processing and so critically depends on the use of poststimulus masks. Here we report three experiments which re-examine the role of masking in the WLP by contrasting the effects of postmasked displays with the effects of premasked displays in which words and isolated letters werepreceded by a pattern mask and followedby a completely blank field. Despite the critical role generally assigned to poststimulus pattern masks, similar WLPs were obtained with pre- and postmasked displays. Implications for theories of word and letter recognition are discussed.     

Identification Model Based on the Maximum Information Entropy Principle

A new theoretical approach to stimulus identification is proposed through a probabilistic multidimensional model based on the maximum information entropy principle. The approach enables us to derive the multidimensional scaling (MDS) choice model, without appealing to Luce's choice rule and without defining a similarity function. It also clarifies the relationship between the MDS choice model and the optimal version of the identification model based on Ashby's general recognition theory; it is shown theoretically that the identification model derived from the new approach includes these two models as special cases. Finally, as an application of our approach, a model of similarity judgment is proposed and compared with Ashby's extended similarity model. Copyright 2001 Academic Press.     

Cognitive processing and time perception

When a visual field is presented for 40 or 80 msec and a subject is asked to judge the duration of the stimulus, judged duration is found to be less when the field is blank than when the field contains three letters, but is the same whether the three letters form a word or not. The perceived difference between “filled” and “blank” fields increases when the subject is required to memorize the presented letters. These data are consistent with a theory which assumes,inter alia, that a stimulus is analyzed by a visual information processor and a timer, that attention is shared between these processors, and that temporal judgments are based on the output of both processors.     

The word-superiority effect does not require a T-scope

Six experiments examined the possibility of obtaining a word-superiority effect (WSE) without the use of brief stimulus exposures or a poststimulus mask. In each experiment, subjects were presented a stimulus string and two alternative strings that differed by a single letter (Reicher, 1969). The alternatives and stimulus remained in view until subjects responded, and subjects were under no pressure to respond quickly. In Experiments 1–3, the stimuli were presented in very small type so that they were difficult to see. Subjects were significantly more accurate with words than with nonwords, letters embedded among digits, or letters embedded among number signs (#s). In Experiments 4 and 5, the stimuli were embedded in a simultaneously present pattern mask. Subjects were significantly more accurate with words than with single letters by themselves. In the final experiment, the stimuli were presented in a mask with specific spatial frequency characteristics, and performance was significantly better with words than with nonwords. The WSE is a more general phenomenon than previously supposed; it is not limited to a tachistoscopic exposure.     

Application of geometric models to letter recognition: distance and density

This article reviews studies in which a single letter is visually presented under adverse conditions and the subject's task is to identify the letter. The typical results for such studies are (a) certain pairs of letters are more often confused than other pairs of letters; (b) certain letters are more easily recognized than others; and (c) confusion errors for a letter pair are often asymmetric, the number of errors differing depending on which letter of the pair is presented as the stimulus. A geometric model incorporating the properties of distance and spatial density (after Krumhansl) is presented to account for these results. The present application of the distance-density model assumes that each letter is constructed in a typical 5 X 7 dot matrix. Each letter is represented in 35-dimensional space based on its constituent dots. A central idea behind the model, embodied in the property of spatial density, is that an explanation of typical results must take into account the relationship of the entire stimulus set to both the presented letter and the responded letter. Specifically, according to the model, (a) pairs of letters that are close in geometric space are more often confused than pairs of letters that are distant; (b) letters that are in less spatially dense regions are more easily recognized than letters that are in more spatially dense regions; and (c) asymmetric confusion errors result when one member of a letter pair is in a denser region than the other member of the letter pair. The distance-density model is applied to published and unpublished results of the authors as well as published results from two other laboratories. Alternative explanations of the three typical letter recognition results are also considered. The most successful alternative explanations are (a) confusions are an increasing function of the number of dots that two letters share; (b) letters constructed from fewer dots are easier to recognize; and (c) asymmetries arise when one member of a letter pair is more easily recognized, since that letter then has fewer confusion errors to give to the other letter of the pair. The model is discussed in terms of the distinction between template matching and feature analysis. An alternative classification of letter recognition models is proposed based on the global versus local qualities of features and the spatial information associated with each feature. The model is extended to explain reaction time study results. It is suggested that the distance-density model can be used to create optimal letter fonts by minimizing interletter confusions and maximizing letter recognizability.     

The word-superiority effect does not require a T-scope.

Six experiments examined the possibility of obtaining a word-superiority effect (WSE) without the use of brief stimulus exposures or a poststimulus mask. In each experiment, subjects were presented a stimulus string and two alternative strings that differed by a single letter (Reicher, 1969). The alternatives and stimulus remained in view until subjects responded, and subjects were under no pressure to respond quickly. In Experiments 1-3, the stimuli were presented in very small type so that they were difficult to see. Subjects were significantly more accurate with words than with nonwords, letters embedded among digits, or letters embedded among number signs (#s). In Experiments 4 and 5, the stimuli were embedded in a simultaneously present pattern mask. Subjects were significantly more accurate with words than with single letters by themselves. In the final experiment, the stimuli were presented in a mask with specific spatial frequency characteristics, and performance was significantly better with words than with nonwords. The WSE is a more general phenomenon than previously supposed; it is not limited to a tachistoscopic exposure.     

Tests of the psychological meaning of the power law.

The purpose of this study was to establish a theoretical framework for Stevens' empirically derived power law. Three models were proposed to explain the power law. They respectively outline how sensory, stimulus, and response variables determine the judgmental behavior in a psychophysical task. A correlational study on individual differences in exponents was carried out to test the predictions derived from each model. The use of four different sensory continua and four scaling procedures provided the experimental means of manipulating the sensory, stimulus, and response variables in the scaling situation. The results showed that response variables are important determinants of judgmental behavior in psychophysical scaling. These findings suggest that subjects' responses to stimulus intensities in a scaling task are largely cognitive.     

Stimulus proba]bility and choice reaction time

Two experiments, in which three stimuli were paired with two responses in a 2∶1, 1∶1 arrangement, showed choice RT to be a decreasing function of the relative frequency of stimulus occurrence when response frequencies are equated. The size of effect varied significantly with stimulus type (Experiment 1), being larger for circular light patches of differing diameter than for sets of colors, letters, and spatially distributed light sources, but was independent of differences in the similarity of stimulus alternatives within a set (Experiment 2). The results are discussed in terms of various strategies of stimulus identification.     

Interference in letter identification: A test of feature-specific inhibition

The role of perceptual interference in letter identification was investigated in three experiments designed to test the feature-specific inhibition model proposed by Bjork and Murray (1977). According to their extension of Estes’ (1972, 1974) interactive channels model, input channels leading to the same feature detector inhibit one another more than do channels leading to different detectors. The model therefore predicts perceptual interference between two letters to be a function of the degree of their feature overlap. Experiment 1 confirmed the feature-specific inhibition model and Bjork and Murray’s finding that the accuracy of report is lower when a briefly presented target letter is flanked by an identical letter than when flanked by another target letter or by a nontarget letter. Results from Experiment 2 indicated that single-target performance is a function of the degree of feature similarity between the target letter and background characters in a stimulus display. Experiment 3 ruled out a spatial-uncertainty explanation of feature-specific inhibition in a new paradigm that does not require subjects to process a poststimulus cue. The results of these experiments are discussed in relation to recent studies exhibiting strong effects of noise letters at the response stage of processing. It is suggested that discrepancies between feature-specific interference and response-interference studies may be a function of the particular mode of stimulus presentation and of the dependent measures that are used.     

Surveying a blank field with the attentional spotlight

Spatial localization is a unique aspect of selective attention that precedes and facilitates other aspects of sensory processing. A common model of spatial attention is an attentional spotlight that enlarges to fit attentional demands. It is unclear if this attentional spotlight expands to survey a blank field or to scan the spatial environment with a smaller attentional spotlight. Two tachistoscopic experiments with young adults investigated how attention is surveyed in a blank field. Exp. 1 consisted of single letters at two concentric regions and under different conditions of attentional demand. Reaction times were proportionally slower for stimuli occurring in a combination of the two regions located at different distances from the fixation point than for stimuli occurring in each region alone. This finding is not consistent with attentional spread to encompass the entire attentional field. The addition of more stimulus locations within each single region yielded significantly slower reaction times. Together these findings suggest that a small attentional spotlight serially monitors different regions of the visual field when there are anticipated locations to be attended.     

Local and global factors of similarity in visual search

Effects of the similarity between target and distractors in a visual search task were investigated in several experiments. Both familiar (numerals and letters) and unfamiliar (connected figures in a 5 × 5 matrix) stimuli were used. The observer had to report on the presence or absence of a target among a variable number of homogeneous distractors as fast and as accurately as possible. It was found that physical difference had the same clear effect on processing time far familiar and for unfamiliar stimuli: processing time decreased monotonically with increasing physical difference. Distractors unrelated to the target and those related to the target by a simple transformation (180° rotation, horizontal or vertical reflection) were also compared, while the physical difference was kept constant. For familiar stimuli, transformational relatedness increased processing time in comparison with that fort unrelated stimulus pairs. It was further shown in a scaling experiment that this effect could be accounted for by the amount of perceived similarity of the target-distractor pairs. For unfamiliar stimuli, transformational relatedness did have a smaller and less pronounced effect. Various comparable unrelated distractors resulted in a full range of processing times. Results from a similarity scaling experiment correlated well with the outcome of the experiments with unfamiliar stimuli. These results are interpreted in terms of an underlying continuum of perceived similarity as the basis of the speed of visual search, rather than a dichotomy of parallel versus serial processing.     

An experimental and theoretical investigation of the constant-ratio rule and other models of visual letter confusion

The constant-ratio rule (CRR) and four interpretations of R. D. Luce's (In R. D. Luce, R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 1). New York: Wiley, 1963) similarity choice model (SCM) were tested using an alphabetic confusion paradigm. Four stimulus conditions were employed that varied in set size (three, four or five stimulus elements) and set constituency (block letters: A, E, X; F, H, X; A, E, F, H; A, E, F, H, X), and were presented to each subject in independent blocks. The four interpretations of the SCM were generated by constraining one, both, or neither of its similarity and bias parameter sets to be invariant in across-stimulus set model predictions. The strictest interpretation of the SCM (both the similarity and bias parameters constrained), shown to be a special case of the CRR, and the CRR produced nearly equivalent across-set predictions that provided a reasonable first approximation to the data. However, they proved inferior to the least strict SCM (neither the similarity nor bias parameters were constrained; the common interpretation of the SCM in visual confusion). Additionally, the least strict SCM was compared to J. T. Townsend's (Perception and Psychophysics, 1971, 9, 40–50, 449–454) overlap model, the all-or-none model (J. T. Townsend, Journal of Mathematical Psychology, 1978, 18, 25–38), and a modified version of L. H. Nakatani's (Journal of Mathematical Psychology, 1972, 9, 104–127) confusion-choice model. Both the least strict SCM and confusion-choice models produced nearly equivalent within stimulus set predictions that were superior to the overlap and all-or-none within-set predictions. Measurement conditions related to model structure and equivalence relations among the models, many of them new, were examined and compared with the statistical fit results of the investigation.     

Studies of letter identification using qualitative error analysis: effects of speed stress, tachistoscopic presentation, and word context

In Experiment 1 subjects named letters under a response deadline chosen so that an appreciable number of errors would be produced. The stimulus confusions were analyzed via the same mathematical models of stimulus recognition that have been applied to the confusion matrices generated in tachistoscopic experiments. Both the Luce choice model and the informed guessing model (a new model having a simple and elegant process interpretation) provided excellent fits to the data. The parameter values of the informed guessing model changed in logical and interpretable ways with changes in the response deadline. In Experiment 2 a direct comparison was made of the types of errors produced in the data-limited tachistoscopic situation and the resource-limited response deadline situation. It was found that, relative to the response deadline task, identification in the tachistoscopic task is much more likely to be based on partial information. In Experiments 3 and 4 the same research methodology was applied to the problem of the effect of a word context on letter perception. The methodology allowed this problem to be addressed in the context of both response deadline and tachistoscopic tasks. Several advantages of the methodology for investigating other issues of interest to cognitive psychologists are discussed.     

Identification confusions among letters of the alphabet

Black, uppercase letters, subtending 6.0' of arc in height, were presented tachistoscopically to 6 subjects. An exposure duration was chosen to keep the subject's identification performance at about 50% correct. On each trial a single letter was presented, and the subject was required to identify the letter by verbal response. The resulting 26 X 26 confusion matrix was based on 3,900 trials (150 trials per letter). Several models of visual processing were used to generate predicted confusions among letter pairs. Models based on template overlap, geometric features, and two-dimensional spatial frequency content (Fourier transforms) were tested. The highest correlation (.70) between actual and predicted confusions was attained by the model based on the Fourier transformed letters filtered by the human contrast sensitivity function. These results demonstrate that the spatial frequency content of visual patterns can provide a valuable metric for predicting their psychological similarity. The results further suggest that spatial frequency models of visual processing are competitive with feature analysis models.     

A COMPARATIVE STUDY OF SOME MULTIDIMENSIONAL VECTOR MODELS FOR SUBJECTIVE SIMILARITY

E kehammar B. A comparative study of some multidimensional vector models for subjective similarity. Scand. J. Psychol ., 1972, 1 3 , 190–197.—h this report, two theoretical vector models for subjective similarity were deduced from a "content" definition of subjective similarity. One of the derived similarity equations proved in empirical model testing to describe the similarity principle in perception of form better than earlier, similar models. Deviations between observed similarity estimates and values expected according to the model are discussed, among other things, in terms of the heterogeneity of the stimulus set.