Identifiability and statistical properties of two-stage learning with no successes in the initial stage

A model is considered for learning where there is an initial stage with only errors, an intermediate state with errors and correct responses, and an absorbing state with only correct responses. A model with observable states is constructed, and sufficient identifiable parameters are given for the original model. Distribution statistics and other properties of data are derived as functions of the identifiable parameters. Informal estimates and sufficient statistics are given for the identifiable parameters. A number of testable hypotheses about the theoretical parameters are described. Some identifying restrictions for the model are given, along with the estimates for the unrestricted free parameters which follow. An application is made to data from a pairedassociate learning experiment.This research was sponsored by NSF Grant GB2791 and by PHS Grant MH12717. Part of the work was done while the author held a visiting faculty appointment at Stanford University.     

Problematic standard errors and confidence intervals for skewness and kurtosis

Many statistics packages print skewness and kurtosis statistics with estimates of their standard errors. The function most often used for the standard errors (e.g., in SPSS) assumes that the data are drawn from a normal distribution, an unlikely situation. Some textbooks suggest that if the statistic is more than about 2 standard errors from the hypothesized value (i.e., an approximate value for the critical value from the t distribution for moderate or large sample sizes when α = 5%), the hypothesized value can be rejected. This is an inappropriate practice unless the standard error estimate is accurate and the sampling distribution is approximately normal. We show distributions where the traditional standard errors provided by the function underestimate the actual values, often being 5 times too small, and distributions where the function overestimates the true values. Bootstrap standard errors and confidence intervals are more accurate than the traditional approach, although still imperfect. The reasons for this are discussed. We recommend that if you are using skewness and kurtosis statistics based on the 3^rd and 4^th moments, bootstrapping should be used to calculate standard errors and confidence intervals, rather than using the traditional standard. Software in the freeware R for this article provides these estimates.     

Now you see it, now you don't: controlling for contingencies and stimulus repetitions eliminates the Gratton effect

The Gratton (or sequential congruency) effect is the finding that conflict effects (e.g., Stroop and Eriksen flanker effects) are larger following congruent trials relative to incongruent trials. The standard account given for this is that a cognitive control mechanism detects conflict when it occurs and adapts to this conflict on the following trial. Others, however, have questioned the conflict adaptation account and suggested that sequential biases might account for the Gratton effect. In two experiments, contingency biases were removed from the task and stimulus repetitions were deleted to control for stimulus bindings. This eliminated the Gratton effect in the response times in both experiments, supporting a non-conflict explanation of the Gratton effect. A Gratton effect did persist in the errors of Experiment 1; however, this effect was not produced by the type of errors (word reading errors) that a conflict adaptation account should predict. Instead, tentative support was found for a congruency switch cost hypothesis. In all, the conflict adaptation account failed to account for any of the reported data. Implications for future work on cognitive control are discussed.     

Derivation of learning process statistics for a general markov model

A Markov learning model may be stated in the form of a transition matrix, starting vector, and response probability vector. Utilizing these and some general properties of absorbing Markov chains, general expressions are derived for several statistics of the learning process which can be applied to any model of this form. Included are derivations for the mean learning curve, number of total errors, trial numbers of the first success and the last error, and the number of error runs. As an illustration, all derivations are worked out for the simple two-state one-element model.     

Standard errors of fit indices using residuals in structural equation modeling

The asymptotic standard errors of the correlation residuals and Bentler's standardized residuals in covariance structures are derived based on the asymptotic covariance matrix of raw covariance residuals. Using these results, approximations of the asymptotic standard errors of the root mean square residuals for unstandardized or standardized residuals are derived by the delta method. Further, in mean structures, approximations of the asymptotic standard errors of residuals, standardized residuals and their summary statistics are derived in a similar manner. Simulations are carried out, which show that the asymptotic standard errors of the various types of residuals and the root mean square residuals in covariance, correlation and mean structures are close to actual ones.The author is indebted to the reviewers for their comments and suggestions which have led to an improvement of this work.     

‘You Gotta See Both at the Same Time’: Visually Analyzing Player Performances in Basketball Coaching

Developing novices’ proficiency in skilful activities is central to the reproduction of human societies. The interactional practices through which instruction is accomplished have provided a rich focus for ethnomethodological and conversation analytic studies examining classroom settings, and, more recently, non-classroom environments of instruction in practical and manual skills. This paper examines the work of instruction in basketball training and in particular the correction of player performances, which are a ubiquitous and central feature of instruction in basketball training sessions. A central part of this instructional action relies on the coach observing training activities to determine players’ competencies and to extract relevant correctables from the players’ embodied displays, which are in turn embedded within complex arrangements of rapidly moving bodies situated in material environments. In this paper we examine the visual-analytic work involved in both organizing and observing a basketball training activity, demonstrating the sequential layering of multiple membership categorization devices drawn upon in producing and recognizing actions in this setting. We argue that the coach deploys spatial orientations which function analogously to membership categorization devices, with players’ bodily positions relative to one another and the material structure of the surround generating category-like sets of rights, responsibilities, and sequential relevancies. As we demonstrate, these orientations provide crucial resources for the identification of players’ errors and thereby for the organization of instruction in interaction in this setting.     

Segmentation of the speech stream in a non-human primate: statistical learning in cotton-top tamarins

Previous work has shown that human adults, children, and infants can rapidly compute sequential statistics from a stream of speech and then use these statistics to determine which syllable sequences form potential words. In the present paper we ask whether this ability reflects a mechanism unique to humans, or might be used by other species as well, to acquire serially organized patterns. In a series of four experimental conditions, we exposed a New World monkey, the cotton-top tamarin (Saguinus oedipus), to the same speech streams used by Saffran, Aslin, and Newport (Science 274 (1996) 1926) with human infants, and then tested their learning using similar methods to those used with infants. Like humans, tamarins showed clear evidence of discriminating between sequences of syllables that differed only in the frequency or probability with which they occurred in the input streams. These results suggest that both humans and non-human primates possess mechanisms capable of computing these particular aspects of serial order. Future work must now show where humans' (adults and infants) and non-human primates' abilities in these tasks diverge.     

Autocorrelation of choice-reaction times.

A choice-reaction (CR) task requires that the subject estimate, raking the warning signal or his response on the preceding trial as a reference point, the time when the reaction stimulus is due, so that he can begin deciding on his response at an appropriate time. This paper presents a model for the reproduction of temporal intervals, with particular emphasis on the sequential statistics of a series of such reproductions. When this model is concatenated with the sequential probability ratio test model for 2CRT, it provides a quantitative account of the pattern of autocorrelation found in a series of RTs. There is no corresponding autocorrelation in the incidence of errors, however, because after an error the subject systematically adjusts the epoch at which he begins sampling as a precaution against a further error. These post-error adjustments can readily be incorporated into the model. The ideas presented enable several different CR phenomena to be related, and they have implications for the relation between speed and accuracy, for the form of empirical distributions of RTs, and for the effects of temporal uncertainty.     

Learning in reverse: Eight-month-old infants track backward transitional probabilities

Numerous recent studies suggest that human learners, including both infants and adults, readily track sequential statistics computed between adjacent elements. One such statistic, transitional probability, is typically calculated as the likelihood that one element predicts another. However, little is known about whether listeners are sensitive to the directionality of this computation. To address this issue, we tested 8-month-old infants in a word segmentation task, using fluent speech drawn from an unfamiliar natural language. Critically, test items were distinguished solely by their backward transitional probabilities. The results provide the first evidence that infants track backward statistics in fluent speech.     

On the multivariate asymptotic distribution of sequential Chi-square statistics

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-squaredifference tests are asymptotically independent. Some Monte Carlo evidence on the applicability of the theory is provided.This research was carried out while the first author was Visiting Professor in the Department of Statistics in the University of South Africa, and was supported in part by a research grant (NSERC #67-4640) from the National Sciences and Engineering Council of Canada to the first author. The support of both of these organizations is acknowledged with gratitude.     

THE EFFECT OF QUALITY CONTROL REVISIONS ON MIXED STANDARD SCALE RATING ERRORS

Evaluations of performance evaluation ratings conventionally use various psychometric criteria, with reliability being the measure most commonly reported. Rating errors have been attributed to a variety of sources, including the statistical properties of the format or content, ratee performance variability, rater biases, and characteristics of the work setting. This article reports research on error statistics that can be generated using the Mixed Standard Scale (MSS) evaluation format. The reduction of system error rates following revision guided by statistical analysis is a clear indication that the quality control features of this format are useful in the management of performance evaluation systems.     

Recommendations for Describing Statistical Studies and Results in General Readership Science and Engineering Journals

This paper recommends how authors of statistical studies can communicate to general audiences fully, clearly, and comfortably. The studies may use statistical methods to explore issues in science, engineering, and society or they may address issues in statistics specifically. In either case, readers without explicit statistical training should have no problem understanding the issues, the methods, or the results at a non-technical level. The arguments for those results should be clear, logical, and persuasive. This paper also provides advice for editors of general journals on selecting high quality statistical articles without the need for exceptional work or expense. Finally, readers are also advised to watch out for some common errors or misuses of statistics that can be detected without a technical statistical background.     

Standard errors of two-level scalability coefficients

For the construction of tests and questionnaires that require multiple raters (e.g., a child behaviour checklist completed by both parents) a novel ordinal scaling technique is currently being further developed, called two-level Mokken scale analysis. The technique uses within-rater and between-rater coefficients to assess the scalability of the test. These coefficients are generalizations of Mokken's scalability coefficients. In this paper we derived standard errors for the two-level coefficients and for their ratios. The coefficients, the estimates, the estimated standard errors and the software implementation are discussed and illustrated using a real-data example, and a small-scale simulation study demonstrates the accuracy of the estimates.     

Shaw’s stored information as a quantitative measure of sequential structure

In this paper, we describe a method to study the sequential structure in interevent times. The technique uses the stored information of an iterative map developed by-Shaw (1984). The stored information is a quantitative measure of the sequential organization or predictability in data. This paper discusses the concept of stored information and provides a FORTRAN routineto compute the stored information of interevent time data. Several synthetic data sets with known sequential structures are examined. Finally, we present some initial results from computing the stored information of experimental interresponse time data.     

Can independence be observed in a dependent system? The case of tip-of-the-tongue states.

Caramazza and Miozzo (1997) found that speakers experiencing tip-of-the-tongue states are able to report phonological information independently from syntactic information. They used this finding to reject sequential models of production, in which syntactic units (lemmas) are retrieved before form units (lexemes). To see whether this conclusion is warranted, we performed two simulation experiments based on sequential architectures. Both models we simulated produced statistically uncorrelated syntax and phonology despite sequentially retrieving lemmas and lexemes. Finally, we analyzed a corpus of Spanish errors, finding syntactic constraints on phonological word substitution errors that are not easily explained without sequentiality.     

A general class of latent variable models for ordinal manifest variables with covariate effects on the manifest and latent variables

Previous work on a general class of multidimensional latent variable models for analysing ordinal manifest variables is extended here to allow for direct covariate effects on the manifest ordinal variables and covariate effects on the latent variables. A full maximum likelihood estimation method is used to estimate all the model parameters simultaneously. Goodness‐of‐fit statistics and standard errors are discussed. Two examples from the 1996 British Social Attitudes Survey are used to illustrate the methodology.     

Operant learning principles applied to teaching introductory statistics

A grade of A was given in an introductory statistics course for meeting a set of contingencies that included no work outside of class (except by request), near-perfect performance on exams following each unit of work in a programmed text, correction of all exam errors, self pacing of work, and the chance to finish the course early. A grade of incomplete was given otherwise. Correlations among performance measures failed to show any meaningful relationships between time taken to finish the course, errors made on exams, and errors made in the programmed text. Responses to a five-part questionnaire were overwhelmingly favorable to the course, but did not vary as a function of grade point average, time taken to finish the course, or number of errors made on exams. The uniformly high level of performance, the students' lack of interest in social contact with the instructor during class, and the absence of drop-outs are all attributed to the contingencies employed, chief among which, according to the instructor's judgment and student rankings, were self-pacing, frequent non-punitive exams and a guaranteed grade of A for near-perfect work at every stage.     

Auditory cueing facilitates temporospatial accuracy of sequential movements

Effectively executing goal-directed behaviours requires both temporal and spatial accuracy. Previous work has shown that providing auditory cues enhances the timing of upper-limb movements. Interestingly, alternate work has shown beneficial effects of multisensory cueing (i.e., combined audiovisual) on temporospatial motor control. As a result, it is not clear whether adding visual to auditory cues can enhance the temporospatial control of sequential upper-limb movements specifically. The present study utilized a sequential pointing task to investigate the effects of auditory, visual, and audiovisual cueing on temporospatial errors. Eighteen participants performed pointing movements to five targets representing short, intermediate, and large movement amplitudes. Five isochronous auditory, visual, or audiovisual priming cues were provided to specify an equal movement duration for all amplitudes prior to movement onset. Movement time errors were then computed as the difference between actual and predicted movement times specified by the sensory cues, yielding delta movement time errors (ΔMTE). It was hypothesized that auditory-based (i.e., auditory and audiovisual) cueing would yield lower movement time errors compared to visual cueing. The results showed that providing auditory relative to visual priming cues alone reduced ΔMTE particularly for intermediate amplitude movements. The results further highlighted the beneficial impact of unimodal auditory cueing for improving visuomotor control in the absence of significant effects for the multisensory audiovisual condition.     

Asymptotic standard errors of irt observed-score equating methods

A method of the IRT observed-score equating using chain equating through a third test without equating coefficients is presented with the assumption of the three-parameter logistic model. The asymptotic standard errors of the equated scores by this method are obtained using the results given by M. Liou and P.E. Cheng. The asymptotic standard errors of the IRT observed-score equating method using a synthetic examinee group with equating coefficients, which is a currently used method, are also provided. Numerical examples show that the standard errors by these observed-score equating methods are similar to those by the corresponding true score equating methods except in the range of low scores.The author is indebted to Michael J. Kolen for access to the real data used in this article and anonymous reviewers for their corrections and suggestions on this work.     

Serial order and consonant-vowel structure in a graphemic output buffer model

We review features of the spelling errors of dysgraphic patients with "Graphemic Buffer Disorder" (GBD). We argue that the errors made by such patients suggest the breakdown of a system used to generate serial order in the output stages of spelling production, and we develop a model for this system based on an existing theory of sequential behaviour--"Competitive Queuing." We show that constraints on response categories may be straightforwardly applied during sequence production in such a model, and this enables us to account for the preservation of consonant-vowel status in the spelling errors of GBD patients. When the sequence generation process is disrupted by the addition of random noise the model shows the major features of GBD. The results are compared in detail against data from a number of patients.