Acquisition of the Linearization Process in Text Composition in Third to Ninth Graders: Effects of Textual Superstructure and Macrostructural Organization

Two complementary experiments analyzed the acquisition of text content linearization in writing, in French-speaking participants from third to ninth grades. In both experiments, a scrambled text paradigm was used: eleven ideas presented in random order had to be rearranged coherently so as to compose a text. Linearization was analyzed on the basis of the conceptual ordering of ideas and writing fluency. The first experiment focused on the effect of superstructural facilitation (in decreasing order: 1—instructional, 2—narrative, 3—argumentative), while the second experiment studied the effect of prewriting conditions: 1—scrambled presentation, 2—macrostructural facilitation, 3—ideas given in optimal order (control condition). As expected, scores in conceptual ordering and writing fluency improved through the grade levels. Students were most successful with respect to conceptual ordering in the instructional superstructure, followed by the narrative and finally the argumentative superstructures. The prewriting assignment also had the expected effect (control better than macrostructural presentation which, in turn, was better than the random order) but only with the argumentative superstructure. Contrary to conceptual ordering, writing fluency was not affected by the type of superstructure, although we did record an effect of the prewriting condition. The results are discussed in light of Bereiter and Scardamalia’s knowledge transforming strategy (1987) taking into account cognitive development and French language curriculum.     

Incidental task sequence learning: perceptual rather than conceptual?

In four experiments we investigated whether incidental task sequence learning occurs when no instructional task cues are available (i.e. with univalent stimuli). We manipulated task sequence by presenting three simple binary-choice tasks (colour, form or letter case decisions) in regular repeated or random order. Participants were required to use the same two response keys for each of the tasks. We manipulated response sequence by ordering the stimuli so as to produce either a regular or a random order of left versus right-hand key presses. When sequencing in both, or either, separate stream (i.e. task sequence and/or response sequence) was changed to random, only those participants who had processed both sequences together showed evidence of sequence learning in terms of significant response time disruption (Experiments 1-3). This effect disappeared when the sequences were uncorrelated (Experiment 4). The results indicate that only the correlated integration of task sequence and response sequence produced a reliable incidental learning effect. As this effect depends on the predictable ordering of stimulus categories, it suggests that task sequence learning is perceptual rather than conceptual in nature.     

Short-range ordering of heavy-element columns in nickel-based superalloys

In order to obtain comprehensive performance, heavy elements were added into superalloys for solid-solution hardening. It is found that, rather than adopting random distributions, the heavy atoms prefer to form short-range ordered columns with heavy-element stripes 1–2 nm in length. This is supported by our ab initio calculations. Owing to the strong bonding strength between the refractory elements and nickel atoms, this short-range ordering may be beneficial to the mechanical performances of superalloys.     

Short-range order in the arrangement of grains in two-dimensional polycrystals

Abstract

Experimental results for two-dimensional grain growth are compared with the results obtained from computer-generated random threefold vertex networks with a fixed one-particle distribution function. A considerable discrepancy in the two-particle distributions implies some kind of short-range order. New results in the computer simulation of normal grain growth are reported, demonstrating a similar kind of ordering. A simple relation is suggested for the quantity m _n, introduced by Aboav and the second moment of the one-particle distribution μ₂     

Collecting paired-comparison data with a sorting algorithm

Monte Carlo techniques were used to evaluate the performance of an on-line paired-comparisons data collection procedure that makes use of a common computer sorting algorithm. The results revealed that the sorting method can reduce the number of trials per subject substantially even when a considerable amount of random error is present. While a complete paired-comparisons design requires N(N?1)/2 trials (where N is the number of objects), the sorting procedure requires a theoretical minimum of N(log₂N) trials. The savings in the number of trials consequently increases with N. Furthermore, the negative effect of random error on the final ordering of the data from the sorting method is small and decreases with the number of stimuli. The data from a small empirical study reinforces the Monte Carlo observations. It is recommended that the sorting method be used in place of the complete paired-comparisons procedure whenever a substantial number of stimuli are included in the design.     

The Measurement of Qualitative Probability

This essay presents necessary and sufficient conditions for representing a binary relation on a space of bounded random variables with a unique quantitative expectations operator. This result is used to provide a new characterization of qualitative probability. We also show that two distinct probability measures can induce the same qualitative ordering of events, even though they always produce different qualitative expectations relations. Copyright 2000 Academic Press.     

Variability of the MAX and MIN Statistic: A Theory of the Quantile Spread as a Function of Sample Size

The maximum and minimum of a sample from a probability distribution are extremely important random variables in many areas of psychological theory, methodology, and statistics. For instance, the behavior of the mean of the maximum or minimum processing time, as a function of the number of component random processing times (n), has been studied extensively in an effort to identify the underlying processing architecture (e.g., Townsend & Ashby, 1983; Colonius & Vorberg, 1994). Little is known concerning how measures of variability of the maximum or minimum change with n. Here, a new measure of random variability, the quantile spread, is introduced, which possesses sufficient strength to define distributional orderings and derive a number of results concerning variability of the maximum and the minimum statistics. The quantile spread ordering may be useful in many venues. Several interesting open problems are pointed out. This work was supported by an NIH Grant R01 MH57717 to the first author. Some of the collaboration took place during the year 2000 while J.T. Townsend was a Fellow at the Hanse Institute for Advanced Study (HWK), sponsored by H. Colonius at Oldenburg University.     

Deflecting Arrow by Aggregating Rankings of Multiple Correlated Criteria According to Borda

This paper has two objectives. The first is to review and address concerns raised by Hazelrigg that Arrow's impossibility theorem prevents the selection of rational aggregation methods for use in engineering trade studies. In addressing these concerns, the work of Saari is cited to establish the fact that the Borda count is the only ‘non‐dictatorial’ positional voting method that satisfies the criteria for a rational decision procedure while using complete information. Hence, the resulting rank ordering of the alternatives is the most reliable outcome. Several previous studies that use other aggregation methods are critiqued, and Borda is applied to examples to illustrate the differences in the outcomes. The second objective is to extend the applicability of Borda to include attributes such as cost, schedule duration, and certain technical and performance measures that are generally more reasonably described as correlated random variables. Exact Probabilities by Simulation with Borda, a method introduced by Hulkower that improves a technique by Book for determining which candidate in a trade study is the probable lowest‐cost alternative, is generalized to include multiple correlated criteria, each of which is expressed as a random variable and thus incorporates probabilistic uncertainty. Copyright © 2016 John Wiley & Sons, Ltd.     

Representation of on-line questionnaires in an editable,auditable database

A general way of describing multiple-choice questionnaires for on-line presentation is described. Some of the important features supported include random ordering of and sampling among questions, substitution of specific-question text into boilerplate question and response formats, a limited ability to bypass irrelevant questions, experimenter editing of response arrays, and automatic production of hard-copy versions of the questionnaire for use during computer breakdowns and for archival documentation. All editing operations on both questionnaires and response data create audit trails for future reference.     

Blur discrimination and its relation to blur-mediated depth perception

Retinal images of three-dimensional scenes often contain regions that are spatially blurred by different amounts, owing to depth variation in the scene and depth-of-focus limitations in the eye. Variations in blur between regions in the retinal image therefore offer a cue to their relative physical depths. In the first experiment we investigated apparent depth ordering in images containing two regions of random texture separated by a vertical sinusoidal border. The texture was sharp on one side of the border, and blurred on the other side. In some presentations the border itself was also blurred. Results showed that blur variation alone is sufficient to determine the apparent depth ordering. A subsequent series of experiments measured blur-discrimination thresholds with stimuli similar to those used in the depth-ordering experiment. Weber fractions for blur discrimination ranged from 0.28 to 0.56. It is concluded that the utility of blur variation as a depth cue is constrained by the relatively mediocre ability of observers to discriminate different levels of blur. Blur is best viewed as a relatively coarse, qualitative depth cue.     

Implications of the Dutch Book: Following Ramsey��s axioms

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made.     

Young children's non‐numerical ordering ability at the start of formal education longitudinally predicts their symbolic number skills and academic achievement in maths

Ordinality is a fundamental feature of numbers and recent studies have highlighted the role that number ordering abilities play in mathematical development (e.g., Lyons et al., 2014 ), as well as mature mathematical performance (e.g., Lyons & Beilock, 2011 ). The current study tested the novel hypothesis that non‐numerical ordering ability, as measured by the ordering of familiar sequences of events, also plays an important role in maths development. Ninety children were tested in their first school year and 87 were followed up at the end of their second school year, to test the hypothesis that ordinal processing, including the ordering of non‐numerical materials, would be related to their maths skills both cross‐sectionally and longitudinally. The results confirmed this hypothesis. Ordinal processing measures were significantly related to maths both cross‐sectionally and longitudinally, and children's non‐numerical ordering ability in their first year of school (as measured by order judgements for everyday events and the parents’ report of their child's everyday ordering ability) was the strongest longitudinal predictor of maths one year later, when compared to several measures that are traditionally considered to be important predictors of early maths development. Children's everyday ordering ability, as reported by parents, also significantly predicted growth in formal maths ability between Year 1 and Year 2, although this was not the case for the event ordering task. The present study provides strong evidence that domain‐general ordering abilities play an important role in the development of children's maths skills at the beginning of formal education.     

On a connection between factor analysis and multidimensional unfolding

Given the preference ordering of each of a number of individuals over a set of stimuli, it is proposed that if the preference orderings are generated in a Euclidean space ofr dimensions which can be recovered by unfolding the preference orderings, then a factor analysis of the correlations between individual's preference orderings will yield a space ofr + 1 dimensions with the originalr-space embedded in it, and the additional dimension will be one of social utility. The proposition is clearly shown to be satisfied by means of the Monte Carlo technique for both random and lattice stimuli in three dimensions and for two other examples with random stimuli in one and two dimensions.The preparation of this paper was supported in part by a grant from the National Science Foundation and in part by Project MICHIGAN, a project of the University of Michigan in the field of Combat Surveillance sponsored by the Department of the Army. The contract (DA-36-039 ac 78801) is administered by the U. S. Army Signal Corps. The authors are indebted to L. A. Raphael, Caroline K. Tefft, and F. M. Goode for programming assistance, and to L. W. Staugas for providing other computer services during various stages of this study.     

The Beck Depression Inventory: item order and the impact of response sets

The lack of subtle content in the item groups of the Beck Depression Inventory (BDI) and the consistency in the ordering of the items from least to most pathological make this instrument unduly susceptible to either defensive or malingering response sets. Two experimental forms were developed for the BDI: a backwards version (a simple reversal of the order of items within each group) and a random-order version. These forms, together with the original item order, were given to college undergraduate women along with the Depression scale from the MMPI and the Burks-Martin Questionnaire covering recent life changes and current stressful situations. The random order BDI results in a significantly higher depression score than did either the original or backwards version. Correlations with the other instruments were comparable for all three forms. The random order of items within each set appears to break up a response set to endorse either the first or last item and is, therefore, recommended.     

The Beck Depression Inventory: Item Order and the Impact of Response Sets

The lack of subtle content in the item groups of the Beck Depression Inventory (BDI) and the consistency in the ordering of the items from least to most pathological make this instrument unduly susceptible to either defensive or malingering response sets. Two experimental forms were developed for the BDI: a backwards version (a simple reversal of the order of items within each group) and a random-order version. These forms, together with the original item order, were given to college undergraduate women along with the Depression scale from the MMPI and the Burks-Martin Questionnaire covering recent life changes and current stressful situations. The random order BDI results in a significantly higher depression score than did either the original or backwards version. Correlations with the other instruments were comparable for all three forms. The random order of items within each set appears to break up a response set to endorse either the first or last item and is, therefore, recommended.     

Similarities and differences in social attitudes in four Western countries1

A referents scale (single words and short phrases) constructed to measure social attitudes and values was administered to 500 graduate students of education in the United States, 427 mature evening students in Spain, 130 German students, 270 Dutch students, and 685 Dutch adults, a random sample of the Netherlands. The attitudes of the samples were compared by analysis of the means of clusters of referents associated with the factors common to all samples. The means of selected individual referents of social significance were similarly compared across samples. In general, the U.S. student sample and the Netherlands random sample were more conservative than the Spanish, Dutch, and German student samples. On the other hand, the Dutch, Spanish, and American students were more liberal than the Dutch random sample and the German students. The correlations between the profiles of means of referents common to pairs of samples were mostly substantial (average r's of .75 for conservative referents and .62 for liberal referents), indicating considerable cross-cultural agreement in the rank ordering of the referents within the conservative and within the liberal categories, and thus, presumably, common cores of reaction to the two kinds of referents. The use of attitude-value referents, especially in cross-cultural research, was judged valid and useful.     

Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models

It is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability. Such an ordering is an invariant item ordering (IIO). An IIO facilitates the interpretation of test results. For dichotomously scored items, earlier research surveyed the theory and methods of an invariant ordering in a nonparametric IRT context. Here the focus is on polytomously scored items, and both nonparametric and parametric IRT models are considered.The absence of the IIO property in twononparametric polytomous IRT models is discussed, and two nonparametric models are discussed that imply an IIO. A method is proposed that can be used to investigate whether empirical data imply an IIO. Furthermore, only twoparametric polytomous IRT models are found to imply an IIO. These are the rating scale model (Andrich, 1978) and a restricted rating scale version of the graded response model (Muraki, 1990). Well-known models, such as the partial credit model (Masters, 1982) and the graded response model (Samejima, 1969), do no imply an IIO.     

Invariant Ordering of Item-Total Regressions

A new observable consequence of the property of invariant item ordering is presented, which holds under Mokken’s double monotonicity model for dichotomous data. The observable consequence is an invariant ordering of the item-total regressions. Kendall’s measure of concordance W and a weighted version of this measure are proposed as measures for this property. Karabatsos and Sheu proposed a Bayesian procedure (Appl. Psychol. Meas. 28:110–125, 2004), which can be used to determine whether the property of an invariant ordering of the item-total regressions should be rejected for a set of items. An example is presented to illustrate the application of the procedures to empirical data.     

A Tractarian Universe

In this paper we develop a reconstruction of the Tractatus ontology. The basic idea is that objects are unsaturated and that Sachlagen are like molecules. Bisimulation is used for the proper individuation of the Sachlagen. We show that the ordering of the Sachlagen is a complete distributive, lattice. It is atomistic, i.e., each Sachlage is the supremum of the Sachverhalte below it. We exhibit three normal forms for Sachlagen: the bisimulation collapse, the canonical unraveling and the canonical bisimulation collapse. The first of these forms is unique modulo isomorphism, the second and third are simply unique. The subset ordering on normal forms of the second and third kind reflects the ordering of the Sachlagen.     

A General Family of Preferential Belief Removal Operators

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339–1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174:1339–1368, 2010) to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases.