The fallacy of “two years below grade level for age” as a diagnostic criterion for reading disorders

The use of grade equivalent scores contrasted against grade placement is widespread in the diagnosis of dyslexia and other reading disabilities. This method substantially overstates disabilities at upper grade levels while underestimating the severity of difficulties in the early grades. Other difficulties and difficulties and distortions of this methods are also pointed out. An accurate, alternative method for reliably determining aptitude/achievement discrepancies is presented and its use discussed.     

Context, categorization, and recall: The “change-of-standard” effect

A psycholinguistically based conception of the relation among context, categorization, and memory is tested by examining what happens to people's memory of an object when the object is initially categorized in terms of the context in which it appears, but, when the object is later recalled, this context is no longer salient. Subjects read about the sentencing decisions of a target trial judge in the context of other trial judges who consistently gave either higher sentences or lower sentences than the target judge. As predicted, subjects tended to categorize the target judge as “lenient” in the former, harsh context condition, and as “harsh” in the latter, lenient context condition. A week later, subjects read about the sentencing decisions of some additional judges, and then recalled the sentencing decisions of the target judge they had read about the week before. Across the two sessions, either a harsh, moderate, or lenient category norm for judges' sentencing decisions was established by having subjects read about decisions that involved either high, medium, or low sentences, respectively. The results indicated that subjects recalled the target judge's decisions by interpreting their prior categorization of his behavior in terms of the category norm established across the two sessions rather than the original context. Thus, subjects who were exposed to the same target in the same circumstances, and initially categorized the target in the same way, nevertheless remembered his behavior differently if their category norm was different at the moment of recall. Other types of “change of standard” and their implications for human judgment and memory are discussed.     

Some theory and results for metrics for bounded response scales

In an earlier note, a new metric for bounded response scales (MBR) was introduced which resembles the city-block metric but is bounded above. It was suggested the MBR may be more appropriate than minkowski metrics for data obtained with bounded response scales. In this article, some formal properties of the MBR are investigated and it is shown that it is indeed a metric. Empirical predictions are then derived from the MBR and contrasted with those of a “monotonicity hypothesis,” which holds that dissimilarity judgements tend to be biased towards overestimation of larger distances, and with the predictions of the minkowski metrics, which imply additivity of collinear segments. Some empirical results are presented which contradict the monotonicity hypothesis and the minkowski metrics, and favor the MBR. Finally, the logic used to motivate the MBR is invoked to define a subadditive concatenation for bounded norms in the one-dimensional case, which may be useful in psychophysical work where the upper bounds are often real, rather than due to the response scale. This concatenation predicts understimation for doubling and overestimation for halving and middling tasks.     

A characterization of stochastic independence by association,with an application to random utility theory

A characterization of stochastic independence in terms of association of random variables is given. The result is applied to yield a simple proof of the Sattath-Tversky inequality without continuity assumptions.     

A procedural theory of eye movements in doing arithmetic

A procedural theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction is presented. The best-fitting distribution of fixation durations with a relatively simple theoretical justification consists of a mixture of an exponential distribution and the convolution of two exponential distributions. The eye movements themselves were found to approximate a random walk that fits rather closely in both adult and juvenile subjects the motion postulated by the normative algorithm ordinarily taught in schools. Certain structural features of addition and subtraction exercises, such as the number of columns, the presence or absence of a carry or a borrow, are well known to affect their difficulty. In this study, regressions on such structural variables were found to account for only a relatively small part of the variation in eye-fixation durations.     

“Impossible figures” and interpretations of polyhedral figures

The concept “impossible figure” is analyzed by formalizing the interpretations of a polyhedral figure by an observer, and defining several types of inconsistency in such interpretations. Tests for these inconsistencies are developed using simple graph theory, and a sufficient condition is established for the feasibility of an interpretation. Finally, techniques are derived for the automatic construction of usual or unusual multibar figures.     

Some deterministic models of concept identification

It is shown that deterministic models can compete effectively with stochastic models in summarizing concept identification behavior. Three groups of deterministic models are examined. Examination of individual learners' trial by trial behavior in a concept experiment shows: (1) One person exhibited behavior consistent with a Hypothesis Permutation (HP) model despite being a nonlearner who showed no evidence of improvement over a period of 24 trials. However, when all 50 persons studied in each of two treatment groups were examined, only 22 members of one group and 10 of the other showed no inconsistencies with deterministic local consistency assumptions. (2) Certain deterministic computer programs could find at least one satisfactory order for predicting all responses by 18 of the 22 consistent solvers and 6 of the 10 consistent solvers, respectively, in the two groups just mentioned. For these 24 persons, then, a less restrictive deterministic model is adequate than for the others. (3) Those 38 original members of the first treatment group who met a stringent learning criterion were compared with respect to predictions generated by stochastic and mathematized deterministic models. One deterministic model (RSS-U 9-state) is in some respects the best of the models examined, but this success is a partial reflection of estimating eight parameters from the data.     

An axiomatization of the ratio/difference representation

If ≥_r and ≥_d are two quaternary relations on an arbitrary set A, a ratio/difference representation for ≥_r and ≥_d is defined to be a function f that represents ≥_r as an ordering of numerical ratios and ≥_d as an ordering of numerical differences. Krantz, Luce, Suppes and Tversky (1971, Foundations of Measurement. New York, Academic Press) proposed an axiomatization of the ratio/difference representation, but their axiomatization contains an error. After describing a counterexample to their axiomatization, Theorem 1 of the present article shows that it actually implies a weaker result: if ≥_r and ≥_d are two quaternary retations satisfying the axiomatization proposed by Krantz et al. (1971), and if ≥_r′ and ≥_d′ are the relations that are inverse to ≥_r and ≥_d, respectively, then either there exists a ratio/difference representation for ≥_r and ≥_d, or there exists a ratio/difference representation for ≥_r′ and ≥_d′, but not both. Theorem 2 identifies a new condition which, when added to the axioms of Krantz et al. (1971), yields the existence of a ratio/difference representation for relations ≥_r and ≥_d.     

Brilliant but cruel: Perceptions of negative evaluators

Using edited excerpts from actual negative and positive book reviews, this research examined the hypothesis that negative evaluators of intellectual products will be perceived as more intelligent than positive evaluators. The results strongly supported the hypothesis. Negative reviewers were perceived as more intelligent, competent, and expert than positive reviewers, even when the content of the positive review was independently judged as being of higher quality and greater forcefulness. At the same time, in accord with previous research, negative reviewers were perceived as significantly less likable than positive reviewers. The results on intelligence ratings are seen as bolstering the self-presentational explanation of the tendency shown by intellectually insecure individuals to be negatively critical. The present methodology is contrasted to that of previous research which obtained apparently contradictory results.     

The effects of control on perceived fairness of procedures and outcomes

On the basis of Thibaut and Walker's theory of procedural justice, it was predicted that subjects who experienced control through choosing a trial decision rule would be more satisfied with the outcome of a dispute and the conflict resolution procedure than would yoked subjects who were not given control. Two additional conditions were added to the design in order to investigate the extent to which control had an influence on trial evaluations independent of being allowed to discuss the rules and obtaining a preferred rule in the absence of actual choice. Regardless of role in the dispute (accuser, accused, or no knowledge) and the nature of the rule adopted, those subjects who exercised control through rule choice evaluated all aspects of the trial experience more positively than subjects who did not exercise control through rule choice. The results also revealed that discussion of the rules and obtaining the preferred rule without choice contributed positively to evaluations of the trial procedure and verdict.