Ordinal consistency and ordinal true scores

This paper argues that test data are ordinal, that latent trait scores are only determined ordinally, and that test data are used largely for ordinal purposes. Therefore it is desirable to develop a test theory based only on ordinal assumptions. A set of ordinal assumptions is presented, including an ordinal version of local independence. From these assumptions it is first shown that the gamma-correlation between two tests is the product of their gamma-correlations with the true latent order. The theory is generalized to allow for heterogeneous tests by defining a weighted average local independence. The tau-correlations between total score and the latent order can be found in both homogeneous and heterogeneous cases, and a system of differential item weighting to maximize the tau-correlation between weighted items and the latent order is provided. Thus a purely ordinal test theory seems possible.Part of this work was done while the author was a Visiting Fellow at Macquarrie University. The paper has benefitted from discussions with Professors Thomas J. Reynolds and Roderick P. McDonald and from the comments of several anonymous reviewers.     

Perceptions of ambiguously unpleasant interracial interactions: a structural equation modeling approach

Despite a general consensus in the United States that overtly racist acts are unacceptable, many ambiguous situations in everyday life raise questions of whether racism has influenced a person's behavior in an interracial encounter. The authors of the present study sought to (a) examine simultaneously an array of variables thought to be related to perceived racism and (b) investigate how the contribution of these variables may differ with respect to the asymmetry hypothesis, which suggests that acts of discrimination from a dominant person toward a subordinate person will be viewed as more biased than if the situation were reversed. The authors used a dual structural equation modeling approach. Results indicated that ethnic identity significantly predicted perceived racism. In addition, the extent to which cognitive interpretation style significantly predicted perceived racism depended on the ethnicity of participants involved in the interaction.     

Adaptive procedures in psychophysical research.

As research on sensation and perception has grown more sophisticated during the last century, new adaptive methodologies have been developed to increase efficiency and reliability of measurement. An experimental procedure is said to be adaptive if the physical characteristics of the stimuli on each trial are determined by the stimuli and responses that occurred in the previous trial or sequence of trials. In this paper, the general development of adaptive procedures is described, and three commonly used methods are reviewed. Typically, a threshold value is measured using these methods, and, in some cases, other characteristics of the psychometric function underlying perceptual performance, such as slope, may be developed. Results of simulations and experiments with human subjects are reviewed to evaluate the utility of these adaptive procedures and the special circumstances under which one might be superior to another.     

Estimation of psychometric functions from adaptive tracking procedures.

Because adaptive tracking procedures are designed to avoid stimulus levels far from a target threshold value, the psychometric function constructed from the trial-by-trial data in the track may be accurate near the target level but a poor reflection of performance at levels far removed from the target. A series of computer simulations was undertaken to assess the reliability and accuracy of psychometric functions generated from data collected in up-down adaptive tracking procedures. Estimates of psychometric function slopes were obtained from trial-by-trial data in simulated adaptive tracks and compared with the true characteristics of the functions used to generate the tracks. Simulations were carried out for three psychophysical procedures and two target performance levels, with tracks generated by psychometric functions with three different slopes. The functions reconstructed from the tracking data were, for the most part, accurate reflections of the true generating functions when at least 200 trials were included in the tracks. However, for 50- and 100-trial tracks, slope estimates were biased high for all simulated experimental conditions. Correction factors for slope estimates from these tracks are presented. There was no difference in the accuracy and reliability of slope estimation due to target level for the adaptive track, and only minor differences due to psychophysical procedure. It is recommended that, if both threshold and slope of psychometric functions are to be estimated from the trial-by-trial tracking data, at least 100 trials should be included in the tracks, and a three- or four-alternative forced-choice procedure should be used. However, good estimates can also be obtained using the two-alternative forced-choice procedure or less than 100 trials if appropriate corrections for bias are applied.     

The relation between sample and population characteristic vectors

Data are reported which show the statistical relation between the sample and population characteristic vectors of correlation matrices with squared multiple correlations as communality estimates. Sampling fluctuations were found to relate only to differences in the square roots of characteristic roots and to sample size. A principle for determining the number of factors to rotate and interpret after rotation is suggested.This study was supported by the National Science Foundation, Grant GB 4230. The author wishes to express his appreciation for the use of Western Data Processing Center and the Health Sciences Computing Facility, UCLA. He also thanks Dr. Roger Pennell for extremely valuable assistance in a number of phases of the study.     

Axiomatic foundations of a three-set guttman simplex model with applicability to longitudinal data

In this paper the usual two-set Guttman simplex model is extended to three sets. The axiomatic foundations of this extention are presented. Two cases are discussed. In Case 1 there is a three-set joint order, while in Case 2 there is a two-set joint order consistent across all levels of the third set. Case 2 represents the first clear formulation of a longitudinal developmental scale. The model is discussed in terms of its most straightforward application, longitudinal developmental data, and in terms of other possible applications.This research was supported in part by NSF grant BNS 8108145.     

Rationality as Effective Organisation of Interaction and Its Naturalist Framework

The point of this paper is to provide a principled framework for a naturalistic, interactivist-constructivist model of rational capacity and a sketch of the model itself, indicating its merits. Being naturalistic, it takes its orientation from scientific understanding. In particular, it adopts the developing interactivist-constructivist understanding of the functional capacities of biological organisms as a useful naturalistic platform for constructing such higher order capacities as reason and cognition. Further, both the framework and model are marked by the finitude and fallibility that science attributes to organisms, with their radical consequences, and also by the individual and collective capacities to improve their performances that learning organisms display. Part A prepares the ground for the exposition through a critique of the dominant Western analytic tradition in rationalising science, followed by a brief exposition of the naturalist framework that will be employed to frame the construction. This results in two sets of guidelines for constructing an alternative. Part B provides the new conception of reason as a rich complex of processes of improvement against epistemic values, and argues its merits. It closes with an account of normativity and our similarly developing rational knowledge of it, including (reflexively) of reason itself.     

An examination of graduate students' statistical judgments: statistical and fuzzy set approaches

The present study examined how statistical significance levels are treated and interpreted by graduate students who use hypothesis-testing in their scientific investigation. To test underlying psychological aspects of hypothesis-testing, the idea of fuzzy set theory was employed to identify the uncertain points in judgments. 34 graduate students in a psychology department made judgments about hypothetical statistical decisions. The results indicated that (1) the majority of these students treated significance levels on a continuum and rated them according to the magnitude of statistical significance; (2) the subjects shifted their decisions based on the types of hypothetical scenarios but not by the sample sizes; instead, they interpreted a smaller sample size as being less reliable. (3) The subjects frequently chose formally used statistical terms, e.g., Significant and Not Significant, more than graduated verbal expressions, e.g., Marginally Significant and Borderline Significant; and (4) the Fuzziness (degree of confidence in decision-making) was dependent on individuals and existed more in the critical points of transition where judgments are most difficult. The Fuzziness Index illustrated the subtle shifts of human decision-making patterns in statistical judgments. Underlying decision uncertainties and difficulties can be illustrated by functions generated from fuzzy set theory, which may more closely resemble human psychological mechanism. This integrative study of fuzzy set theory and behavioral measurements appears to provide a technique that is more natural for examining and understanding imprecise boundaries of human decisions.     

Increasing the reliability of Wechsler Intelligence Scale for Children--Third Edition difference scores with reliable component analysis

Wechsler Intelligence Scale for Children--Third Edition index score differences are generally interpreted cautiously, if at all, primarily because of their poor reliability. On the basis of prior analyses with the Wechsler Adult Intelligence Scale--Third Edition (J. C. Caruso & N. Cliff, 1999), it was hypothesized that differences between scores defined by reliable component analysis would have higher reliability than those defined by traditional equal weighting. Differences between the reliable component scores showed substantially higher reliability than equally weighted score differences. The differences between reliable component scores were also substantially more reliable than those derived from the weighted scores suggested by K. C. H. Parker and L. Atkinson (1994). Using the weights provided in this article will allow researchers and practitioners to compute the RCA scores and have the assurance of high reliability with its attractive consequences.