Further evidence for Coren and Hakstian’s “Methodological implications of interaural correlation: Count heads not ears” and an alternative correction formula

Coren and Hakstian (1990) identified a serious methodological problem that arises in auditory research because of interaural correlation. When measures from both ears of the subjects are pooled together in an experimental design that assumes independence of measures, there can be spuriously high apparent statistical significance. The present paper provides further evidence in support of Coren and Hakstian’s argument and also derives a formula that effectively corrects inflated test statistics resulting from interaural correlation. This formula is a special case of a more general one that applies in many other experimental contexts in which nonindependence of measures is a problem. We found that statistical tests based on our formula have somewhat greater power to detect differences than the kind of correction method advocated by Coren and Hakstian.     

In defense of the right and left audiograms: a reply to Coren (1989) and Coren and Hakstian (1990)

Coren (1989) noticed that the various air-conduction pure-tone thresholds obtained from one ear of an individual in quiet tend to display a high correlation. In addition, Coren and Hakstian (1990) reported a consistently high correlation between pure-tone thresholds in the two ears of the same individual. On the basis of these observations, these authors proposed that pure-tone thresholds measured at audiometric frequencies in one ear, and those measured in both ears of an individual, be collapsed into a single average threshold value. The present paper disputes the usefulness and the appropriateness of such a proposal.     

Methodological implications of interaural correlation: count heads not ears

In a sample of 425 subjects, pure-tone hearing thresholds between the right and left ears were shown to have an average correlation of .885 (or .783 with age partialed out). This high interaural correlation is shown to invalidate the experimental procedure of entering data on the basis of "ears," where each subject can contribute one or two audiograms to the data pool, since such aggregation is demonstrated to produce spuriously high levels of apparent statistical significance in inferential statistical tests.     

Inferential procedures for multifaceted coefficients of generalizability

A two-facet measurement model with broad application in the behavioral sciences is identified, and its coefficient of generalizability (CG) is examined. A normalizing transformation is proposed, and an asymptotic variance expression is derived. Three other multifaceted measurement models and CGs are identified, and variance expressions are presented. Next, an empirical investigation of the procedures follows, and it is shown that, in most cases, Type I error control in inferential applications is precise, and that the estimates are relatively efficient compared with the correlation coefficient. Implications for further research and for practice are noted. In an Appendix, four additional models, CGs, and variance expressions are presented.The research reported herein formed part of a doctoral dissertation conducted by Marsha Schroeder (Schroeder, 1986), under the direction of Ralph Hakstian, at the University of British Columbia. We acknowledge with thanks the contributions to this research of Todd Rogers and James Steiger. We are also very indebted to an mous reviewer who provided some important clarifications in connection with two of the models considered. Some support for this research was provided by a grant to Ralph Hakstian from the Natural Sciences and Engineering Research Council of Canada.     

Psychoticism and creativity

Eysenck and Eysenck (1976) cited a number of studies showing that creativity and originality are associated with high scores on their Psychoticism factor, P. In this study, we examined the generality of this claim by using a different set of creativity measures, scales from the Comprehensive Ability Battery (Hakstian & Cattell, 1976) and the Eysenck Personality Questionnaire (Eysenck & Eysenck, 1975), with a sample of 173 students. No appreciable overlap was found between the creativity scales and P. A number of possible explanations for this result are discussed, and we concluded that this finding may cast doubt on the generality of the link between creativity and P.     

Similarity of the perimeters in the Ebbinghaus illusion

Coren and Miller (1974) and Coren and Enns (1993) argued that the magnitude of the Ebbinghaus illusion is a function of the rated or conceptual similarity of the inducing objects to the test object. In three experiments, we examined the convergence between conceptual similarity and illusion magnitude. The first failed to find support for this parallel. Two further experiments yielded support for an alternative hypothesis that the magnitude of the Ebbinghaus illusion is a function of the similarity of the perimeters of the inducing object to the test object. The similarity of the centers had no effect. These results suggest that the information used to estimate size is computed earlier in the visual system than suggested by Coren and colleagues and apparently does not involve the use of conceptual information.     

Lateralization of two-transient stimuli

In this study of the precedence effect in binaural hearing, subjects adjusted the interaural delay of a wideband acoustic pointer to match the perceived intracranial position of transient test stimuli presented over headphones. The test stimuli had leading and lagging components (either brief noise bursts or clicks), each with its own interaural delay. In some test conditions, the leading and lagging stimuli were coherent copies of one another, whereas in others, they were independent samples of noise. The duration of the stimuli and the delay from the leading component to the lagging component were also varied. All the stimulus conditions showed a moderate or strong precedence effect (i.e., covariation of perceived lateral position of the composite two-transient stimulus with the interaural delay of the leading component). Predictions of the lateralization data are presented for variants of models based on temporal weighting and/or bandpass correlation. In one model variant, the binaural stimuli are temporally weighted to emphasize the onset and then subjected to bandpass correlation analysis. In another variant, it is assumed that the onset mechanism provides a rough estimate of the initial interaural delay that guides a slower and more focused bandpass correlation analysis. The accuracies of these two model's predictions were equivalent and superior to those of models that either represent leading and lagging cues equally (bandpass correlation with no onset effect) or do not represent lagging cues at all (a complete precedence effect). The results of these analyses show the need for both a strong onset effect and for bandpass correlation analysis and suggest two modeling approaches for achieving that goal.     

Cognitive Abilities and Creative Behaviors: CAB-5 and Consequences

The validity of six indices of divergent production is examined with reference to creative output in eight content domains: visual arts, music, literature, theater, science and engineering, business ventures, apparel design, and video and photographic work. Undergraduates (n = 144) completed Consequences, four scales from the Comprehensive Ability Battery, and a specially developed self-report inventory that produced eight creative content scores and a total score. Correlational analysis determined that Semantic Fluency, Ideational Fluency, Originality and Remote Consequences were substantially correlated with most creative behaviors and were uncorrelated with grade point average. A factor analysis of criteria revealed two underlying patterns of creativity, suggesting that proficiency in one creative domain is predictive of proficiency in several others. The study of creativity has traditionally been propelled by aesthetic, scientific, and economic concerns. While revolutionary breakthroughs in science, technology, and design often command our attention and respect, it is the small, evolutionary innovations that typically have the greatest immediate economic impact (Haustein, 1981). From any vantage point there has always been an interest in the prediction and measurement of creative behavior and aptitude. The available measurement approaches for creativity include cognitive abilities, personality traits, self-reports of creative behavior and peer and teacher ratings of creative works (Hocevar, 1981). The purpose of this study is to assess the validity of an underresearched set of cognitive measures: four subtests of the Comprehensive Ability Battery (CAB-5; Hakstian & Cattell, 1976) and the Consequences test (Christensen, Merrifield, & Guilford, 1958). Our validity strategy was correlational; criteria were eight self-report indices of creative endeavor. The following paragraphs elaborate the underlying theory from which these measures originated and some unresolved issues. Perhaps the largest single breakthrough in the cognitive approach to understanding creativity came from Guilford's (1967) 120-factor structure of intellect model. While commonly used intelligence tests measure convergent forms of thinking, creativity involves divergent thought processes which, according to Guilford, account for 30 of the 120 factors of intelligence. Working through a factor analytic paradigm, Guilford was able to identify over 100 out of 120 factors. Guilford's structure of intellect may be criticized for having fractured intellectual functioning into too narrowly defined units relative to what human faculties are actually engaged in ordinary intellectual endeavors. Nonetheless, the theory did provide a provocative explanation for the nature of creative thought and some interesting measurements of same. Measurements of creative thought (divergent production) involve word fluency, category formation and reformation, ideational fluency original uses for common objects (opposite of functional fixedness). One test, Consequences (Christensen et al., 1958), is of particular concern to this research project and involves a certain amount of social awareness on the part of the examinee in conjunction with divergent production. In a typical test item, examinees are presented with a hypothetical situation, “What would be the consequences if people no longer needed to sleep?” along with a few common responses. Examinees are then given five minutes to write as many consequences of the hypothetical situation as they can think of. Responses are scored by, first, eliminating responses that are redundant with the samples or other responses or that are completely irrelevant Remaining responses are then categorized as obvious and remote. The numbers of obvious and remote responses are counted to produce two scores. Consequences continues to be listed as a research instrument by its publisher. Norms in the manual (Guilford & Guilford, 1980) are only available for 331 engineers who took two forms of the test, 665 ninth-graders, 80 twelfth graders, and a college sample of 87 cases. According to Guilford & Guilford, the consequences scores are closely related to other divergent production measures, remote more so than obvious. The CAB-5 developed by Hakstian & Cattell (1976, 1978) who also worked in the factor analytic mode, consists of 20 subscales that appear to capture the essentials of convergent and divergent thinking in a timed battery of manageable size. The four divergent thinking scales — semantic fluency, ideational fluency, word fluency, and originality — are of particular interest to this project While the usual types of validity and norm-building research have been done with the convergent scales (Hakstian & Cattell, 1976; Hakstian & Woolsey, 1985) little external validation work is available for the divergent scales. Hakstian & Woolsey (1985) found that semantic fluency and ideational fluency were significantly correlated with grades in an introductory psychology course (r = .33 and .30 respectively). The rationale for why divergent production would be related to grades in that course was vague. Norms for the divergent scales are currently available for 216 college and 1098 high school students. While the validation question is framed around a limited set of scales in this research project, it does represent an issue of more general concern. According to Storfer (1990), several researchers have questioned whether measures of divergent production have any external validity with actual creative works. He cited a study where teachers' ratings of their students' creativity were based on logical or convergent measures but had no relationship to divergent measures. In his review of creativity measures, Hocevar (1978) noted a generally low level of interrelationship among personality, cognitive, self-report, and rating measures of creativity; from this trend he opined that self-report measures of creative behavior were perhaps the most defensible indices of creativity. On the other hand, a study of approximately 500 college students showed that those that had won science prizes, or who published or exhibited their work scored higher than others on ideational fluency (Wallach & Wing, 1969). While the latter finding is reassuring, we are not convinced that prizes, publication, or exhibition represent the full range of creative behavior to be found at the college level. Prizes require a propensity to compete among the participants, and a proclivity toward subjectivity, among the judges. As academic researcher know, earth-shattering ideas are not quickly snapped up by scientific journals, and much of what is published is indicative of the evolutionary progress mentioned at the outset of this article. There is reason to assume that there is much valuable creative effort taking place that does not reach wide audiences or that is otherwise shoved into drawers. From a statistical point of view, it is preferable to conduct a criterion related validity study that encompasses a wide (if not complete) range of criterion values and to avoid an extreme groups methodology, such as a comparison of prizewinners and others. The latter has the impact of exaggerating the predictor-criterion effect size. Altogether, Hocevar (1981) identified 15 studies showing a positive relationship between divergent production and other measures of creativity, and 15 other studies that showed no such relationship. With the foregoing theoretical and methological points in mind, the following hypotheses were examined: 1. Consequences and CAB-5 divergent scale scores would be significantly related to several types of creative behavior. 2. Consequences and CAB-5 divergent scale scores would be significantly related to each other. 3. There would be a substantial interrelationship among the various types of creative behavior. Significant findings would dispel the notion among critics of divergent thinking theory (cf. Stolper, 1990) that the prediction of creativity is situationally specific. 4. Divergent measures and indices of creative behavior would not be related to college students' grade point average (GPA). While we recognize that no point is proven by failing to reject the null hypothesis, a null relationship with GPA is expected from the general theory, on the basis of findings concerning teachers' rates cited in Stolper (1990) and our own assumptions that much creative work goes unnoticed in favor of traditional academic demand. An expected null relationship thus adds an element of convergent-discriminant validity analysis to the research plan.     

On measuring fuzziness: a comment on "A fuzzy set approach to modifiers and vagueness in natural language"

Hersh and Caramazza's application of fuzzy set theory to vagueness in natural language is criticized for including in their measures of fuzziness response variability due to experimental and statistical procedures.     

Interaural and monaural clicks and clocks: tempo difference versus attention switching

We describe a quantitative model capable of explaining the results of all reported investigations of the counting of interaural and monaural click sequencies. The model is developed by means of three convergent operations: (a) reanalyzing absolute-estimation data of apparent repetition rates of interaural and monaural sequences, (b) deriving interaural and monaural counting times from numerosity-judgement data, and (c) analyzing the time that observers needed to respond to the end of interaural and monaural sequences. The combined evidence demonstrates that the perceived onset asynchrony (POA) between interaural events is 24 msec longer than that between monaural events. The model has three components: (a) a "stimulus clock," which represents the stimulus onset synchrony (SOA) between events; (b) a "memory clock," which represents the POA between events, and (c) a "counting clock," which represents the counter increment time. The transfer functions between the three clocks are deduced from empirical data. Other proposals to explain interaural click counting results (attention switching, streaming by locus, counterincrement deficit) are discussed and rejected.     

Real and subjective contour Poggendorff illusions: no differences based on eye color

Measures of illusion magnitude for a real contour and two subjective contour Poggendorff figures were obtained from a large number of dark-eyed and light-eyed undergraduates. Illusion magnitude varied as a function of figure type. However, eye color neither had a significant overall effect on illusion magnitude, nor did it interact with the figure-type variable. These data indicate that the presence of intersecting lines is not the basis of the iris-pigmentation effect reported by Coren and Porac.     

Optimal sample sizes for the design of reliability studies: Power consideration

Intraclass correlation coefficients are used extensively to measure the reliability or degree of resemblance among group members in multilevel research. This study concerns the problem of the necessary sample size to ensure adequate statistical power for hypothesis tests concerning the intraclass correlation coefficient in the one-way random-effects model. In view of the incomplete and problematic numerical results in the literature, the approximate sample size formula constructed from Fisher’s transformation is reevaluated and compared with an exact approach across a wide range of model configurations. These comprehensive examinations showed that the Fisher transformation method is appropriate only under limited circumstances, and therefore it is not recommended as a general method in practice. For advance design planning of reliability studies, the exact sample size procedures are fully described and illustrated for various allocation and cost schemes. Corresponding computer programs are also developed to implement the suggested algorithms.     

Primitive representation and misrepresentation

This paper develops a statistical approach to the problem of primitive representation. Representation of the kind commonly attributed to litmus paper, fuel gauges and tree rings occurs when, so to speak, there is a sufficiently good correlation between two variables. The fundamental distinction between misrepresentation and non-representation is explained in terms of the notion of an informationally useful correlation. The paper further argues that the statistical approach satisfactorily resolves well known puzzles such as Fodor's disjunction problem.     

Interaural time vs. interaural intensity in a lateralization paradigm

In a two-interval lateralization procedure, observers judged whether a stimulus presented with an interaural intensive difference was right or left in lateral space of the same stimulus presented with only an interaural temporal difference. The stimuli were pure tones of 500 and 1,000 Hz and 1,000-Hz low-pass noise. All stimuli were presented at both 65 and 55 dB SPL. For each of several values of interaural time (ranging from 0 to 1,000 microsec across all stimuli), a function was determined which related proportion of “right” relative position judgments to the value of the interaural intensive difference. The intercepts of these functions indicated that a progressively smaller amount of interaural intensive difference was required for the two stimuli to occupy a similar lateral location as the interaural temporal difference was increased. The slopes of the function suggested that the images associated with larger values of the interaural temporal differences are less distinct and blend together more than the images associated with small values of the temporal difference. Thus, the procedure provided a means for comparing the lateral location of images produced by interaural differences of time and intensity.     

Lateral preferences and writing hand posture in left-handers: A reply to Levy

In reply to the commentary from J. Levy about a recent article of ours (A. Searleman, C. Porac, & S. Coren, 1984, Brain and Cognition, 3, 86–93), we find that she has shifted the level of analysis from between-sex comparisons (as demanded by our original hypothesis) to within-sex comparisons. Since she is addressing a different set of questions, we therefore find no compelling reasons to alter any of our conclusions or the confidence that we have in these conclusions.     

Spatial stimulus cue information supplying auditory saltation

Auditory saltation is a misperception of the spatial location of repetitive, transient stimuli. It arises when clicks at one location are followed in perfect temporal cadence by identical clicks at a second location. This report describes two psychophysical experiments designed to examine the sensitivity of auditory saltation to different stimulus cues for auditory spatial perception. Experiment 1 was a dichotic study in which six different six-click train stimuli were used to generate the saltation effect. Clicks lateralised by using interaural time differences and clicks lateralised by using interaural level differences produced equivalent saltation effects, confirming an earlier finding. Switching the stimulus cue from an interaural time difference to an interaural level difference (or the reverse) in mid train was inconsequential to the saltation illusion. Experiment 2 was a free-field study in which subjects rated the illusory motion generated by clicks emitted from two sound sources symmetrically disposed around the interaural axis, ie on the same cone of confusion in the auditory hemifield opposite one ear. Stimuli in such positions produce spatial location judgments that are based more heavily on monaural spectral information than on binaural computations. The free-field stimuli produced robust saltation. The data from both experiments are consistent with the view that auditory saltation can emerge from spatial processing, irrespective of the stimulus cue information used to determine click laterality or location.     

A necessary and sufficient formula for matric factoring

For the purpose of extracting factors from matrices, it is proved that a certain formula is both necessary and sufficient. In factor analysis, the formula may be applied either to the correlation matrix, or directly to the score matrix (assuming the communality problem is solved). As many factors as desired can be extracted in one operation. Having such a compact formulation is useful for teaching as well as computing purposes, since it includes all techniques of factor extraction as special cases.On leave from the Israel Institute for Applied Social Research. This research was facilitated in part by a grant from the Lucius N. Littauer Foundation to the American Committee for Social Research in Israel, Inc.     

The role of binaural and fundamental frequency difference cues in the identification of concurrently presented vowels

The relative importance of voice pitch and interaural difference cues in facilitating the recognition of both of two concurrently presented synthetic vowels was measured. The interaural difference cues used were an interaural time difference (400 μsec ITD), two magnitudes of interaural level difference (15 dB and infinite ILD), and a combination of ITD and ILD (400 μsec plus 15 dB). The results are analysed separately for those cases where both vowels are identical and those where they are different. When the two vowels are different, a voice pitch difference of one semitone is found to improve the percentage of correct reports of both vowels by 35.8% on average. However, the use of interaural difference cues results in an improvement of 11.5% on average when there is a voice pitch difference of one semitone, but only a non-significant 0.1% when there is no voice pitch difference. When the two vowels are identical, imposition of either a voice pitch difference or binaural difference reduces performance, in a subtractive manner. It is argued that the smaller size of the interaural difference effect is not due to a “ceiling effect” but is characteristic of the relative importance of the two kinds of cues in this type of experiment. The possibility that the improvement due to interaural difference cues may in fact be due to monaural processing is discussed. A control experiment is reported for the ITD condition, which suggests binaural processing does occur for this condition. However, it is not certain whether the improvement in the ILD condition is due to binaural processing or use of the improvement in signal-to-noise ratio for a single vowel at each ear.     

Writing hand position, birth stress, and familial factors

The incidence of birth stress was found to be slightly lower in individuals writing with an inverted hand position than in those writing with a normal position, a result in the opposite direction to that reported by Searleman, Porac, and Coren (1982). A familial study suggested that an inverted writing hand position was primarily related to maternal (but not paternal) writing hand position, suggesting a modeling or imitative origin, rather than a genetic basis for writing position.     

An investigation of the interaural time difference threshold for speech

The interaural time difference threshold for speech has been reported to be approximately 35 μsec (Cherry & Sayers, 1956), a value substantially larger than the 6 ~sec reported for broadband noise signals by other experimenters (e.g., Tobias & Zerlin, 1959). In the two studies just mentioned, however, different subjects and psychoacoustical methods were employed; thus, it is unclear whether larger interaural time differences are needed to lateralize speech signals. The purpose of this experiment, therefore, was to compare lateralization performance for speech and nonspeech stimuli. Interaural time difference thresholds were obtained for speech, speech spectrum noise, speech multiplied noise, and 200-, 500-, and 1,000-Hz sinusoids for the same subjects using a 2 IFC experimental paradigm. Under these conditions, speech and speech-multiplied noise yielded essentially the same interaural time difference thresholds.