Individual half-judgment brightness functions

Nine Ss made half-judgments of each of nine brightness standards. Individual half-judgment brightness functions were constructed, one for each of the two threshold forms of the power law. The ω-Law (translation on the psychological axis) provided a better fit to the half-judgment data than did the ?-Law (translation on the intensity axis). A test of scale consistency for the fractionation method was confounded with the power law hypothesis, but the data are interpreted as providing fair support for the method independent of the form of the power law. The effect of Standard on exponent estimates was significant for both forms of the law, and the effect of Standard on threshold estimates was significant for the ?-Law but not for the ω-Law. Both forms of the law contain a so-called threshold parameter, but the interpretation of this parameter as a threshold was rejected for the ?-Law and accepted for the ω-Law.     

An experimental comparison of stimulus and response translated power functions for brightness

A threshold parameter has been introduced into the power law in two different ways, one involving, translation on the stimulus axis (the Ф-Law) and the second involving translation on the response axis (the Ψ-Law). In this study the two laws were compared using the data from 6 Ss making magnitude estimation judgments of brightness. Although the prevalent view appears to favor the Ф -Lau, the data of this study clearly dictate a choice of the Ψ-Law over the $-Law for brightness.     

Monotonicity,convexity, and other qualitative psychophysical laws

General methods are described for directly testing qualitative psychophysical laws, such as monotonicity and convexity. These methods consist of estimating lower and higher orders of derivatives and procedures for verifying qualitative laws involving these derivatives. The quantitative power law hypothesis is compared for goodness of fit with the qualitative hypothesis that the psychophysical function is monotone and convex, in application to bisection brightness data. Other topics include discussion of a possible topological formulation of the distinction between qualitative and quantitative laws; the search for psychophysical invariants; and the failure of qualitative laws such as convexity to conform to Luce's invariance-theoretic principles of theory construction.     

Variations in the relationship between radius of curvature and velocity as a function of joint motion

A power law describes the relationship between the geometric properties of a trajectory (radius of curvature) and movement kinematics (tangential velocity) in curved drawing movements. Although the power law is a general law of motion, there are conditions under which it degrades. In particular, the power law may be less explanatory of movements around certain joints. The present study considered how varying motion around different joints influenced the fit of the power law. Motions associated with finger and wrist, or elicited by an isometric force production task, were compared. The power law was most explanatory of finger motion and isometric production and least explanatory of wrist motion. The fit of the power law for finger and wrist motion suggested separate laws for each joint system. Since the fit of the power law was better for finger than for wrist motion, there is some suggestion that the power law better explains motion around fewer or simpler joint systems.     

On the psychophysical law and estimation procedures in psychophysical scaling

A general formulation of the power law is presented which has two special features: (1) negative exponents are admissible; and (2) the log law is a special limiting case. Estimation procedures, which provide joint estimates of the exponent and the absolute threshold, are derived for the direct ratio scaling methods. A solution is provided for theaveraging problem for ratio production and bisection scaling, two methods generating observations on the physical scale, and Monte Carlo methods are used to evaluate the resulting estimators.     

Magnitude scales for electrocutaneous stimulation

The application of Stevens’s power law to the sensation resulting from electrocutaneous stimulation is reviewed. Its use for data from individual observers as well as pooled data from several observers is discussed. Magnitude estimates were obtained from 33 observers of the sensation resulting from electrocutaneous stimulation over the median nerve. Seven mathematical functions were applied to the data and tested for goodness of fit. The power function with or without threshold correction factor did not emerge as better than alternative functions. Difficulties in using the power function in studies of individual differences are reviewed. It is concluded that there is no adequate reason at present to discard the linear function in favor of more complex functions in psychophysical scaling of sensation induced by electric shock.     

A power-law model of psychological memory strength in short- and long-term recognition

A classic law of cognition is that forgetting curves are closely approximated by power functions. This law describes relations between different empirical dependent variables and the retention interval, and the precise form of the functional relation depends on the scale used to measure each variable. In the research reported here, we conducted a recognition task involving both short- and long-term probes. We discovered that formal memory-strength parameters from an exemplar-recognition model closely followed a power function of the lag between studied items and a test probe. The model accounted for rich sets of response time (RT) data at both individual-subject and individual-lag levels. Because memory strengths were derived from model fits to choices and RTs from individual trials, the psychological power law was independent of the scale used to summarize the forgetting functions. Alternative models that assumed different functional relations or posited a separate fixed-strength working memory store fared considerably worse than the power-law model did in predicting the data.     

Loudness bisection and masking in the rat (Rattus norvegicus).

The bisection method of animal psychophysical scaling was examined as a measurement procedure. The critical assumptions of bisection scaling, as described by Pfanzagl (1968), were tested to determine if a valid equal-interval scale could be derived. A valid scale was derived in which loudness for the rat (Rattus norvegicus; n = 13) was a power function of sound pressure for 4-kHz tones. Masking noise reduced the discriminability of tonal stimuli but did not affect the bisection point. This result is consistent with an interval scale representation of loudness and demonstrates scale meaningfulness. Loudness bisection data that have been reported in the literature for 3 species (humans, rats, and pigeons) are in substantial agreement with our results.     

The power law repealed: The case for an exponential law of practice

The power function is treated as the law relating response time to practice trials. However, the evidence for a power law is flawed, because it is based on averaged data. We report a survey that assessed the form of the practice function for individual learners and learning conditions in paradigms that have shaped theories of skill acquisition. We fit power and exponential functions to 40 sets of data representing 7,910 learning series from 475 subjects in 24 experiments. The exponential function fit better than the power function in all the unaveraged data sets. Averaging produced a bias in favor of the power function. A new practice function based on the exponential, the APEX function, fit better than a power function with an extra, preexperimental practice parameter. Clearly, the best candidate for the law of practice is the exponential or APEX function, not the generally accepted power function. The theoretical implications are discussed.     

Bisection of loudness

In a loudness bisection task, subjects varied one sound to lie halfway between two given sounds in terms of loudness. The two given sounds were varied from 30 to 90 dB in a 4 by 9 factorial design. Functional measurement methods based on monotone analysis provided good support for the bisection model, and yielded a loudness scale with an exponent of about .3, except for a falloff at lower intensities. Two other tasks, judging average loudness and difference in loudness of the two given sounds, yielded mixed results. In Experiment 2, in particular, the differencing judgments were not additive, even under monotone transformation. These analyses also indicated that previous applications of monotone analysis have typically lacked adequate power to allow any conclusion about the operative model. Overall, the present bisection scale agrees with Garner’s lambda scale, and the present theoretical approach agrees with that of Garner in its emphasis on algebraic models as a foundation for psychological measurement.     

Crossover by Line Length and Spatial Location

It is well known that line length has a systematic influence on line bisection error in neglect. Most patients with neglect misbisect long lines on the same side of true center as their brain lesion but then cross over on short lines, misbisecting them on the opposite side (i.e., crossover by line length). What is less recognized is that the spatial location of lines relative to the viewer can similarly induce a crossover effect when one considers line bisection error scores that have been averaged across individual line lengths. Patients with right hemisphere injury and neglect classically make averaged line bisection errors that fall right of true center on lines located either at midline or to the left of the viewer; however, we observed that the averaged line bisection error can fall left of true center when lines are located to the right of the viewer (i.e., crossover by spatial location). We hypothesized that crossover by both line length and spatial location stem from systematic errors in magnitude estimation, i.e., perceived line length. We tested predictions based on this hypothesis by examining how the crossover effect by line length is altered by the spatial location of lines along a horizontal axis relative to the viewer. Participants included patients with unilateral lesions of the right and left cerebral hemispheres and age-appropriate normal subjects. All groups demonstrated a crossover effect by line length at the midline location but the effect was altered by placing lines to the right and left of the viewer. In particular, patients with right hemisphere injury and neglect crossed-over across a broader range of line lengths when the lines were located to the right of the viewer rather than at either midline or left of the viewer. It is proposed that mental representations of stimulus magnitude are altered in neglect, in addition to mental representations of space, and that traditional accounts of neglect can be enhanced by including the psychophysical concept of magnitude estimation.     

Career adapt-abilities scale — Icelandic form: Psychometric properties and construct validity

This study examined the psychometric characteristics and construct validity of the Icelandic form of the Career Adapt-Abilities Scale (CAAS-Iceland). The CAAS consists of four scales that measure concern, control, curiosity, and confidence as psychosocial resources for managing occupational transitions, developmental tasks, and work traumas. The 24-item measure was translated from English and administered to 1566 Icelandic students aged 14–30. Internal consistency estimates of reliability for the subscale and total scores ranged from .77 to .92. The construct validity of the measure was tested using confirmatory methods. The results indicated that the four-factor hierarchical model of career adaptability shows an acceptable fit in Iceland. The mean scores on the scales are high compared to the other countries, indicating that there may be problems with the translation of the response scale. The results indicate that the CAAS-Icelandic Form is reliable and valid and can be used with minor modifications in career counseling and research in Iceland.     

Human Psychophysical Functions,an Update: Methods for Identifying their form; Estimating their Parameters; and Evaluating the Effects of Important Predictors

Stevens’ power law for the judgments of sensation has a long history in psychology and is used in many psychophysical investigations of the effects of predictors such as group or condition. Stevens’ formulation \(\varPsi = {aP}^{n}\), where \(\varPsi \) is the psychological judgment, P is the physical intensity, and \(n\) is the power law exponent, is usually tested by plotting log \((\varPsi )\) against log (P). In some, but by no means all, studies, effects on the scale parameter, \(a\), are also investigated. This two-parameter model is simple but known to be flawed, for at least some modalities. Specifically, three-parameter functions that include a threshold parameter produce a better fit for many data sets. In addition, direct non-linear computation of power laws often fit better than regressions of log-transformed variables. However, such potentially flawed methods continue to be used because of assumptions that the approximations are “close enough” as to not to make any difference to the conclusions drawn (or possibly through ignorance the errors in these assumptions). We investigate two modalities in detail: duration and roughness. We show that a three-parameter power law is the best fitting of several plausible models. Comparison between this model and the prevalent two parameter version of Stevens’ power law shows significant differences for the parameter estimates with at least medium effect sizes for duration.     

Individual differences in magnitude estimation of loudness

Twenty-two male and female subjects, aged 15 to 31 years, participated in two sessions, 11 weeks apart, of magnitude estimations of loudness. Stable individual differences in the exponent of the psychophysical power law, ψ=k?ⁿ, were shown. The correlation between subjects’ exponents of the first and second sessions was +.59. The generality of these findings and the origin of the individual differences were discussed.     

"Time flies in the presence of angry faces"… depending on the temporal task used!

A number of studies have reported that the perception of an arousing emotional stimulus, such as an angry face, results in temporal overestimations which are probably due to the speeding up of a clock-like system. The aim of the present study was to examine whether this emotional effect can be generalized to all temporal tasks irrespective of the underlying cognitive processes involved in each task. Five different temporal tasks involving the presentation of neutral and angry faces were therefore tested: bisection, generalization, verbal estimation, production and reproduction. Our results showed an overestimation of time for the angry compared to the neutral faces in the temporal bisection, verbal estimation and production tasks but not in the temporal generalization and reproduction tasks. Moreover, the results obtained in the temporal verbal estimation and production tasks suggest that this temporal overestimation of the angry faces was associated with relatively more accurate estimates. The involvement of both arousal and attention mechanisms in the effect of emotional facial expressions on time perception is discussed in the light of the differences in the impact of the same emotional stimulus as a function of the temporal task considered.     

Representational neglect for words as revealed by bisection tasks

In the present study, we showed that a representational disorder for words can dissociate from both representational neglect for objects and neglect dyslexia. This study involved 14 brain-damaged patients with left unilateral spatial neglect and a group of normal subjects. Patients were divided into four groups based on presence of left neglect dyslexia and representational neglect for non-verbal material, as evaluated by the Clock Drawing test. The patients were presented with bisection tasks for words and lines. The word bisection tasks (with words of five and seven letters) comprised the following: (1) representational bisection: the experimenter pronounced a word and then asked the patient to name the letter in the middle position; (2) visual bisection: same as (1) with stimuli presented visually; and (3) motor bisection: the patient was asked to cross out the letter in the middle position. The standard line bisection task was presented using lines of different length. Consistent with the literature, long lines were bisected to the right and short lines, rendered comparable in length to the words of the word bisection test, deviated to the left (crossover effect). Both patients and controls showed the same leftward bias on words in the visual and motor bisection conditions. A significant difference emerged between the groups only in the case of the representational bisection task, whereas the group exhibiting neglect dyslexia associated with representational neglect for objects showed a significant rightward bias, while the other three patient groups and the controls showed a leftward bisection bias. Neither the presence of neglect alone nor the presence of visual neglect dyslexia was sufficient to produce a specific disorder in mental imagery. These results demonstrate a specific representational neglect for words independent of both representational neglect and neglect dyslexia.     

Pure timing in temporal differentiation

Temporal control appears to depend on whether the critical durations are those of stimuli or those of responses. Stimulus timing (temporal discrimination) supports Weber's law, whereas response timing (temporal differentiation) indicates decreasing relative sensitivity with longer time intervals. The two types of procedure also yield different conclusions in scaling experiments designed to study the functional midpoint of two or more durations (temporal bisection procedures). In addition, the fractional-exponent power relation between emitted and required duration usually found with animals in differentiation experiments conflicts with deductions from formal analyses. The experiment reported here derived from considering differentiation arrangements as schedules of reinforcement. When analyzed from this perspective, the procedures are tandem schedules involving a required pause followed by a response, and it is the pause alone that involves temporal control. A choice procedure separated timing from responding, and enabled observations of pause timing in isolation. Pure temporal control in differentiation consisted of linear overestimation of the standard duration, and Weber's law described sensitivity. These results indicate that the two problems, the fractional-exponent power relations and the apparently different nature of sensitivity in differentiation and discrimination, disappear when temporal control is observed alone in differentiation.     

Lateral biases and reading direction: a dissociation between aesthetic preference and line bisection

Perceptual asymmetries for tasks involving aesthetic preference or line bisection can be affected by asymmetrical neurological mechanisms or left/right reading habits. This study investigated the relative contribution of these mechanisms in 100 readers of Japanese and English. Participants made aesthetic judgments between pairs of mirror-reversed pictures showing: (a) static objects, (b) moving objects and (c) landscapes. A line bisection task was also administered. There was a strong effect of reading direction for static and mobile objects whereby Japanese readers preferred objects with a right-to-left directionality (and vice versa for English readers). In contrast, similar patterns were observed for the Japanese and English readers for the landscape and line bisection tasks. The results show that reading habits affect aesthetic judgments for static and moving object tasks, but not the landscape and line bisection tasks. The difference between the tasks may be related to the horizontal/vertical geometry of the stimuli, which makes the landscape and line bisection tasks more prone to universal effects related to cerebral dominance.