Scale values derived from the method of choices

In many a psychometric problem, particularly in practical problems, the only data conveniently obtainable are the first choices given to certain stimuli among a list of stimuli that are available for selection. By assuming that such choices represent real comparative judgments, we may apply Thurstone's law of comparative judgments, extract experimental proportions from the numbers of first choices, and compute psychological scale values for the stimuli. Two procedures are proposed for estimating such proportions and examples of their applications are given. A procedure for allocating a meaningful zero point on the scale by the use of absolute judgments is explained and demonstrated. Suggestions are added for overcoming certain weaknesses and limitations of the method of choices.     

On a metric,unidimensional unfolding model for attitudinal and developmental data

If stimulus responses are linearly related to squared distances between stimulus scale values and person scores along a latent continuum, (a) the stimulus × stimulus correlation matrix will display a simplex-like pattern, (b) the signs of first-order partial correlations can be specified in an empirically testable manner, and (c) the variables will have a semicircular, two-factor structure. Along the semicircle, variables will be ordered by their positions on the latent dimension. The above results suggest procedures for examining the appropriateness of the model and procedures for ordering the stimuli. Applications to developmental and attitudinal data are discussed. This research was supported by a grant from the Graduate School of the University of Minnesota to the author and by a grant from the U. S. Public Health Service (Grant No. 1-R01-MH27861-01) to Dr. James Rest, Principal Investigator.     

A proposed method for absolute ratio scaling

A method of ratio scaling is described for treating comparative judgments of paired stimuli. A method of comparative judgment developed by Metfessel is employed. Formulas for scale values and the solution of a sample problem are provided. The method is designed to provide internal-consistency checks on the scale values. Experimental interpretations of equal-unit and ratio properties of measurement scales are inherent in the procedure.The author wishes to express his appreciation to Professor J. P. Guilford for his helpful comments and encouragement in connection with the preparation of this article.     

The law of comparative judgment in the successive intervals and graphic rating scale methods

The law of comparative judgment is applied to the successive intervals and graphic rating scale methods. A procedure for estimating the modal discriminal process and discriminal dispersion of the stimuli, as well as the value of the boundaries of the intervals on the continuum, is given. From the estimated values it is possible to determine the theoretical proportions and to compare them with the actual experimental proportions. The agreement between these values is an indication of the adequacy of the assumptions made.     

An internal consistency check for scale values determined by the method of successive intervals

The method of successive intervals is a psychological scaling procedure in which stimuli are classified into successive intervals according to the degree of some defined attribute which they are judged to possess. A psychological continuum is defined and the scale values are then taken as the medians of the distributions of judgments on the psychological continuum. It is assumed that the distributions of judgments for each stimulus are normal on the psychological continuum as defined.An internal consistency check indicates that the cumulative distributions of empirical judgments for the various stimuli can be reproduced by means of a limited number of parameters with an average error that compares favorably with that usually reported for paired comparison data. Furthermore, the scale values obtained by successive interval scaling, for the data reported, are shown to be linearly related to those obtained by the method of paired comparisons.This paper was written while the first author was a post-doctoral Research Training Fellow of the Social Science Research Council studying at the University of Chicago. It reports research undertaken in cooperation with the Quartermaster Food and Container Institute for the Armed Forces. The views or conclusions contained in this report are those of the authors. They are not to be construed as necessarily reflecting the views or endorsement of the Department of Defense.     

Two operations for "ratios" and "differences" of distances on the mental map

Ss judged "ratios of distances" and "differences of distances" between pairs of U.S. cities. Results fit the theory that Ss used two comparison processes as instructed. A ratio scale of distances between cities was constructed from the 2 rank orders. From this scale, an interval scale of the city locations on an east-west continuum was derived. This scale agrees with the subtractive model fit to "ratios" and "differences" of easterliness and westerliness, and it also agrees with multidimensional scaling of judged distances between cities. These findings are consistent with the theory that Ss use subtraction when instructed to judge either "ratios" or "differences," but that they can use both ratio and difference operations when the stimuli (in this case, distances) constitute a ratio scale on the subjective continuum.     

Stimulus-response with reciprocal kernels: The rise and fall of sensation

The paper presents a theory for constructing response scales based on the reciprocal property of paired comparisons of stimuli from the same sensory continuum. Reciprocal paired comparisons define the pair estimator function K(s, t), the kernel of a Fredholm integral equation of the second kind. The solution of this equation yields a response scale of the form s^αe^−βs, where s is the stimulus scale. The response scale provides a basis for a theory to describe how images and sensation patterns are formed from stimuli.     

Visual discrimination, categorical identification, and categorical rating in brief displays of curved lines: implications for discrete encoding processes

Visual discrimination, categorical identification, and categorical rating measurements were made on sets of curved-line stimuli drawn from a theoretically uniform continuum with curvature parameter s. In Experiment 1, discriminability of pairs of curved lines separated by a constant distance on the s scale was measured at successive points along the scale. Curved lines were presented four at a time in a 100-msec display, which was followed by a random-dot mask. Discrimination performance was found to vary nonsmoothly with s. In Experiment 2, a categorical identification task was performed in which subjects labeled the curved-line stimuli of Experiment 1 straight, just curved, and more than just curved. From these data, a theoretical discrimination performance was computed that was closely congruent to the discrimination performance of Experiment 1. In Experiment 3, three different categorical rating scales with two, three, and four intervals were tested and each was shown to be less effective than the categorical identification scale for predicting discrimination performance. Mean ratings were, however, highly linear with s, suggesting that the curved-line continuum was psychometrically uniform. Experiment 4 provided further evidence for the uniformity of the curved-line continuum by measuring conventional acuity for curvature. Two rather than four curved lines were presented in each display; duration was increased to 2 sec; and the poststimulus mask was omitted. Acuity was found to vary linearly with s. It was concluded that under conditions in which attention is distributed over a number of elements in the field and in which viewing and effective visual processing time are restricted, performance in discriminating curved-line stimuli may be determined by relatively coarse, discrete visual processes.     

Comparative judgments of distal size: A chronometric analysis

Observers were required to make comparative judgments of the distal sizes of squares at various perceived distances in a pictorial array. It was predicted that observers would normalize distance prior to judgment. Chronometric analyses indicated that the time to make “same” judgments increased systematically with the relative distance of the two stimuli. The time required to make “different” judgments depended on the nature of the difference. When the stimuli differed in proximal size, distal size, and distance, response time increased with distance ratio. However, when the stimuli differed in distal size and distance but not proximal size, response time decreased with distance ratio. In addition, when the stimuli differed in both distal and proximal size but not distance, RT decreased with size ratio. These results are consistent with a class of models that incorporate distance normalization into the comparative size-judging process. These and alternative models are discussed.     

The additive constant problem in multidimensional scaling

The problem of choosing the correct additive constant to convert relative interstimulus distances to absolute interstimulus distances in multidimensional scaling is investigated. An artificial numerical example is constructed, and various trial values of the constant are inserted to demonstrate the effect on the multidimensional map of making a variety of incorrect choices. Finally, a general solution to the problem, suggested by Dr. Ledyard R Tucker, is presented; each of the computational steps in this solution is set down for easy reference.This study was supported in part by Office of Naval Research Contract N6onr-270-20 and by National Science Foundation Grant G-642 to Princeton University.     

Reduction of rating scale data by means of signal detection theory

A d’-index computed from ratings of psychological stimuli does not necessarily represent the unbiased psychological distance between these stimuli. Such ratings may not be considered as discrimination tasks in the signal detection sense, because the rater has to discriminate between the psychological impact of the stimuli on some internal continuum rather than between the stimuli as such. The rater therefore can use stimulus-specific criteria for his decisions. As a result, the d’-index computed from the rating data will be biased.     

Binocular fixation in the newborn baby.

Three experiments are reported in which the newborn baby's ability to fixate binocularly was investigated, using the corneal reflection technique for measuring eye fixation position. Two criteria for consistent binocular fixation were assessed. These are (1) the two eyes will be optically more divergent when fixating more distant targets, and (2) each eye will be scored as being on-target when corrections for the expected deviations of the pupil center from the fixated stimulus are introduced.In the first experiment vertical arrays of lights were separately shown at distances of 10 and 20 in. from the subjects' eyes (with the retinal image size and luminance of the stimuli held constant). The 12 newborns who gave results at both viewing distances reliably converged to both stimuli, the optical divergence of the pupil centers of the eyes increasing with presentation of the more distant stimulus. In Expt 2 similar stimuli at 5 and 10 in. from the eyes were shown. It was again the case that the subjects reliably converged to the stimulus at 10 in. This was no so for the stimulus at 5 in., and many subjects fixated this stimulus with monocular vision. The failure to converge is probably due to an inability to accommodate to this near distance. In Expt 3 different stimuli (a vertical strip of light, an outline triangle and square, and an array of squares) were presented a constant distance (10 ± 1 in.) from the eyes. The majority of the 15 subjects binocularly fixated all three stimuli: for those subjects who failed to converge consistently to these stimuli the observed alternatives to binocular fixation were monocular fixation, divergent strabismus, and a third category of response that is most probably an indication of inattention to the stimulus. It can be concluded that the newborn baby possesses the ability to fixate binocularly an appropriately presented stimulus, and has the basic requirements for binocular vision.     

Assessing effects of viewing distance on normal Chinese reading: Some methodological and theoretical implications

Viewing distance determines a range of factors affecting reading performance. Previous studies of Chinese-character reading have shown considerable disagreement and inconsistency in their choice of viewing distances, however, with obvious implications for research in this area. The present study aimed to resolve this issue by determining the optimal viewing distance for studies of normal Chinese reading. Stimuli were pages of text that were composed of a standard Chinese typeface (Song) that was presented in a standard size (10.5 pt). Forty reading distances were used, ranging from 2.5 to 100.0 cm. Distances within the range of 7.5–55.0 cm produced faster reading rates than did the distances at either end of the continuum, and a regression model showed that 35 cm was the optimal viewing distance. These findings indicate an optimal range of retinal image sizes between 2.0° and 0.3° per character. The implications of these findings for understanding the processes that are involved in Chinese reading and for the appropriate presentation of Chinese stimuli in experiments are discussed.     

An ecological analysis of binocular vision

Summary Underlying the classic binocularity problems of singleness and three-dimensionality is a theory that the stimulus for binocular vision constitutes two two-dimensional images and metric differences between parts of those images. This characterization of the stimulus is criticized here and in its stead an ecologically-based characterization is presented wherein a binocular transformational invariant is shown to specify absolute (body-scaled) size, shape, and distance. The transformation is characterized as a rotation and its specificity to distance assumes a constant interocular distance and either homogeneously textured or extended surfaces. Four experiments demonstrate perceivers' abilities to detect this information and report (verbally or by reaching) the absolute distances of surfaces in stereograms. A fifth experiment revealed that accurate performance did not depend on oculomotor information. The assumptions of texture extent and distribution and constant interocular distance and their possible violations were discussed. A sixth experiment demonstrated that violations of interocular distance are absorbed by surface shapes. The existence and detection of a binocular rotation dissolves the putative problems of singleness and stereopsis, indicates that the importance of having two frontal eyes is for perception of absolute distance, and reformulates the problems for an algorithmic (physiological) theory of vision.     

A general procedure for obtaining paired comparisons from multiple rank orders

From a theoretical point of view, paired comparisons and the law of comparative judgment provide an excellent approach to the problem of psychological measurement. However, if a reasonably large number of stimuli are to be investigated, paired comparisons become extremely time-consuming and fatiguing to the subjects. A balanced incomplete block design, requiring multiple rank order judgments for each subject, provides an efficient experimental method for obtaining paired comparisons judgments. Features of the analysis proposed for this design are discussed in detail. A program for the analysis is available for the IBM 650 electronic computer.Prepared in connection with research done under Office of Naval Research Contract Nonr 1858-(15), Project Designation NR 150-088, and National Science Foundation Grant G-3407. Reproduction of any part of this material is permitted for any purpose of the United States Government.     

Direct and indirect perception of size

Three experiments, using a reaction time paradigm, examine the direct (stimulus bound) and indirect (mediational inference) approaches to size perception. Subjects determine which of two stimuli is the larger when the two can be at different egocentric distances. The effects of two variables on reaction times are examined—distal ratio, the ratio of physical sizes of the stimuli, and proximal ratio, the ratio of the angular projections of the stimuli on the retina. In Experiment 1, both ratios are found to affect reaction times, with the proximal ratios yielding the larger effect, more in line with the predictions of the indirect approach. But the results of Experiments 2 and 3 indicate that distance is taken into greater account, the more similar the distal sizes of the stimuli. In one stimulus condition, distance appears not to affect reaction times. It is suggested that direct size perception occurs for large stimulus differences, indirect size perception for smaller differences. The identical results of the two experiments, one with and one without texture, point to some variable other than texture occlusion or interception as the stimulus for direct size perception. Some aspect of distance from the eye-level plane is suggested as an alternative.     

The role of part—whole information in reasoning about relative size

Models of comparative judgment have assumed that relative magnitude is computed from knowledge about absolute magnitude rather than retrieved directly. In Experiment 1, participants verified the relative size of part-whole pairs (e.g., tree-leaf) and unrelated controls (e.g., tree-penny). The symbolic distance effect was much smaller for part-whole pairs than for unrelated controls. In two subsequent experiments, participants determined either which of two objects was closer in size to a third object or which of two pairs had a greater difference in the size of its constituents. In contrast to the paired comparison task in Experiment 1, judgments of part-whole items were more sensitive to the influence of symbolic distance than were unrelated controls. The fact that the part-whole relation attenuates the effects of symbolic distance in a paired comparison task but not in tasks that require an explicit comparison of size differences suggests that the part-whole relation provides a source of information about relative magnitude that does not depend on knowledge about absolute magnitude.     

Accommodation and apparent distance

The ability to judge egocentric distance was assessed in sixteen normal observers under conditions where monocular blur-driven accommodation provided the only source of information regarding changes in target dioptric distance. Accommodation and apparent distance were measured over an optical range of 2 to 6 D for each of three targets which differed in their effectiveness as accommodative stimuli (excellent, moderate, and poor). For the excellent and moderate accommodative targets, apparent distance decreased as accommodation increased, with both targets sharing a common linear function. Apparent distance, however, tended to exceed accommodative distance and was relatively compressed in scale. As expected, accommodative response and apparent distance diminished in range as target effectiveness was reduced. The poor accommodative target represented the limiting case wherein accommodation failed to deviate from the tonic level, and apparent distance remained constant. There were considerable intersubject differences in the ability to judge distances on the basis of accommodation. The results indicate that accommodation can indeed serve as a source of distance information, particularly for some individuals.     

Anchor effects using numerical estimates of simple dot patterns

Shifts due to anchor stimuli using absolute judgments have been ascribed to “semantic” and “scale modulus” changes. To test this explanation, random dot patterns of 10, 12, 14, 16 and 18 dots were exposed for 0.30 sec with anchors of 4, 13 or 32 dots preceding each of the stimuli. In the control only the series of stimuli were judged. It was found that numerical estimates of the number of dots increased with small anchor, decreased with large anchor, and were not significantly changed with anchor in the vicinity of AL. These results exactly parallel those found using methods of absolute and comparative ratings and hence cannot be ascribed to semantic shifts especially in view of the fact that independent groups of Ss served in the four anchor and control conditions. Since the anchor effects were significant but not so large that they can be ascribed to change of scale modulus this theory must also be rejected. The AL model seems to offer the simplest and most unitary explanation of these as well as many other results obtained with different types of stimuli and different methods of judging.     

The role of discriminative stimuli in concurrent performances

Key pecking in pigeons was examined under concurrent and parallel arrangements of two independent and simultaneously available variable-interval schedules. Pecks on the changeover key alternated the schedule of reinforcement for responses on the main key. Under concurrent schedules, discriminative stimuli were paired with the reinforcement schedule arranged in each component and changeover responses also alternated these stimuli. Under parallel schedules, changeover responses alternated the effective reinforcement schedule, but did not change the discriminative stimulus. On concurrent procedures, changeover response rate was inversely related to the difference in reinforcement rate between the two components, whereas on parallel schedules no consistent relationship was found. With both schedules, absolute response and reinforcement rates were positively related, although for a given set of reinforcement frequencies, rates were often higher on the concurrent schedules. On concurrent schedules, relative response rates and relative times were equal to relative reinforcement rates. On parallel schedules these ratios were positively related, but response and time ratios were much smaller than were obtained with comparable concurrent schedules. This inequality was most pronounced when absolute reinforcement frequencies were lowest.