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.     

Judgments relative to patterns: how temporal sequence patterns affect judgments and memory

Six experiments studied relative frequency judgment and recall of sequentially presented items drawn from 2 distinct categories (i.e., city and animal). The experiments show that judged frequencies of categories of sequentially encountered stimuli are affected by certain properties of the sequence configuration. We found (a) a first-run effect whereby people overestimated the frequency of a given category when that category was the first repeated category to occur in the sequence and (b) a dissociation between judgments and recall; respondents may judge 1 event more likely than the other and yet recall more instances of the latter. Specifically, the distribution of recalled items does not correspond to the frequency estimates for the event categories, indicating that participants do not make frequency judgments by sampling their memory for individual items as implied by other accounts such as the availability heuristic (Tversky & Kahneman, 1973) and the availability process model (Hastie & Park, 1986). We interpret these findings as reflecting the operation of a judgment heuristic sensitive to sequential patterns and offer an account for the relationship between memory and judged frequencies of sequentially encountered stimuli.     

Transitive indistinguishability and approximate measurement with standard finite ratio-scale representations

Ordinary measurement using a standard scale, such as a ruler or a standard set of weights, has two fundamental properties. First, the results are approximate, for example, within 0.1 g. Second, the resulting indistinguishability is transitive, rather than nontransitive, as in the standard psychological comparative judgments without a scale. Qualitative axioms are given for structures having the two properties mentioned. A representation theorem is then proved in terms of upper and lower measures.     

Multidimensional scaling: I. Theory and method

Multidimensional scaling can be considered as involving three basic steps. In the first step, a scale of comparative distances between all pairs of stimuli is obtained. This scale is analogous to the scale of stimuli obtained in the traditional paired comparisons methods. In this scale, however, instead of locating each stimulus-object on a given continuum, the distances between each pair of stimuli are located on a distance continuum. As in paired comparisons, the procedures for obtaining a scale of comparative distances leave the true zero point undetermined. Hence, a comparative distance is not a distance in the usual sense of the term, but is a distance minus an unknown constant. The second step involves estimating this unknown constant. When the unknown constant is obtained, the comparative distances can be converted into absolute distances. In the third step, the dimensionality of the psychological space necessary to account for these absolute distances is determined, and the projections of stimuli on axes of this space are obtained. A set of analytical procedures was developed for each of the three steps given above, including a least-squares solution for obtaining comparative distances by the complete method of triads, two practical methods for estimating the additive constant, and an extension of Young and Householder's Euclidean model to include procedures for obtaining the projections of stimuli on axes from fallible absolute distances.This study was carried out while the author was an Educational Testing Service Psychometric Fellow at Princeton University. The author expresses his appreciation to his thesis adviser, Dr. H. Gulliksen, for his guidance throughout the study and to Dr. B. F. Green, Jr., for valuable assistance on several of the derivations.     

Cross-modal additive conjoint structures and psychophysical scale convergence

I investigated a variety of issues related to the measurement of the magnitude of psychological experience, especially the magnitude of sensations. Different groups of subjects made pair comparisons, magnitude estimations, and category judgments of the "total sensory magnitude" of light and sound stimuli presented conjointly. Another group judged the dissimilarity of pairs of conjoint stimuli. Various axioms, especially double cancellation, were tested on the resulting rank orders of conjoint stimuli. Judgements of the total magnitude of conjoint combinations of sound and light stimuli formed an additive conjoint structure. Dissimilarity judgments gave rise to a closely related lattice structure. Moreover, various scales of the individual attributes (loudness and brightness) calculated from the two types of judgments of the conjoint stimuli displayed substantial convergence, each scale for a given modality being linear with all other scales for that modality.     

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.     

Estimation ofJ scales for unidimensional unfolding

In Coombs' unidimensional unfolding theory each individual ranks all stimuli, often in terms of preference judgments. These ranks, calledI scales, are used to infer the latent continuum called aJ scale which is presumed to have generated theI scale rankings. A major problem concerns the inference of theJ scale given a set ofI scales because anI scale is not unique to any oneJ scale. This paper presents a procedure for estimatingJ scale probabilities given a set ofI scales. Models for three and four or more stimuli are presented. Results of computer tests are reported.     

Expressivist to the core: Metaaesthetic subjectivism is stable and robust

Two common observations about aesthetics are in tension: that people generally consider aesthetic judgments subjective, and that people generally behave like objectivists (arguing over judgments, making choices based on judgments of trusted critics, rejecting strong assertions of aesthetic equivalence). This tension would be resolved if the first observation turned out to be false—if people endorsed subjectivism weakly, flexibly, or rarely. We tested whether people can be pushed to endorse objectivism under certain circumstances. Across a large sample (N = 588), aesthetic subjectivism proved consistent and robust to experimental manipulations. Even judgments that reflected participants' own evaluations of artworks were considered just as subjective as judgments directly opposed to their personal evaluations. We conclude that the apparent tension can be explained by the philosophical position of expressivism and discuss expressivism's prospects as a framework for understanding aesthetic judgment.     

A note on the use of triads for paired comparisons

When scaling a large number of stimuli from comparative judgments, considerable savings in time and labor may be realized if stimuli are presented in triad form rather than in pairs. If, forN stimuli, the proper configuration of triads can be assembled so that all possible pairs appear once, the paired judgment matrix may be reproduced with one-third fewer judgments and two-thirds fewer presentations than would be required with complete pairing. A simple procedure is described for enumerating triad configurations for whichN is an odd multiple of three.     

Perceptual separability and spatial models

Highly analyzable two-dimensional color stimuli were generated using stimulus cards such that one part of each card varied only on the first dimension and the other part varied only on the second. Subjects were required to make judgments of similarity between pairs of these analyzable stimuli, between pairs of relatively unanalyzable color stimuli, and between pairs of geometric stimuli. The results support previous findings that the Euclidean combining rule is appropriate for judgments of single color patches but indicate that the city block combining rule may be appropriate for simple stimuli that vary on perceptually distinct dimensions.     

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.     

Pythagorean distance and the judged similarity of schematic stimuli

Independent groups of Ss rated the similarity of pairs of patterns belonging to the same class, either bef ore or af ter a discrimination task of schematic concept formation (SCF). Mean similarity increased as a function of SCF pretraining. A linear relationship was found between a Pythagorean distance measure on the patterns and subjective similarity of pairs of stimuli (r=.88). No such relationship was obtained from an analysis of judgments from a group that viewed random, nonschematic stimuli. A secondary analysis of the discrimination judgments in the SCF task showed that the Pythagorean distance measure was predictive of judgments on pairs of stimuli from the same schema family, but the relationship did not hold for pairs representing two different schemata. Multidimensional scaling analyses indicated that mildly deviant schematic stimuli were perceived to be instances of a single family. The dimensions describing a schema cluster appeared to be specific to the sample of stimuli. A tendency for the Kruskal procedures to collapse certain types of stimulus clusters was observed and discussed.     

Reversed better-than-average effect in direct comparisons of nonsocial stimuli depends on the set size

Studies on direct comparative judgments typically show that, for items that are positively evaluated, a single item randomly drawn from a larger set of similar items tends to be judged as better than average (the BTA effect). However, Windschitl, Conybeare, and Krizan (2008) demonstrated that, under timing conditions that do not favor focusing attention on the single item, the reversal of the BTA effect occurs. We report two experiments showing that the magnitude of the reversed BTA effect increases as a function of the size of a multiitem referent with which a single item target is compared. Specifically, in direct comparative judgments of the attractiveness of positively evaluated objects (nice-looking cloth buttons, attractive buildings, or cupcakes), underestimation of the attractiveness of singletons, as compared with a multiitem set (reversed BTA effect), increased with the increased set size. Analysis of absolute judgments obtained for singletons and for small and large multiitem sets suggests that, for attractive stimuli, both the reversed BTA effect in comparative judgments and its sensitivity to set size occur as a result of a positive relationship between set size and perceived attractiveness in absolute judgments.     

Effects of objective feedback and "single other" or "average other" social comparison feedback on performance judgments and helping behavior

In two studies, participants received positive or negative feedback about their performance on a verbal task and then provided hints to another person on a subsequent, different task. It was expected that participants would give more helpful hints after positive than after negative feedback but that this would be more apparent when the feedback was based on performance comparisons with the "average participant" than on comparisons with another person or an objective standard. This effect was expected to be mediated by judgments of one's performance on the first task. These predictions were supported. Participants seemed aware of the effect of feedback on their hint choices, and their hint choices did not alter their affect levels. Also, participants receiving comparative (single or aggregated target) feedback exhibited changes in self-ascribed importance of the performance domain. Implications for social comparison theory and self-evaluation maintenance theory are discussed.     

College Students' Given Names: A Test of the Preference‐Feedback Hypothesis1

According to the preference‐feedback hypothesis, liking generally increases with familiarity up to a point and then declines. However, for stimuli such as given names, liking increases monotonically with familiarity, because given names that become too familiar tend to be chosen less frequently by parents, thus becoming less familiar once again. A college sample of 160 men and 211 women provided potential names for first son and first daughter, as well as reasons for their selections. Comparing given names of the research participants with names that they chose for sons and daughters, high‐frequency participants' names occurred less frequently as choices for sons and daughters' names, although this effect was significant for women's names only. Frequency was mentioned as a reason for choices by 10% to 20% of the sample, and significantly more often for daughters' names than for sons' names.     

Comparative judgments as an alternative to ratings: identifying the scale origin

Although comparative judgment methods have a number of distinct advantages over ratings, they share one common problem: On the basis of comparative judgments, it is not possible to recover the origin of item evaluations. One item may be judged more positively than another, but this result does not allow any conclusions about whether either of the items are attractive or unattractive. This article discusses the implications of this limitation for the interpretation of individual differences in comparative judgments. It also presents 3 different methods that may allow determination of the scale origin using a nested model comparison approach. An application illustrates the proposed approach as well as the benefits of determining the scale origin in understanding value judgments.     

Judgments of mean speed and predictions of route choice

How are driving speeds integrated when speeds vary along a route? In a first study, we examined heuristic processes used in judgments of mean speed when the mean speeds on parts of the trip varied. The judgments deviated systematically from objective mean speeds because the distances driven at different speeds were given more weight than travel time spent on the different distances. The second study showed that when there was a 10–15 min pause during a travel the effect on the mean speed decrease was underestimated for driving speeds of 90 km/h and higher. In the third study, the objective mean speeds and the subjective biased mean speed judgments were used to predict choices between routes with different speed limits. The results showed that subjective judgments predicted decisions to maximize mean speed significantly better than objective mean speeds. Finally, some applied and basic research implications of the results were discussed.     

Judgments of learning and improvement

Can learners accurately judge the rate of their learning? Rates of learning may be informative when study time is allocated across materials, and students' judgments of their learning rate have been proposed as a possible metacognitive tool. Participants estimated how much they improved between presentations in multitrial learning situations in which n-gram paragraphs (in Experiments 1 and 2) or word pairs (Experiments 3 and 4) were learned . In the first experiment, participants rated improvement on a percentage scale, whereas on the second and third, judgments were given on a 0–6 scale. Experiment 4 used both a percentage scale and an absolute number scale. The main result was that judgments of improvement were poorly correlated with actual improvement and, in one case, were negatively correlated. Although judgments of improvement were correlated with changes in judgments of learning, they were not reliable indicators of actual improvement. Implications are discussed for theoretical work on metacognition.     

Structural comparison and consumer choice

Psychological research has demonstrated important parallels between the structural alignment process involved in judgments of similarity and the processes that are involved in analogical reasoning. Gradually, this work on comparisons was applied to consumer choice. In this paper, we review the influence of structural alignment on choices among a set of options. Then, we discuss extensions of this work to comparative advertising and to the role of analogy in marketing communication. Finally, we discuss important extensions to structural alignment suggested by this work such as the key role that affect plays in comparisons made during the choice process.     

The judgment-choice discrepancy: Noncompatibility or restructuring?

The study examines the relative merits of a noncompatibility and a restructuring explanation of the recurrent empirical finding that a prominent attribute looms larger in choices than in judgments. Pairs of equally attractive options were presented to 72 undergraduates who were assigned to six conditions in which they performed (1) only preference judgments or choices, (2) preference judgments or choices preceded by judgments of attractiveness of attribute levels, or (3) preference judgments or choices accompanied by think-aloud reports. The results replicated the prominence effect for choices, but a prominence effect was also found for preference judgments. In accordance with the restructuring explanation, the think-aloud protocols indicated that options were more often restructured in choices than in preference judgments. However, restructuring could not explain the prominence effect observed for preference judgments. A modified compatibility hypothesis is offered as an alternative explanation.