Nonmetric tests of ratio vs. subtractive theories of stimulus comparison

Theories of stimulus comparison were tested by examining ordinal properties of data obtained with six scaling tasks. Subjects judged simple “ratios” or “differences” of stimulus pairs constructed from a factorial design. In four additional tasks, the same judges also compared relations between pairs of stimulus pairs, judging “ratios of ratios,” “ratios of differences,” “differences of ratios,” and “differences of differences.” The data were consistent with a subtractive theory, which asserts that two stimuli are compared by subtraction, regardless of the task, but that judges can compare two stimulus differences by either a ratio or a difference. All six tasks could be related by the subtractive theory using a single set of scale values. Other simple theories, including the theory that “ratio” judgments can be represented by a ratio model, could not reproduce the six rank orders (of the six sets of data) using a single set of scale values.     

Facilitation of both “same” and “different” judgments of letter strings by familiarity of letter sequence

Three experiments employing simultaneous matching were performed to extend recent findings that three kinds of familiarity—familiarity of letter sequences, familiarity of display configuration, and familiarity of letter orientation—facilitate the matching of letter strings for “same” responses and sometimes for “different” responses. It was found that letter sequence familiarity facilitated “same” responses even when the letter strings were in an unfamiliar orientation or configuration and also facilitated “different” responses whenever the task required that a substantial portion of the display be processed before a response could be initiated. A three-stage model of the simultaneous letter-string matching task was developed. This model, which assumes that the same processes account for both “same” and “different” responses, was consistent with findings obtained when there were small differences between string pairs. Discrepant findings obtained when there were large differences between string pairs may have been produced by the premature initiation of responses.     

The effects of stimulus structure and familiarity on same-different comparison

It was hypothesized that performance in the same-different comparison task is based on two modes of processing: (1) structural processes that organize the detailed parts of a stimulus into a well-formed whole, and (2)analytic processes that decompose the stimulus into features. This hypothesis was supported, but with the unexpected finding of individual differences in the mode of processing underlying “same” responses. Those Ss in the “same” condition whose reaction times were faster for symmetrical than for asymmetrical patterns supported the hypothesis for structural processes. The remaining Ss in the “same” condition, as well as all the Ss in the “different” condition, were unaffected by symmetry. These Ss supported the hypothesis for analytic processes. Although familiarity effects were obtained for both structural and analytic Ss, the rotation of the familiar patterns into an unfamiliar orientation virtually eliminated familiarity effects for the structural Ss, but left them intact for analytic Ss.     

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.     

Averaging: An empirical validity criterion for magnitude estimation

Ss judged grayness of neutral value Munsell chips under two response conditions: magnitude estimation and graphic rating. In addition, they judged average grayness of pairs of chips under the same two response modes. The averaging data were evaluated in terms of a simple model for subjective averaging. The graphic rating data fitted the model, but the magnitude estimates showed consistent discrepancy. It was concluded that the Ss were averaging, but that magnitude estimation distorted their judgments.     

Laterality effects in perceptual matching

Two experiments are reported in which Ss had to indicate whether pairs of simple geometric forms were “same” or “different.” In Experiment I the two forms were either both in the left visual hemifield or both in the right hemifield. Reaction times were unaffected by the locus of the stimuli. In Experiment 2, in addition to left and right pairs, there were pairs in which one of the stimuli was on the left and the other was on the right. Under these conditions, reaction times were faster for pairs totally on the left than for pairs totally on the right. The data support the notion that implicit scanning patterns are important in determining laterality differences. When such scanning is not involved and when simple nonverbal stimuli and responses are employed, laterality differences are eliminated.     

A comparison of semantic. acoustic and visual criteria for matching of word pairs

Ss judged the some pairs of words “same” or “different” under semantic, acoustic and visualcriteria. RTs were compared for each criterion, and the effects of different kinds of confusabittty, such as acoustic similarity in the semantic matching task, or semantic similarity in the acoustic matching task, were also studied.     

Stroop interference in naming and verifying spatial locations

Two experiments are reported that were designed to assess effects of semantic similarity on naming and verification of spatial locations. In Experiment I, the wordsabove, below, left, andright occurred as distractors when Ss named the location of the word relative to a dot, or the location of a dot relative to the word. In Experiment II. the same dot-word displays were used, but Ss reported whether or not the word correctly specified its own location relative to the dot or the location of the dot relative to itself. The naming task showed some within-dimension facilitation and interference effects, most notably when Ss named the location occupied by the distractor word. The verification tasks showed quite substantial retardation of “no” responses when the word and location represented different values on either the horizontal or the vertical dimension.     

Judgments of differences and ratios of numerals

Each subject performed two tasks, dividing a line segment so that either (a) theratio of subjective lengths corresponded to the ratio of the magnitudes of two numerals or (b) thedifference in length was proportional to the numerical difference. Had subjects actually performed two operations on the same scale, the responses would have been nonmonotonically related. Instead, data for the two tasks were nearly identical and ordinally compatible with either a ratio or a subtractive model. The ratio model implied scale values for numerals that were a positively accelerated function of numerical value, inconsistent with previous results. With a nonlinear response function for graphic length, the subtractive model fit well, yielding scale values that were a negatively accelerated function of numerical value and a linear function of previously obtained scales. These results, together with other recent findings, suggest that subjects may perform the same operation in spite of instructions to judge “ratios” or “differences” and that this operation can be best represented by a subtractive model.     

Retrieval processes in recognition

Retrieval processes in the long-term recognition of well organized material showed the expected organizational effects on “slow” recognition responses. Ss sorted 100 words into two to seven categories until a stable organization was achieved. The data showed the usual correlations between organization (number of categories used) and recall and recognition. Recognition tests a week after the sorting task revealed no differences between Ss using many or few categories for the “fast” recognition responses, defined as the faster 50% of each S’s latency distribution. The organizational effect was clearly evident for the “slow” 50% of the responses. The data support the retrieval check hypothesis in recognition under the assumption that retrieval operations take additional time during the recognition process.     

Tests of product and additive scaling axioms

A product axiom for ratio judgments and an additive axiom for difference judgments were tested for six Ss judging brightness. The product axiom was rejected for all six Ss whereas the additive axiom was accepted for two Ss. Power functions did not fit the data well, although somewhat better for difference judgments than ratio judgments. A two-stage model fitted somewhat better, but failed to satisfy one important implication of that model, previously confirmed for lifted weights. The data gave stronger support for a theory of brightness estimation based on an additive axiom for difference judgments than a product axiom based on ratio judgments.     

Differential specialization of the cerebral hemispheres for the perception of sameness and difference

The Johns Hopkins University, Baltimore, Maryland 21218 Pairs of letters were presented 4 deg left or right of fixation, and Ss were asked to indicate as quickly as possible whether the letters in a pair were the same or different. Reaction times for “different” responses were faster when stimuli were in the left visual field than in the right, but reaction times for “same” responses were faster when stimuli were in the right visual field than in the left. These results may indicate that the right hemisphere is better specialized for difference detection, while the left hemisphere is better specialized for sameness detection.     

Direct quantitative judgments of sums and a two-stage model for psychophysical judgments

Judged magnitudes of differences between stimuli have previously been shown to support a two-stage interpretation of magnitude estimation, in which input transformations and output transformations are each describable as power functions. In an effort to provide support for the model independent of the difference estimation procedure. the present investigation employed two additional judgment tasks. We obtained magnitude judgments and category judgments of the combined magnitudes (sums) of paired weights from two groups of Ss. Values of the inferred input exponent k calculated from the two sets of data were very similar and were also remarkably similar to the exponent previously calculated from magnitude estimations of differences between weights. The output exponent calculated from magnitude judgments of sums described a concave upward function; however. the similar function describing category judgments was essentially linear. These results show that the inferred input exponent is not the result of the difference estimation task, and in addition provides support for the contention that the interval scale may be a less biased sensory measure than the magnitude scale. The introduction of an additive constant to the model improved its fit to the data but the rule by which it was introduced made very little difference.     

Confidence ratings in speech perception research: Evaluation of an efficient technique for discrimination testing

Discriminability of voice onset time was determined for four naive Ss in order to evaluate the relative efficiency of a testing procedure which utilized confidence ratings along with the conventional oddity task. Ss rated their judgments on oddity trials as “very very sure,” “somewhat sure,” or “just guessing.” Each S’s discrimination scores were given weights according to his ratings, yielding functions that were compared with those computed using unweighted percent correct scores. The confidence-rating technique produced readily interpretable results with about one-third as many judgments as are needed when the conventional procedure is used. Possible problems with the interpretation of the functions and the generalizability of the technique are discussed.     

Loudness “ratios” and “differences” involve the same psychophysical operation

Subjects judged both “atios” of loudness and “differences” in loudness between pairs of tones that varied in intensity. The pairs were constructed from factorial designs, permitting separation of stimulus and response scaling for each subject. Ratings of “differences” and estimations of “ratios” were monotonically related, inconsistent with the hypothesis that subjects perform both subtractive and ratio operations on a common scale. Instead, the data suggest that both tasks involve the same psychophysical comparison operation with different response transformations. If the operation can be represented by the subtractive model, then category ratings involve a nearly linear transformation and magnitude estimations involve a nearly exponential transformation.     

Distinctive feature control of decision time: Same-different judgments of simultaneously heard phonemes

Ss decided whether dichotically presented consonant or vowel phonemes were “same” or “different” in a reaction time (RT) task. Results indicated that “different” responses were made on the basis of a serial, self-terminating scan of distinctive feature differences between phonemes. “Same” responses were considered too fast to be accounted for by this process and were discussed as a separate parallel process. Recognition of dichotically presented syllables appears to involve a third process in which phonemes are also identified in terms of their distinctive features.     

The elusive tradeoff: Speed vs accuracy in visual discrimination tasks

Theoretical models for choice reaction time and discrimination under time pressure must account for Ss’ ability to trade accuracy for increased speed. The fast guess model views these tradeoffs as different mixtures of “all-or-none” strategies, while incremental models assume they reflect different degrees of thoroughness in processing the stimulus. Three experiments sought tradeoffs for difficult visual discriminations, using explicit payoffs to control and manipulate pressures for speed and accuracy. Although guessing was pervasive, the simple fast guess model could be rejected; Experiments II and III obtained tradeoffs even when fast guesses were purged from Ss’ data. Tradeoff functions fit by several formulations revealed: (1) slower rates of increase in accuracy for more similar stimuli, and (2) substantial “dead times” (80–100 msec slower than detection times) before discrimination responses could exceed chance accuracy. Errors were sometimes faster and sometimes slower than correct responses (depending on S’s speed-accuracy trade); the latter effect may reflect a ceiling on S’s achievable accuracy. A final discussion examines implications of the results for models of discrimination under time pressure; it suggests modifications in present models, focusing on the random walk model, and describes an alternative “deadline” model.     

Time Urgency and the Type A Coronary-Prone Behavior Pattern1

Two experiments were conducted to examine behavioral consequences of a sense of time urgency, which presumably characterizes individuals classified as manifesting a so-called “Type A” coronary-prone behavior pattern. Experiment I indicated that time-urgent Type A Ss were reliably less successful than noncoronary-prone “Type Bs” in performing a task requiring a low rate of response for reinforcement (DRL). Type As were not only unable to delay their responses; they also showed greater evidence of tension and hyperactivity than Type Bs during DRL performance. Experiment II extended these results to the interpersonal domain. Time-urgent Ss became more impatient and irritated than less urgent Ss when both types were systematically slowed down in their efforts to reach a solution on a joint decision-making task. The results were discussed in terms of a conceptualization of the A-B dimension as reflecting differential expectations of and needs for environmental control. Additional evidence was presented in support of this approach. Consideration was also given to possible physiologic mechanisms mediating the relationship between psychological variables such as the Type A pattern and actual occurrence of coronary heart disease.     

Stimulus discriminability in the magnitude estimation and category rating of loudness

Thirty-three Ss made category ratings and magnitude estimations of 10 auditory stimuli differing in loudness. The results from each task were examined in terms of the response uncertainty conditional upon each stimulus. The results did not support the suggestion that category judgments are influenced by the relative discriminability of stimuli in a way which is not characteristic of magnitude estimates, but were found to be consistent with the subjective Standard hypothesis. It is argued that the observed quasi-logarithmic relationship between category scale and ratio scale values reflects the constraints placed upon responses in category rating tasks.     

Contextual effects in difference judgments

Manipulating stimulus spacing, stimulus frequency, or stimulus range usually affects intensity judgments. In six experiments, I investigated the locus of analogues of these contextual effects in a “difference” estimation task. When all stimuli elicited the same taste quality, stimulus distribution affected the scale values only when water was included in the stimulus set (Experiments 1–3). When the subjective ranges of two taste qualities were manipulated, different scale values were obtained for the separate qualities in the two conditions (Experiment 4). Manipulation of the expected response distribution did not affect the scale values or the responses (Experiments 5–6). It is concluded that shifts in stimulus distributions or stimulus ranges result in shifts in subjective scale values. The contextual effects can be interpreted as relative shifts of a number of gustatory continua, with water lying on a separate continuum. Proposed is a model for context-dependent judgments, consisting of four stages: stimulus classification, stimulus placement, continuum placement, and continuum projection.