Some theory and results for metrics for bounded response scales

In an earlier note, a new metric for bounded response scales (MBR) was introduced which resembles the city-block metric but is bounded above. It was suggested the MBR may be more appropriate than minkowski metrics for data obtained with bounded response scales. In this article, some formal properties of the MBR are investigated and it is shown that it is indeed a metric. Empirical predictions are then derived from the MBR and contrasted with those of a “monotonicity hypothesis,” which holds that dissimilarity judgements tend to be biased towards overestimation of larger distances, and with the predictions of the minkowski metrics, which imply additivity of collinear segments. Some empirical results are presented which contradict the monotonicity hypothesis and the minkowski metrics, and favor the MBR. Finally, the logic used to motivate the MBR is invoked to define a subadditive concatenation for bounded norms in the one-dimensional case, which may be useful in psychophysical work where the upper bounds are often real, rather than due to the response scale. This concatenation predicts understimation for doubling and overestimation for halving and middling tasks.     

A procedural theory of eye movements in doing arithmetic

A procedural theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction is presented. The best-fitting distribution of fixation durations with a relatively simple theoretical justification consists of a mixture of an exponential distribution and the convolution of two exponential distributions. The eye movements themselves were found to approximate a random walk that fits rather closely in both adult and juvenile subjects the motion postulated by the normative algorithm ordinarily taught in schools. Certain structural features of addition and subtraction exercises, such as the number of columns, the presence or absence of a carry or a borrow, are well known to affect their difficulty. In this study, regressions on such structural variables were found to account for only a relatively small part of the variation in eye-fixation durations.     

Some deterministic models of concept identification

It is shown that deterministic models can compete effectively with stochastic models in summarizing concept identification behavior. Three groups of deterministic models are examined. Examination of individual learners' trial by trial behavior in a concept experiment shows: (1) One person exhibited behavior consistent with a Hypothesis Permutation (HP) model despite being a nonlearner who showed no evidence of improvement over a period of 24 trials. However, when all 50 persons studied in each of two treatment groups were examined, only 22 members of one group and 10 of the other showed no inconsistencies with deterministic local consistency assumptions. (2) Certain deterministic computer programs could find at least one satisfactory order for predicting all responses by 18 of the 22 consistent solvers and 6 of the 10 consistent solvers, respectively, in the two groups just mentioned. For these 24 persons, then, a less restrictive deterministic model is adequate than for the others. (3) Those 38 original members of the first treatment group who met a stringent learning criterion were compared with respect to predictions generated by stochastic and mathematized deterministic models. One deterministic model (RSS-U 9-state) is in some respects the best of the models examined, but this success is a partial reflection of estimating eight parameters from the data.     

An axiomatization of the ratio/difference representation

If ≥_r and ≥_d are two quaternary relations on an arbitrary set A, a ratio/difference representation for ≥_r and ≥_d is defined to be a function f that represents ≥_r as an ordering of numerical ratios and ≥_d as an ordering of numerical differences. Krantz, Luce, Suppes and Tversky (1971, Foundations of Measurement. New York, Academic Press) proposed an axiomatization of the ratio/difference representation, but their axiomatization contains an error. After describing a counterexample to their axiomatization, Theorem 1 of the present article shows that it actually implies a weaker result: if ≥_r and ≥_d are two quaternary retations satisfying the axiomatization proposed by Krantz et al. (1971), and if ≥_r′ and ≥_d′ are the relations that are inverse to ≥_r and ≥_d, respectively, then either there exists a ratio/difference representation for ≥_r and ≥_d, or there exists a ratio/difference representation for ≥_r′ and ≥_d′, but not both. Theorem 2 identifies a new condition which, when added to the axioms of Krantz et al. (1971), yields the existence of a ratio/difference representation for relations ≥_r and ≥_d.     

Brilliant but cruel: Perceptions of negative evaluators

Using edited excerpts from actual negative and positive book reviews, this research examined the hypothesis that negative evaluators of intellectual products will be perceived as more intelligent than positive evaluators. The results strongly supported the hypothesis. Negative reviewers were perceived as more intelligent, competent, and expert than positive reviewers, even when the content of the positive review was independently judged as being of higher quality and greater forcefulness. At the same time, in accord with previous research, negative reviewers were perceived as significantly less likable than positive reviewers. The results on intelligence ratings are seen as bolstering the self-presentational explanation of the tendency shown by intellectually insecure individuals to be negatively critical. The present methodology is contrasted to that of previous research which obtained apparently contradictory results.     

The effects of control on perceived fairness of procedures and outcomes

On the basis of Thibaut and Walker's theory of procedural justice, it was predicted that subjects who experienced control through choosing a trial decision rule would be more satisfied with the outcome of a dispute and the conflict resolution procedure than would yoked subjects who were not given control. Two additional conditions were added to the design in order to investigate the extent to which control had an influence on trial evaluations independent of being allowed to discuss the rules and obtaining a preferred rule in the absence of actual choice. Regardless of role in the dispute (accuser, accused, or no knowledge) and the nature of the rule adopted, those subjects who exercised control through rule choice evaluated all aspects of the trial experience more positively than subjects who did not exercise control through rule choice. The results also revealed that discussion of the rules and obtaining the preferred rule without choice contributed positively to evaluations of the trial procedure and verdict.     

A biased random walk model for two choice reaction times

This paper generalizes Stone's (1960, Psychometrika 25, 251–260) random walk model of two choice response times (RTs) that is based on the sequential probability ratio test (SPRT) and that predicts equal correct and incorrect RTs to the same response. The generalized version allows a bias of the type found in signal detection theory to enter directly into the accumulation process so that ambivalent evidence may be seen as slightly favoring one alternative. The resulting biased SPRT model can predict any relation between correct and incorrect mean RTs. In particular, unlike the special symmetric case of Link and Heath's (1975, Psychometrika 40, 77–105) relative judgment theory (RJT), the biased SPRT model can predict that correct mean RTs are faster for one response but slower for the other. The biased SPRT model, the classical SPRT model, and the symmetric RJT model are all fit to the data of an RT deadline experiment reported by Green and Luce (1973, Attention and performance, New York: Academic Press) and it is shown that, of the three, the biased SPRT model provides the best account. Finally, a method for incorporating the same sort of bias into RJT models is sketched out.     

The effects of distributed training on retention of operant conditioning in human infants

Long-term retention of operant footkicking acquired in the mobile conjugate reinforcement paradigm was assessed as a function of the distribution of training time. In the first study, 3-month-old infants were trained for either one 18-min session or for two 9-min or three 6-min sessions separated by 24-hr intervals. All infants exhibited retention during a test administered immediately after training, but only those trained in a single session continued to perform the conditioned response during cued-recall tests 7 or 14 days later. Infants trained in three sessions showed no evidence of remembering the contingency even after a week. A warm-up decrement, seen in the day-to-day performance of infants in the distributed conditions, was eliminated in the second study by the interpolation of a nonreinforcement period at the outset of daily sessions. This procedure also enhanced long-term retention such that infants trained in three 6-min session now remembered the contingency for 14 days and did not differ from infants who had received a single 18-min session. Whether distributed training facilitates or impairs long-term retention appears to depend on the opportunity for infants to acquire a sufficient number (or kind) of effective retrieval cues during original learning.     

Speaker bias in children's evaluation of the external consistency of statements

The hypothesis of this study is that an assumption of speaker credibility affects children's judgments of the external consistency of statements. In two experiments, first and third grade children (6 and 8 years of age, respectively) and college adults were read short paragraphs containing contradictory information from a contextual source and a speaker. The contextual source was described as either authoritative or nonauthoritative and discredited. The speaker was either an adult or child. Thus the contextual source was either more or less reliable than the speaker. Subjects were asked to affirm or contradict the speaker's statement, and to choose either the source or the speaker as most believable. The results showed that adult responses varied with the contextual source alone, while the responses of the first graders varied primarily with the speaker's age. The responses of the third graders varied with both factors. The results suggest young children can assess the external consistency of statements but frequently do not because of their assumptions about speakers and other performance factors.     

Does reward depletion influence spatial memory performance?

If spatial memory tasks are considered as foraging problems, it can be predicted that rats' difficulty in learning a win-stay task—revisiting part of a maze where food has recently been found—should be partly overcome if the food is not fully consumed at the first visit (nondepleted reward) rather than being all eaten (depleted reward). Three experiments confirmed and further analysed this result. Experiments 1 and 2 showed that it does not depend on the amount of food initially found; nor is win-stay performance affected by the amount of food actually eaten. Experiment 3 suggested that the effects of nondepleted reward are mainly due to the animals' being interrupted while eating, and very little to the fact that uneaten food is left behind. The results are discussed with regard to their implications for learning theory, and for the application of foraging theory to learning and memory experiments.