When proportion consensus scoring works

Most objectively scored tests use items with easily identifiable correct answers. When such veridical scoring keys cannot be constructed, researchers sometimes use proportion consensus scoring (PCS) to identify the best answers. To determine if PCS identifies the best answers, we scored a test using both PCS and veridical scoring. Among 353 undergraduates, regular PCS, two-stage PCS, and expert PCS all had high correlations for easy items, but no PCS methods had high correlations for difficult items. Thus, PCS cannot reliability identify the best answers to individual items. However, PCS worked well for total scores. For easy items, total scores had correlations above .99 for all PCS methods. For difficult items, expert and two-stage PCS had correlations of .92 and .82 for the 60-item test. Thus, expert and two-stage PCS can be justified (even for difficult items) if the scoring key is based upon people who truly possess some degree of expertise and if scores are summed over many items.     

Understanding bias in proportion production

The Stevens exponent (beta) can be obtained from proportion estimation judgments using the power model. In this article, the authors extend that model to proportion production, in which the relative magnitudes of 2 stimuli are adjusted to correspond to a numeric proportion (e.g., 1/4 or .25). The model predicts that when beta < 1, small proportions are underproduced, and large proportions are overproduced, but it predicts the reverse when beta > 1, which is the opposite of the predicted patterns for estimation. Eight participants estimated and produced magnitudes and proportions with spatial volume (beta < 1; Experiment 1) and color saturation (beta > 1; Experiment 2). The model's predictions were generally supported. An extension of the model using reference points can account for multicycle patterns shown by some participants.     

Conscious and unconscious proportion effects in masked priming

The global neuronal workspace theory [Dehaene, S., & Naccache, L. (2001). Towards a cognitive neuroscience of consciousness: basic evidence and a workspace framework. Cognition, 79, 1–37.] proposes that it is impossible for an unconscious stimulus to be used strategically to enhance task performance (bottom–up effect), while a fully consciously perceived stimulus can be used to improve task performance (top–down effect). Two experiments were designed to investigate these hypotheses. In a first experiment we investigated whether a manipulation of the proportion of Arabic/number word targets had a top–down effect. Since the subjects were fully aware of the target, we expected that this manipulation could be used to enhance task performance. In a second experiment we determined whether a manipulation of the proportion of Arabic/number word primes had a bottom–up effect. Since the subjects were unaware of the prime, we hypothesized that they would be unable to use the manipulation to enhance task performance and therefore the manipulation would have no effect. Both hypotheses were largely confirmed.     

Contingency proportion systematically influences contingency learning

In the color-word contingency learning paradigm, each word appears more often in one color (high contingency) than in the other colors (low contingency). Shortly after beginning the task, color identification responses become faster on the high-contingency trials than on the low-contingency trials—the contingency learning effect. Across five groups, we varied the high-contingency proportion in 10% steps, from 80% to 40%. The size of the contingency learning effect was positively related to high-contingency proportion, with the effect disappearing when high contingency was reduced to 40%. At the two highest contingency proportions, the magnitude of the effect increased over trials, the pattern suggesting that there was an increasing cost for the low-contingency trials rather than an increasing benefit for the high-contingency trials. Overall, the results fit a modified version of Schmidt’s (2013, Acta Psychologica, 142, 119–126) parallel episodic processing account in which prior trial instances are routinely retrieved from memory and influence current trial performance.     

Attentional control and the relatedness proportion effect in semantic priming

In 2 experiments, participants completed both an attentional control battery (OSPAN, antisaccade, and Stroop tasks) and a modified semantic priming task. The priming task measured relatedness proportion (RP) effects within subjects, with the color of the prime indicating the probability that the to-be-named target would be related. In Experiment 2, participants were cued before each trial with the probability of a related target. Stimulus onset asynchronies traditionally thought to tap automatic processing (267 ms) versus controlled processing (1,240 ms) were used. Across experiments, principal component analysis on the battery revealed a general attentional control component. Moreover, the RP effect increased linearly with attentional control in both experiments. It is concluded that RP effects produced in this paradigm depend purely upon the effortful process of expectancy generation, which renders them sensitive to individual differences in attentional control.     

Questioning conflict adaptation: proportion congruent and Gratton effects reconsidered

Conflict adaptation is one of the most popular ideas in cognitive psychology. It purports to explain a wide range of data, including both brain and behavioral data from the proportion congruent and Gratton paradigms. However, in recent years, many concerns about the viability of this account have been raised. It has been argued that contingency learning, not conflict adaptation, produces the proportion congruent effect. Similarly, the Gratton paradigm has been shown to contain several confounds—most notably, feature repetition biases. Newer work on temporal learning further calls into question the interpretability of the behavioral results of conflict adaptation studies. Brain data linking supposed conflict adaptation to the anterior cingulated cortex has also come into question, since this area seems to be responsive solely to time-on-task, rather than conflict. This review points to the possibility that conflict adaptation may simply be an illusion. However, the extant data remain ambiguous, and there are a lot of open questions that still need to be addressed in future research.     

Masked repetition priming and proportion effects under cognitive load.

The authors used a cognitive load manipulation (rehearsing a string of digits during the trial) to test the automaticity of (a) masked repetition priming and (b) the masked repetition proportion (RP) effect (i.e., greater priming when the proportion of repetition-prime trials is higher) in the lexical decision task. The RP (.2 vs. .8) was varied across blocks. Masked priming was not reduced under load compared with a no-load group. Surprisingly, only the load group showed an RP effect in response latencies, although the no-load group showed an RP effect in the error rates. Our results show that masked priming is automatic, yet the influence of masked primes can nonetheless be adjusted at an unconscious level. Implications for accounts of masked priming are discussed.     

Judging proportion with graphs: the summation model

People take longer to judge part-to-whole relationships with bar graphs than with pie charts or divided bar graphs. Subjects may perform summation operations to establish the whole with bar graphs, which would be unnecessary for other graph types depicting the whole with a single object. To test this summation model, the number of components forming the whole was varied with bars, divided bars, reference bars, and pies in three experiments. Response time increased with the number of components for bar graphs but there was little increase for other graph types in Experiment 1. An accuracy emphasis in Experiment 2 produced generally longer response times, but had little effect on the time per summation. The summation operation was not used when graphs were displayed briefly in Experiment 3, although subjects still took longer with bars. The estimated time for a summation operation is consistent with estimates derived from other research. In general, the bar graph is not effective for proportion judgments, and its disadvantage becomes potentially greater as the number of components increases. © 1998 John Wiley & Sons, Ltd.     

Repetition proportion biases masked priming of lexical decisions

Although subjects have little or no awareness of masked primes, Bodner and Masson (2001) found that priming of lexical decisions is often enhanced when masked repetition primes occur on a high proportion of trials. We used baseline prime conditions to specify the locus of this repetition proportion (RP) effect. In Experiments 1A and 1B, a .8-RP group showed more priming than did a .2-RP group, and this RP effect was due to both (1) increased facilitation from repetition primes and (2) increased interference from unrelated primes. In Experiment 2, we used the baseline condition to show that subjects are sensitive to RP rather than to the proportion of unrelated primes. Direct comparisons of a given prime condition (repetition, unrelated) across RP conditions were more stable than were comparisons relative to the baseline condition. The increased costs and benefits of repetition priming when RP is higher implicate a context-sensitive mechanism that constrains accounts of masked priming.     

Repetition proportion affects masked priming in nonspeeded tasks

Masked repetition priming is often greater when a larger proportion of trials involve repetition primes, suggesting that a context-sensitive unconscious process may be operating. Two recent studies have failed to obtain an effect of prime proportion in the perceptual identification (PI) task, suggesting that the effect may not occur in nonspeeded tasks. Contrary to this possibility, we report proportion effects with masked repetition primes in two nonspeeded tasks: PI and fragment completion (FC). A proportion effect occurred in the accuracy measure only in the FC task, but it occurred in the reaction time measure in both tasks. Prior failures to find proportion effects in the PI task thus may have been due, in part, to the dependent measure used. We interpret our findings in light of several recent accounts of prime proportion effects with brief primes.     

Probe-specific proportion task repetition effects on switching costs

In two experiments, participants were presented with successive presentations of animal names (e.g., GORILLA, WHALE)--a prime display followed by a probe display. In response to each display, participants judged either the typical habitat or the relative size of those animals, repeating the same task in response to both displays on half of the experimental trials and switching from one task to the other on the other half of trials. Our results demonstrate that switch costs can be reduced when either the probe's identity or its location is predictive of a change in task. This result establishes that the presentation of a stimulus can serve as a rapid cue for facilitating a switch in task, independent of processes occurring both at the time of the prime task and during the intervening period between the prime and probe tasks. We discuss the implications of these results for prevailing explanations of task switching costs.     

The aesthetics of rectangle proportion: effects of judgment scale and context

Two experiments examined preference for rectangle proportion, using a method that allowed participants to adjust 1 dimension of a rectangle to achieve the most preferred proportion. Instructing participants to use an interestingness response scale resulted in a preference for rectangles having more extreme sides ratios, compared with pleasingness or preferability scales. Instructing participants to produce a rectangle representing the preferred proportions of a painting or a kitchen tile shifted the preferred sides ratio toward a less extreme value than did a no-context rectangle instruction. Implications of the results for the findings of experiments that seek evidence for the special significance of particular ratios, such as the golden section, are discussed.     

Effect of repetition proportion on language-driven anticipatory eye movements

Previous masked priming research in word recognition has demonstrated that repetition priming is influenced by experiment-wise information structure, such as proportion of target repetition. Research using naturalistic tasks and eye-tracking has shown that people use linguistic knowledge to anticipate upcoming words. We examined whether the proportion of target repetition within an experiment can have a similar effect on anticipatory eye movements. We used a word-to-picture matching task (i.e., the visual world paradigm) with target repetition proportion carefully controlled. Participants' eye movements were tracked starting when the pictures appeared, one second prior to the onset of the target word. Targets repeated from the previous trial were fixated more than other items during this preview period when target repetition proportion was high and less than other items when target repetition proportion was low. These results indicate that linguistic anticipation can be driven by short-term within-experiment trial structure, with implications for the generalization of priming effects, the bases of anticipatory eye movements, and experiment design.     

Bias in proportion judgments: the cyclical power model

When participants make part-whole proportion judgments, systematic bias is commonly observed. In some studies, small proportions are overestimated and large proportions underestimated; in other studies, the reverse pattern occurs. Sometimes the bias pattern repeats cyclically with a higher frequency (e.g., overestimation of proportions less than .25 and between .5 and .75; underestimation otherwise). To account for the various bias patterns, a cyclical power model was derived from Stevens' power law. The model proposes that the amplitude of the bias pattern is determined by the Stevens exponent, beta (i.e., the stimulus continuum being judged), and that the frequency of the pattern is determined by a choice of intermediate reference points in the stimulus. When beta < 1, an over-then-under pattern is predicted; when beta > 1, the under-then-over pattern is predicted. Two experiments confirming the model's assumptions are described. A mixed-cycle version of the model is also proposed that predicts observed asymmetries in bias patterns when the set of reference points varies across trials.     

Altering the proportion of components in a mixed fixed-ratio schedule

Pigeons were trained under a schedule consisting of a number of fixed-ratio 100 components followed by a single fixed-ratio 10 component. The proportion of fixed-ratio 100 to fixed-ratio 10 components was varied according to several ascending and descending series within the range of 99:1 to 1:1. When this proportion was reduced to about 20:1 and below, the pause following each fixed-ratio 100 gradually decreased in length. Primes, a burst of responses at the start of the fixed-ratio 100 component, increased in frequency, and then decreased when the proportion became extremely low. Also, when the relative frequency of fixed-ratio 10 components was very high, primes were seldom observed in the first fixed-ratio 100 component following a fixed-ratio 10 component, but were distributed evenly throughout the remaining fixed-ratio 100 components.