Additive Factors Logic Research Articles

Two processing stages of the SNARC effect.

The spatial-numerical association of response codes (SNARC) effect showed that small/large numbers represented in the left/right space facilitated left/right responses, respectively. However, the processing stage (semantic representation or response selection) of the SNARC effect is still controversial. To investigate this issue, we adopted a modified magnitude comparison task in which the effects of SNARC, Stroop (semantic-representation stage), and Simon (response-selection stage) could be simultaneously induced. The processing stages of the SNARC effect were investigated by examining the interactions among these effects. According to the additive factor logic, if two effects are interactive, then they occur in the same stage; if two effects are additive, then they occur in different stages. Across two experiments, the SNARC effect interacted with the Stroop effect and with the Simon effect. These results suggested that the SNARC effect occurred in both the semantic-representation and response-selection stages and provided insight into that the SNARC effect might have two originating sources.

The SNARC effect occurs in the response-selection stage

The dimensional overlap (DO) theory categorizes various stimulus-response compatible effects (e.g., the manual Stroop, Simon, and SNARC effects) into two main types: stimulus-stimulus (S-S) and stimulus-response (S-R) dimensional overlap effects. The S-S type effect (e.g., the manual Stroop) occurs in the semantic-representation stage, while the S-R type effect (e.g., Simon) occurs in the response-selection stage. However, the processing stage of the SNARC effect, which is also categorized as an S-R type, remains controversial. To investigate this issue, we adopted a modified numeral parity judgment task that could simultaneously induce manual Stroop, Simon, and SNARC effects. According to the additive-factor logic, two effects occur in the same processing stage if they are interactive. In our task, we checked the interaction among the three effects to identify the locus of the SNARC effect. In two experiments with different target numbers (exp1: 1, 2, 7, 8; exp2: 0, 1, 2, 3, 6, 7, 8, 9), the manual Stroop, Simon, and SNARC effects were all observed, showing longer response times and higher error rates in the incongruent conditions than in the congruent conditions. Most importantly, only the interaction between SNARC and Simon effects was observed in the two experiments. This result suggests that the SNARC effect, as an S-R type effect like the Simon effect, occurs in the response-selection stage. In addition, the noninteraction of the manual Stroop and Simon effects and the manual Stroop and SNARC effects in our study repeatedly verifies the independence of the S-S and S-R effects. Our results further support the classification of the DO theory.

Examining the Perceptual-Cognitive Mechanism of Deceptive Actions in Sports.

In several kinds of sports, deceptive actions are used to hinder the anticipation performance of an opponent. During a head fake in basketball, a player turns the head to one side but passes the ball to the other side. A pass with a head fake generates a head-fake effect in the observer, which is characterized by slower and more error-prone responses to the pass direction as compared to passes without a head fake. Whereas the head-fake effect has been replicated several times, the question of its origin with dynamic stimuli has not been answered yet. The present study includes four experiments, which are conducted to examine the perceptual-cognitive mechanism underlying the effect by using the model of dimensional overlap (Kornblum et al., 1990) and the additive factors logic (Sternberg, 1969). Results point to multiple processes contributing to the head-fake effect for dynamic stimuli, which operate not only at a perceptual level but also at a level of response selection.

S1-R2 and R1-R2 Backward Crosstalk Both Affect the Central Processing Stage.

A frequent observation in dual-task experiments is that performance in Task 1 is influenced by conceptual or spatial overlap with features of Task 2. Such compatibility-based backward crosstalk effects (BCEs) can occur when overlap exists between the responses of two tasks–the R1-R2 BCE–or between the stimulus in Task 1 and the response in Task 2–the S1-R2 BCE. The present study investigated whether the S1-R2 BCE has a perceptual locus, and by implication, whether the two BCEs have a common processing locus or different ones. To this end, we applied the additive factors logic and manipulated the duration of the Task 1 perceptual stage. The results argue against a perceptual locus for both BCEs. As a possible explanation, we suggest that the R1-R2 BCE and the S1-R2 BCE have their locus within a capacity-limited central stage, but that they arise from different processes within this stage. The R1-R2 BCE influences Task 1 response selection, whereas the S1-R2 BCE influences Task 1 stimulus classification. A plausible though post-hoc model is presented within the Discussion.

Are the inverse-duration and inverse-proximity effects in temporal integration subserved by independent mechanisms?

Displays shorter than about 100 ms are normally seen as lasting longer than their physical duration. This visible persistence can bridge a temporal gap between two sequential stimuli causing them to be temporally integrated into a single percept. We investigated two findings in the temporal-integration literature: the inverse duration effect (temporal integration is progressively impaired as the duration of the first stimulus is increased) and the inverse proximity effect (temporal integration is progressively impaired as the spatial proximity between the stimuli is increased). In two experiments we asked whether the two effects are separable (i.e., whether they are subserved by independent mechanisms) or interact with one another. To estimate the duration of visible persistence we used the missing element paradigm in Experiment 1 and directional stroboscopic motion between two lines in Experiment 2. In both experiments we manipulated the duration of the leading stimulus and the spatial gap between the elements of the two sequential displays. Additive-factors logic was employed to examine the separability of the effects of duration and proximity. Independence (separability) of the two factors would be evidenced in a graph in which the functions of duration over proximity are parallel. The results pointed uniformly to separability. A plausible mechanism for the inverse duration effect is the burst of processing activity time-locked to stimulus onset. A plausible mechanism for the inverse proximity effect is lateral inhibition that acts to reduce the visible persistence of the leading stimulus.

Fluency misattribution and auditory hindsight bias.

We conducted three experiments to test the fluency-misattribution account of auditory hindsight bias. According to this account, prior exposure to a clearly presented auditory stimulus produces fluent (improved) processing of a distorted version of that stimulus, which results in participants mistakenly rating that item as easy to identify. In all experiments, participants in an exposure phase heard clearly spoken words zero, one, three, or six times. In the test phase, we examined auditory hindsight bias by manipulating whether participants heard a clear version of a target word just prior to hearing the distorted version of that word. Participants then estimated the ability of naïve peers to identify the distorted word. Auditory hindsight bias and the number of priming presentations during the exposure phase interacted underadditively in their prediction of participants' estimates: When no clear version of the target word appeared prior to the distorted version of that word in the test phase, participants identified target words more often the more frequently they heard the clear word in the exposure phase. Conversely, hearing a clear version of the target word at test produced similar estimates, regardless of the number of times participants heard clear versions of those words during the exposure phase. As per Roberts and Sternberg's (Attention and Performance XIV, pp. 611-653, 1993) additive factors logic, this finding suggests that both auditory hindsight bias and repetition priming contribute to a common process, which we propose involves a misattribution of processing fluency. We conclude that misattribution of fluency accounts for auditory hindsight bias.

Correction: Transcranial direct current stimulation (tDCS) facilitates overall visual search response times but does not interact with visual search task factors.

[This corrects the article DOI: 10.1371/journal.pone.0194640.].

Transcranial direct current stimulation (tDCS) facilitates overall visual search response times but does not interact with visual search task factors.

Whether transcranial direct current stimulation (tDCS) affects mental functions, and how any such effects arise from its neural effects, continue to be debated. We investigated whether tDCS applied over the visual cortex (Oz) with a vertex (Cz) reference might affect response times (RTs) in a visual search task. We also examined whether any significant tDCS effects would interact with task factors (target presence, discrimination difficulty, and stimulus brightness) that are known to selectively influence one or the other of the two information processing stages posited by current models of visual search. Based on additive factor logic, we expected that the pattern of interactions involving a significant tDCS effect could help us colocalize the tDCS effect to one (or both) of the processing stages. In Experiment 1 (n = 12), anodal tDCS improved RTs significantly; cathodal tDCS produced a nonsignificant trend toward improvement. However, there were no interactions between the anodal tDCS effect and target presence or discrimination difficulty. In Experiment 2 (n = 18), we manipulated stimulus brightness along with target presence and discrimination difficulty. Anodal and cathodal tDCS both produced significant improvements in RTs. Again, the tDCS effects did not interact with any of the task factors. In Experiment 3 (n = 16), electrodes were placed at Cz and on the upper arm, to test for a possible effect of incidental stimulation of the motor regions under Cz. No effect of tDCS on RTs was found. These findings strengthen the case for tDCS having real effects on cerebral information processing. However, these effects did not clearly arise from either of the two processing stages of the visual search process. We suggest that this is because tDCS has a DIFFUSE, pervasive action across the task-relevant neuroanatomical region(s), not a discrete effect in terms of information processing stages.

The locus of taboo context effects in picture naming.

Speakers respond more slowly when naming pictures presented with taboo (i.e., offensive/embarrassing) than with neutral distractor words in the picture-word interference paradigm. Over four experiments, we attempted to localize the processing stage at which this effect occurs during word production and determine whether it reflects the socially offensive/embarrassing nature of the stimuli. Experiment 1 demonstrated taboo interference at early stimulus onset asynchronies of -150 ms and 0 ms although not at 150 ms. In Experiment 2, taboo distractors sharing initial phonemes with target picture names eliminated the interference effect. Using additive factors logic, Experiment 3 demonstrated that taboo interference and phonological facilitation effects do not interact, indicating that the two effects originate at different processing levels within the speech production system. In Experiment 4, interference was observed for masked taboo distractors, including those sharing initial phonemes with the target picture names, indicating that the effect cannot be attributed to a processing level involving responses in an output buffer. In two of the four experiments, the magnitude of the interference effect correlated significantly with arousal ratings of the taboo words. However, no significant correlations were found for either offensiveness or valence ratings. These findings are consistent with a locus for the taboo interference effect prior to the processing stage responsible for word form encoding. We propose a pre-lexical account in which taboo distractors capture attention at the expense of target picture processing due to their high arousal levels.

Locus of word frequency effects in spelling to dictation: Still at the orthographic level!

The present study was aimed at testing the locus of word frequency effects in spelling to dictation: Are they located at the level of spoken word recognition (Chua & Rickard Liow, 2014) or at the level of the orthographic output lexicon (Delattre, Bonin, & Barry, 2006)? Words that varied on objective word frequency and on phonological neighborhood density were orally presented to adults who had to write them down. Following the additive factors logic (Sternberg, 1969, 2001), if word frequency in spelling to dictation influences a processing level, that is, the orthographic output level, different from that influenced by phonological neighborhood density, that is, spoken word recognition, the impact of the 2 factors should be additive. In contrast, their influence should be overadditive if they act at the same processing level in spelling to dictation, namely the spoken word recognition level. We found that both factors had a reliable influence on the spelling latencies but did not interact. This finding is in line with an orthographic output locus hypothesis of word frequency effects in spelling to dictation. (PsycINFO Database Record

The benefit of no choice: goal-directed plans enhance perceptual processing

Choosing among different options is costly. Typically, response times are slower if participants can choose between several alternatives (free-choice) compared to when a stimulus determines a single correct response (forced-choice). This performance difference is commonly attributed to additional cognitive processing in free-choice tasks, which require time-consuming decisions between response options. Alternatively, the forced-choice advantage might result from facilitated perceptual processing, a prediction derived from the framework of implementation intentions. This hypothesis was tested in three experiments. Experiments 1 and 2 were PRP experiments and showed the expected underadditive interaction of the SOA manipulation and task type, pointing to a pre-central perceptual origin of the performance difference. Using the additive-factors logic, Experiment 3 further supported this view. We discuss the findings in the light of alternative accounts and offer potential mechanisms underlying performance differences in forced- and free-choice tasks.

Anticipation of visual form independent of knowing where the form will occur

We investigated how selective preparation for specific forms is affected by concurrent preknowledge of location when upcoming visual stimuli are anticipated. In three experiments, participants performed a two-choice response time (RT) task in which they discriminated between standard upright and rotated alphanumeric characters while fixating a central fixation cross. In different conditions, we gave the participants preknowledge of only form, only location, both location and form, or neither location nor form. We found main effects of both preknowledge of form and preknowledge of location, with significantly lower RTs when preknowledge was present than when it was absent. Our main finding was that the two factors had additive effects on RTs. A strong interaction between the two factors, such that preknowledge of form had little or no effect without preknowledge of location, would have supported the hypothesis that form anticipation relies on depictive, perception-like activations in topographically organized parts of the visual cortex. The results provided no support for this hypothesis. On the other hand, by an additive-factors logic Sternberg (Sternberg, Acta Psychologica 30:276-315, 1969), the additivity of our effects suggested that preknowledge of form and location, respectively, affected two functionally independent, serial stages of processing. We suggest that the two stages were, first, direction of attention to the stimulus location and, subsequently, discrimination between upright and rotated stimuli. Presumably, preknowledge of location advanced the point in time at which attention was directed at the stimulus location, whereas preknowledge of form reduced the time subsequently taken for stimulus discrimination.

Modules and brain mapping

This review highlights the key role of modularity and the additive factors method in functional neuroimaging. Our focus is on structure–function mappings in the human brain and how these are disclosed by brain mapping. We describe how modularity of processing (and possibly processes) was a key point of reference for establishing functional segregation as a principle of brain organization. Furthermore, modularity plays a crucial role when trying to characterize distributed brain responses in terms of functional integration or coupling among brain areas. We consider additive factors logic and how it helped to shape the design and interpretation of studies at the inception of brain mapping, with a special focus on factorial designs. We look at factorial designs in activation experiments and in the context of lesion–deficit mapping. In both cases, the presence or absence of interactions among various experimental factors has proven essential in understanding the context-sensitive nature of distributed but modular processing and discerning the nature of (potentially degenerate) structure–function relationships in cognitive neuroscience.

Trust my face: Cognitive factors of head fakes in sports.

In many competitive sports, players try to deceive their opponents about their behavioral intentions by using specific body movements or postures called fakes. For example, fakes are performed in basketball when a player gazes in one direction but passes or shoots the ball in another direction to avert efficient defense actions. The present study aimed to identify the cognitive processes that underlie the effects of fakes. The paradigmatic situation studied was the head fake in basketball. Observers (basketball novices) had to decide as quickly as possible whether a basketball player would pass a ball to the left or to the right. The player's head and gaze were oriented in the direction of an intended pass or in the opposite direction (i.e., a head fake). Responding was delayed for incongruent compared to congruent directions of the player's gaze and the pass. This head fake effect was independent of response speed, the presence of a fake in the immediately preceding trial, and practice with the task. Five further experiments using additive-factors logic and locus-of-slack logic revealed a perceptual rather than motor-related origin of this effect: Turning the head in a direction opposite the pass direction appears to hamper the perceptual encoding of pass direction, although it does not induce a tendency to move in the direction of the head's orientation. The implications of these results for research on deception in sports and their relevance for sports practice are discussed.

Automatic sequential response priming and intentional response preparation in choice reaction tasks: Evidence from response repetition and response cuing

This study examined the interaction of response repetition and response cuing in a finger cuing task with a short and a long cue-stimulus interval (CSI). We observed shorter reaction times (RTs) with increasing CSI and a substantial response repetition benefit. However, this benefit was abolished at the long CSI, suggesting that response cuing neutralized the repetition effect. According to additive-factors logic, the observed interaction suggests that both repetition and cuing exert their influence on a common processing stage, which we identify as the response selection stage. We argue that cuing and repetition effects are expressions of distinct mental operations: cuing is based on intentional response code activation, whereas repetition is based on sequential, automatic response code priming. Cue-based intentional code activation starts slowly and increases with CSI, but sequential response priming is independent of CSI, explaining why cuing abolishes the response repetition benefit at the long CSI.

Selective effects of partial striatal 6‐OHDA lesions on information processing in the rat

The present study was aimed at characterizing the cognitive deficits caused by the degeneration of nigrostriatal dopamine (DA) pathways by using the additive factor logic [Sternberg, S. (1969) Acta Psychol., 30, 276-315], a powerful reaction time (RT) method developed in humans and recently introduced in the rat [Courtiere, A., Hardouin, J., Hasbroucq, T., Possamai, C.-A. & Vidal, F. (2000) Behav. Process., 50, 113-121]. Long-Evans rats were trained to respond to left or right (lateral) visual cues in a choice RT task. Two task factors, signal intensity and force requirement, were manipulated. Partial bilateral 6-OHDA lesions of DA nerve terminals in the striatum were then performed and their effects tested for up to 7 weeks following surgery. Reaction time was lengthened from the 2nd to the 4th week postlesion. This alteration was independent of force requirement, thereby suggesting that the related motor processes were not influenced by the DA depletion. During the 2nd week postlesion, the RT increase was accompanied by a disappearance of the effect of signal intensity, showing that the lesion altered stimulus-related processes. From the 3rd week the signal intensity effect was re-established although RT was still increased, indicating that the stimulus-related processes had recovered while other central processes were still impaired. From the 5th week after surgery, the lesioned animals had completely recovered from the RT deficits induced by the lesion. These results point at the involvement of striatal DA in sensory and central information processes.

The exhaustive additivity displayed by nitrous oxide has implications for cognitive-energetical theory

The cognitive-energetical approach, which relies on the discrete stage model of additive factors logic, asserts that basal energetical mechanisms such as arousal act via particular information processing stages. The anaesthetic gas nitrous oxide (N 2O) produces additivity at four of the five perceptual and central stages, but its effect on the remaining stage, feature extraction, is unknown. We investigated this stage using 12 subjects who performed a visual oddball experiment in which two levels of stimulus quality, three levels of breathing mixture (air, 25% and N 2O, 35%) and three levels of stimulus probability were combined factorially. Reaction time (RT) and P300 were collected simultaneously. The RT results showed additivity between N 2O, stimulus quality and probability. P300 latency also showed additivity between N 2O and stimulus quality. Since the discrete stage model cannot easily account for the exhaustive additivity displayed by N 2O on perceptual and central stages, we performed a continuous cascade model simulation to determine whether it is better able to account for this phenomenon. We found that exhaustive additivity could be reproduced by adding a time delay to the activation rate of the first stage, which we interpreted as evidence that N 2O causes slowing prior to stage processing. To account for these results, we propose a two-tiered energetical model in which a lower GABAergic reticular system (influenced by N 2O) modulates the activity of upper ‘arousal-like’ multidimensional ascending thalamocortical systems. The applicability of this model to drugs such as the barbiturates, the benzodiazepines and ethanol, as well as the aging process, is discussed.

On the locus of the word frequency effect in visual word recognition.

Abstract The pattern of factor effects on response time (RT) performance in multi-factor experiments provides a powerful technique for inferring the structure of underlying mental processes. The results of the present lexical decision experiment show that additive effects of stimulus quality and word frequency are observed in mean RTs, variances, and the exGaussian parameters of the RT distribution. These findings are consistent with the conclusion that word frequency and stimulus quality affect separate stages of processing. This is consistent with the conclusion that word frequency effects reflect mapping operations between stages, but, when taken in conjunction with other reports in the literature, is inconsistent with the received view in many activation models that word frequency exerts its effect within the word detector level of representation. Resume Le schema des effets du facteur sur l'execution du temps de reponse (TR) dans les experiences a multiples facteurs fournissent une technique efficace pour fixer la structure des processus mentaux sous-jacents. Les resultats de la presente experience de decision lexicale montrent que les effets additifs de la qualite du stimulus et de la frequence du mot sont observes dans les TR moyens, les variances et les parametres ex-gaussiens de la distribution du TR. Ces conclusions confirment que la frequence du mot et la qualite du stimulus influencent les phases separees du traitement. Elles confirment egalement que les effets de la frequence du mot refletent les operations de correspondance entre les phases, mais, lorsque comparees a d'autres rapports, les conclusions ne correspondent pas a la vision etablie dans plusieurs modeles d'activation qui veut que la frequence du mot exerce ses effets au niveau de representation du detecteur du mot. It is well established that a word's frequency of occurrence in printed English is a strong determinant of performance in word recognition tasks such as lexical decision. For example, high frequency words such as CAT are typically recognized more quickly than lower frequency words such as VAT (e.g., Forster & Chambers, 1973; Frederiksen & Kroll, 1976; see also Monsell, 1991, for a review). One account of this word frequency effect is given by a number of models in the Activation class. Thus, models such as Morton's (1969) logogen model and variants of McClelland and Rumelhart's (1981) interactiveactivation model (e.g., Coltheart, Curtis, Atkins, & Haller, 1993; Grainger & Jacobs, 1996) all assume a word level of representation in the form of orthographic and phonological word detectors for each word the reader knows. These word detectors accumulate activation over time, and both models assume that low frequency words take longer to reach a threshold than do high frequency words. The models differ in that the interactive-activation model assumes that high frequency words start with a higher resting level of activation than do low frequency words whereas the logogen model assumes a common resting level of activation but different recognition thresholds for high and low frequency words One difficulty with the activation explanation is that a simple main effect of word frequency in lexical decision does not allow one to determine the locus of the effect; it merely informs us that word frequency affects performance in this task. A number of investigators have therefore applied Sternberg's (1969) additive factors logic to this issue by manipulating word frequency in conjunction with other factors that affect performance in lexical decision because predictions can be derived from the models as to how the effects of these factors on response time (RT) should combine (e.g., Becker & Killion, 1977; Besner & Smith, 1992; Besner & Swan, 1982). WORD FREQUENCY, STIMULUS QUALITY, AND CONTEXT It is well documented that stimulus quality affects word recognition: Clearly presented stimuli are recognized more quickly than degraded ones. …

Limits on the application of additive factors logic: Violations of stage robustness suggest a dual-process architecture to explain flanker effects on target processing

This study aimed to establish whether the logic of the AFM applies when multielement stimuli contain relevant and irrelevant elements. Target Size (TS) and symbolic S-R Compatibility (SRC) were manipulated in three reaction time (RT) experiments. TS and SRC are assumed in the AFM literature to selectively influence the independent stages of feature extraction and S-R translation, respectively. Experiment 1 showed that the effects of TS and SRC on RT were additive when the target was presented in isolation and this additive relation was not changed when the target was flanked by stimuli that contained no information relevant to the response. In Experiment 2, this additivity changed into a superadditive interaction when flankers signaled the same response as the target: The effect of SRC was larger when targets were small rather than large. The overall pattern of findings violated the AFM stage robustness criterion. Neither a discrete stage model nor a continuous flow conception account for the results. To explain flanker effects on target processing a dual-process architecture was formulated that assumes that perceptual information is processed along concurrently engaged routes: An attentive processing route and a direct priming route. Experiment 3 confirmed the prediction of the dual-process model that the relation between TS and SRC would be subadditive when flankers signal the response opposite to that designated by the target.

Adult age differences in the inhibition of return of visual attention.

Responses to targets are slower when they appear at a location to which attention has previously been directed than when they appear at other locations. This inhibition of return (IOR) effect is subserved by posterior brain attentional systems. In 4 experiments the IOR effect in elderly adults was found to be at least as large as in young adults for both discrimination tasks and for detection tasks. The time course and the spread of inhibition within the visual field were also equivalent in the 2 age groups. Additive factors logic was then used to test the hypothesis that the Stroop and IOR effects are due to a common mechanism, a failure to suppress attention. This hypothesis was not confirmed. The results of the 6 experiments are consistent with the hypothesis that there are changes in posterior brain systems responsible for selective attention to a location, contrary to prior claims. They cannot be explained by a general slowing of processing in old age.