Magnitude Judgments Research Articles

Integrating randomized controlled trials and non-randomized studies of interventions to assess the effect of rare events: a Bayesian re-analysis of two meta-analyses

BackgroundThere is a growing trend to include non-randomised studies of interventions (NRSIs) in rare events meta-analyses of randomised controlled trials (RCTs) to complement the evidence from the latter. An important consideration when combining RCTs and NRSIs is how to address potential bias and down-weighting of NRSIs in the pooled estimates. The aim of this study is to explore the use of a power prior approach in a Bayesian framework for integrating RCTs and NRSIs to assess the effect of rare events.MethodsWe proposed a method of specifying the down-weighting factor based on judgments of the relative magnitude (no information, and low, moderate, serious and critical risk of bias) of the overall risk of bias for each NRSI using the ROBINS-I tool. The methods were illustrated using two meta-analyses, with particular interest in the risk of diabetic ketoacidosis (DKA) in patients using sodium/glucose cotransporter-2 (SGLT-2) inhibitors compared with active comparators, and the association between low-dose methotrexate exposure and melanoma.ResultsNo significant results were observed for these two analyses when the data from RCTs only were pooled (risk of DKA: OR = 0.82, 95% confidence interval (CI): 0.25–2.69; risk of melanoma: OR = 1.94, 95%CI: 0.72–5.27). When RCTs and NRSIs were directly combined without distinction in the same meta-analysis, both meta-analyses showed significant results (risk of DKA: OR = 1.50, 95%CI: 1.11–2.03; risk of melanoma: OR = 1.16, 95%CI: 1.08–1.24). Using Bayesian analysis to account for NRSI bias, there was a 90% probability of an increased risk of DKA in users receiving SGLT-2 inhibitors and an 91% probability of an increased risk of melanoma in patients using low-dose methotrexate.ConclusionsOur study showed that including NRSIs in a meta-analysis of RCTs for rare events could increase the certainty and comprehensiveness of the evidence. The estimates obtained from NRSIs are generally considered to be biased, and the possible influence of NRSIs on the certainty of the combined evidence needs to be carefully investigated.

Beyond fixed sets: boundary conditions for obtaining SNARC-like effects with continuous semantic magnitudes.

Previous research has demonstrated the presence of an effect (i.e., the spatial-numerical association of response codes or SNARC) in both numerical parity and magnitude judgment tasks in which smaller numerical magnitudes are manually responded to faster on the left side and larger numerical magnitudes on the right side. Such a result has typically been attributed to a spatially based representation of numerical magnitude in long-term memory, the format of which has recently been postulated to be positional in line with learning of a canonically ordered number sequence. As a test of this view, in the current research, participants made classification judgments involving either the size (N = 88) or the living-nonliving status (N = 114) corresponding to the names of animals/objects etc. to which no learned canonical ordering of size exists. Names were taken from a very large set of 400 animals/objects etc. and each name was presented only once in an experimental session. Responses were made using left and right manual keypresses. In this work, the relation between response time and the relative sizes of the animals/objects did not differ across the left-right side of response indicating that SNARC-like effects did not occur. As such, the results suggest that space is not an inherent aspect of the long-term representation of magnitude in the brain and that some form of positional coding of magnitude is necessary for SNARC-like effects to occur.

Magnitude Judgements Are Influenced by the Relative Positions of Data Points Within Axis Limits

Magnitude Judgements Are Influenced by the Relative Positions of Data Points Within Axis Limits

Cognitive processes that underlie mathematically gifted emergent bilinguals

The purpose of this study was to determine those cognitive measures that increase the likelihood of identifying mathematically gifted students who are emerging bilinguals. Elementary school children (Grades 1, 2, and 3) were administered a battery of math, vocabulary, reading, and cognitive measures (short-term memory, inhibition, and working memory in their first language (L1: Spanish) and second language (L2: English). Multilevel polytomous logistic modeling compared mathematically gifted children with children who were average math achievers or low math achievers. The results indicated that cognitive parameters that included estimation and working memory in the L2 and problem-solving in the L1 were unique predictors that significantly influenced whether a child was categorized as gifted relative to average achievers. Relative to average achievers, L2 parameters (magnitude judgment) and English reading were significantly related to the identification of children with low math computation. The results are discussed in terms of a multidimensional model that taps domain-specific skills and general cognitive processes that increase the ability to correctly identify children who score in the gifted range in both their L1 and L2.

Category versus labeled magnitude scale measures of immediate conscious leisure experiences: Engagement, immersion, and absorption

We developed and validated single-item category (CAT) and labeled magnitude (LM) scales of three recalled immediate conscious leisure experiences: engagement, immersion, and absorption. These minimally invasive scales are suitable for use in experiments, surveys, and evaluations in the travel and leisure industries. The CAT scales followed a familiar Likert-type format, while the LM scales involved calibration by 169 judges using two modalities (drawing lines of differing lengths and providing numeric magnitude judgments) to establish empirically determined ratio-scaled distances among seven modifiers (not at all, slightly, somewhat, quite, very, greatly, and extremely). We collected 3,821 experience observations from 621 visitors to entertainment, recreation, and tourism venues using both scales. Theoretical determinants and results of engagement, immersion, and absorption were measured. Results supported the validity of both scales. LM measures are preferred because they reduced halo effects, generated greater variance, and provided ratio-level measures of intensity of the three immediate conscious experiences.

Functional Near-Infrared Spectroscopy Evidence of Prefrontal Regulation of Cognitive Flexibility in Adults With ADHD

Background: Executive function (EF) deficit is considered to be a core cognitive deficit in ADHD. The current study combined functional near-infrared spectroscopy (fNIRS) and numerical switching tasks to investigate the cognitive flexibility of adult ADHD as an important part of EF. Material and Methods: The Wender Utah Rating Scale and the adult ADHD self-rating scale were respectively used to assess ADHD symptoms in childhood and adulthood. A 22 adults with ADHD and 24 healthy controls (HCs) participated in the large/small and odd/even switching tasks. Results: Behavioral results were indicative of the ADHD switch costs being lower than the HCs. The fNIRS results also showed that ADHD’s frontal eye field was over-activated both in magnitude and switched judgment tasks. The dorsolateral prefrontal cortex was also over-activated in magnitude judgment tasks. Conclusion: These results revealed that adults with ADHD’s cognitive flexibility performed better than the HCs, which result is different from mainstream ideas that EF is a core deficit in ADHD.

Frontal Atrophy and Executive Dysfunction Relate to Complex Numbers Impairment in Progressive Supranuclear Palsy.

Previous research finds a range of numbers impairments in Parkinsonian syndromes (PS), but has largely focused on how visuospatial impairments impact deficits in basic numerical processes (e.g., magnitude judgments, chunking). Differentiation between these basic functions and more complex numerical processes often utilized in everyday tasks may help elucidate neurocognitive and neuroanatomic bases of numbers deficits in PS. To test neurocognitive and neuroanatomic correlates of complex numerical processing in PS, we assessed number abilities, neuropsychological performance, and cortical thickness in progressive supranuclear palsy (PSP) and Lewy body spectrum disorders (LBSD). Fifty-six patients (LBSD = 35; PSP = 21) completed a Numbers Battery, including basic and complex numerical tasks. The Mini-Mental State Exam (MMSE), letter fluency (LF), and Judgment of Line Orientation (JOLO) assessed global, executive, and visuospatial functioning respectively. Mann-Whitney U tests compared neuropsychological testing and rank-transformed analysis of covariance (ANCOVA) compared numbers performance between groups while adjusting for demographic variables. Spearman's and partial correlations related numbers performance to neuropsychological tasks. Neuroimaging assessed cortical thickness in disease groups and demographically-matched healthy controls. PSP had worse complex numbers performance than LBSD (F = 6.06, p = 0.02) but similar basic numbers performance (F = 0.38, p > 0.1), covarying for MMSE and sex. Across syndromes, impaired complex numbers performance was linked to poor LF (rho = 0.34, p = 0.01) but not JOLO (rho = 0.23, p > 0.05). Imaging revealed significant frontal atrophy in PSP compared to controls, which was associated with worse LF and complex numbers performance. PSP demonstrated selective impairments in complex numbers processing compared to LBSD. This complex numerical deficit may relate to executive dysfunction and frontal atrophy.

Is the Discount Really Favorable? The Effect of Numeracy on Price Magnitude Judgment: Evidence From Electroencephalography.

Attractive price promotion will induce an unreasonable willingness to purchase, especially through shopping. However, it is not clear how numeracy, one of the essential abilities for understanding and applying numbers, influences the process of purchase judgment. In total, 61 participants were recruited to perform a price promotion task using electroencephalography. The results showed that consumers with low numeracy performed worse than their peers with high numeracy at the behavioral level, and they also had lower P3b amplitude and less alpha desynchronization, regardless of price promotion frameworks. These findings provided evidence on the processing of price information and provided further insights into how numeracy impacts price magnitude judgment.

Impact of hierarchical processing levels on division of labor: neural electrophysiological evidence from a joint rule shifting.

Although previous studies have revealed the behavioral and neural mechanisms underlying cognitive control, the neural electrophysiological process in joint task switching has rarely been discussed. Moreover, the hierarchy process remains unclear. Therefore, the present study aimed to explore the neural mechanism of a target when two actors use division of labor between action selections in a joint hierarchical rule-shifting situation. The present study employed a joint hierarchical rule shifting paradigm, and each participant was responsible for the selection of one type of action (left key and right key). The cue was the letter 'R' with three features, which indicated the hierarchical rule of the current trial. The target was an Arabic numeral (1-9, except 5). Participants made a magnitude judgement or a parity judgment based on the high and low hierarchical features of cues. The P2 component was smaller in the high-shift condition than in the repeat condition; however, the high-shift condition elicited a larger N2 amplitude than the low-shift and repeat conditions. We believe that the current P2 is related to selective attention to the hierarchical features of rules, and N2 is related to conflict control. In addition, the high-shift condition had the largest P3 amplitude, which indicates that this condition has the largest extent of update and leads to the most unstable association between rule and stimuli. The study demonstrated that participants had dynamic brain responses to target stimuli in the joint rule-shifting situation. In other words, participants first confirmed the actor of the current target and then processed the target stimuli themselves.

The impact of musical training in symbolic and non-symbolic audiovisual judgements of magnitude.

Quantity estimation can be represented in either an analog or symbolic manner and recent evidence now suggests that analog and symbolic representation of quantities interact. Nonetheless, those two representational forms of quantities may be enhanced by convergent multisensory information. Here, we elucidate those interactions using high-density electroencephalography (EEG) and an audiovisual oddball paradigm. Participants were presented simultaneous audiovisual tokens in which the co-varying pitch of tones was combined with the embedded cardinality of dot patterns. Incongruencies were elicited independently from symbolic and non-symbolic modality within the audio-visual percept, violating the newly acquired rule that “the higher the pitch of the tone, the larger the cardinality of the figure.” The effect of neural plasticity in symbolic and non-symbolic numerical representations of quantities was investigated through a cross-sectional design, comparing musicians to musically naïve controls. Individual’s cortical activity was reconstructed and statistically modeled for a predefined time-window of the evoked response (130–170 ms). To summarize, we show that symbolic and non-symbolic processing of magnitudes is re-organized in cortical space, with professional musicians showing altered activity in motor and temporal areas. Thus, we argue that the symbolic representation of quantities is altered through musical training.

The rich-get-richer effect: Prior knowledge predicts new learning of domain-relevant information.

When learning new information, students' prior knowledge related to that information will often vary. Prior research has not systematically explored how prior knowledge relates to learning of new, previously unknown information. Accordingly, the goal of the present research was to explore this relationship. In three experiments, students first completed a prior knowledge test over two domains (football and cooking) and then learned new information from these domains by answering questions and receiving feedback. Students also made a judgment of learning for each. To ensure that the learning was new (i.e., previously unknown) for all students, the to-be-learned information was false. Last, students completed a final test over the same questions from the learning phase. Prior knowledge in each domain was positively related to new learning for items from that domain but not from the other domain. Thus, the relationship between prior knowledge and new learning was domain specific, which we refer to as the rich-get-richer effect. Prior knowledge was also positively related to the magnitude of judgments of learning. In Experiment 3, to explore a potential reason why prior knowledge is related to new learning, students rated their curiosity in learning each item prior to receiving feedback. Critically, students' curiosity judgments mediated the relationship between prior knowledge and new learning. These outcomes suggest that for high-knowledge learners, curiosity may be related to attention-based mechanisms that increase the effectiveness of encoding during feedback. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

An Event-Related Potential Study on Differences Between Higher and Lower Easy of Learning Judgments: Evidence for the Ease-of-Processing Hypothesis.

Easy of learning (EOL) judgments occur before active learning begins, and it is a prediction of how difficult it will be to learn new material in future learning. This study compared the amplitude of event-related potential (ERP) components and brain activation regions between high and low EOL judgments by adopting ERPs with a classical EOL judgment paradigm, aiming to confirm the ease-of-processing hypothesis. The results showed that (1) the magnitudes of EOL judgments are affected by encoding fluency cues, and the judgment magnitude increases with encoding fluency; (2) low EOL judgments are associated with higher N400 amplitude at the left superior frontal gyrus (SFG) and left middle frontal gyrus (MFG). High EOL judgments showed enlarged slow-wave (600–1,000 ms) potentials than low EOL judgments at the left medial temporal lobe (MTL), right ventromedial prefrontal cortex (VMPFC), and dorsolateral prefrontal cortex (DLPFC). Our results support the ease-of-processing hypothesis, particularly, by affirming that EOL judgments are affected by encoding fluency in two processing stages. N400 reflects the process of acquiring encoding fluency cues, while slow-wave indicates that individuals use encoding fluency cues for metacognitive monitoring.

Cognitive and academic growth among emergent bilingual children at risk and not at risk for math difficulties

One purpose of this study was to identify cognitive processes within the English (second language [L2]) and Spanish (first language [L1]) language systems that underlie growth in math problem solving among emergent bilingual (EB) children with and without math difficulties (MD). A second purpose was to determine those L1 cognitive processes that play an essential role in predicting math word-problem-solving difficulties. To this end, children (N = 275; children with MD = 90) in Grades 1, 2, and 3 at Wave 1 were administered a battery of math, reading, vocabulary, and cognitive (short-term memory [STM], working memory [WM], rapid naming, and inhibition) measures. The battery of tests was administered again 1 year and 2 years later to the same participants. Three findings were important. First, multilevel logistic modeling suggested that the log-odds of identifying children with MD were best captured by the level of performance on measures of fluid intelligence, Spanish STM, and English WM. Second, the log-odds of identifying children with MD were uniquely related to growth on WM, computation, and number magnitude judgment measures. Finally, the level of performance on L1 measures of reading, calculation, and naming speed and inhibition facilitated the identification of children with MD. In contrast, growth on all Spanish measures, except vocabulary and estimation, increased the log-odds of identifying children with MD. In general, the results suggest that there are constraints or inefficiencies in cognitive processes within and across both language systems that underlie the development of EB children’s MD. The results highlight the importance of the phonological and executive systems of WM as important predictors of EB children’s math problem-solving difficulties.

Location, location, location: When and how low price locations improve consumer price perceptions

AbstractDoes seeing a price in a physically low (vs. high) location prompt consumers to believe that the featured product is less costly? Recent research supports this possibility by showing that low price locations trigger “down=less” metaphors which prompt price perceptions that are monetarily “low” in magnitude. Extending such work, we offer a two‐stage model to account for price location effects and examine theoretically‐relevant moderators that influence the likelihood of “down=less” metaphors being activated (Stage 1) and being mapped onto a price magnitude judgment (Stage 2). Results demonstrate that price location effects will emerge under conditions where consumers (a) experience feelings of high (vs. low) power that encourage metaphor activation and (b) possess a high (vs. low) need for structure that encourages the mapping, or transfer, of these metaphors onto a price judgment mapping. A final study shows that “down=less” metaphorical influences do not affect price magnitude judgments in the presence of factors that inhibit either metaphor activation (i.e., feelings of low power) or mapping (i.e., a low need for structure). By identifying these contingencies, this research further specifies when price location effects are likely to arise, increasing our understanding of pricing in general and this locational phenomenon in particular.

The Effect of Verbal Task Instruction on Spatial-Numerical Associations of Response Codes Effect Coding of Spatial-Numerical Associations: Evidence From Event-Related Potential.

The spatial-numerical associations of response codes (SNARC) effect reveals that individuals can represent numbers spatially. In this study, event-related potential (ERP) technology was used to probe the effect of verbal-spatial task instructions on spatial-numerical association coding by using digit parity and magnitude judgment tasks, with the numbers 1–9 (except 5) and Chinese word labels (“left” and “right”) as experimental materials. The behavioral results of Experiment 1 showed that the SNARC effect was mainly based on verbal-spatial coding and appeared when the stimulus onset asynchrony (SOA) between the presentation of the verbal labels and the target digit was 0 ms. ERP results did not reveal any significant SNARC-related effects in either the N1 or P3 components. The behavioral results of Experiment 2 again showed that the SNARC effect was dominated by verbal-spatial coding. ERP results showed that significant effects related to verbal-spatial coding were found in both the early positive deflection of the stimulus-locked lateralized readiness potential (S-LRP) and the latency of the response-locked LRP (R-LRP). Hence, in this study, the nature of the spatial coding of the digit magnitudes was influenced by the processing of the word labels and affected both the response selection and response preparation stages.

The Off by 100% Bias: The Effects of Percentage Changes Greater than 100% on Magnitude Judgments and Consumer Choice

Abstract Percentage changes greater than 100% are frequently used in consumer contexts; for example, a cordless vacuum cleaner may boast “125% longer runtime” compared to competitors. Via six studies (n = 2,395) and 11 supplementary studies (n = 3,249), the current research shows that consumers systematically underestimate the magnitude of percentage changes greater than 100%. Specifically, many consumers apply the relative size usage (e.g., “125% of,” equivalent to 25% more) instead of the appropriate relative change (e.g., “125% more,” equivalent to 100% more + 25% more), which leads them to be off by exactly 100% in their magnitude estimates. The rate of bias decreases when the difference between these two usages is emphasized. The Off by 100% bias occurs across a variety of consumer contexts, influencing behavioral intentions and incentive-compatible choice. The findings make theoretical contributions to research on processing of percentages, probability versus frequency formats, and magnitude judgments. Finally, understanding how different presentation formats of the same information can lead to different magnitude judgments enables marketers and policymakers to ensure more effective communication.

Selective interference of hand posture with grasping capability estimation.

Previous studies have shown that judgments about how one would perform an action are affected by the current body posture. Hence, judging one's capability to grasp an object between index and thumb is influenced by their aperture at the time of the judgment. This finding can be explained by a modification of the internal representation of one's hand through the effect of sensorimotor input. Alternatively, the influence of grip aperture might be mediated by a response congruency effect, so that a "less" vs. "more" open grip would bias the judgment toward a "less" vs. "more" capable response. To specify the role of sensorimotor input in prospective action judgments, we asked participants to estimate their capability to grasp circles between index and thumb while performing a secondary task that requires them to squeeze a ball with these two fingers (precision grip) or with a different hand configuration (palm grip). Experiment 1 showed that participants underestimated their grasping capability when the squeezing task involved the same grip as the judged action (precision grip) and their estimates were bound to the relative size of objects as revealed by size-contrast illusions (Ebbinghaus). Experiment 2 showed that the grip reduction caused by the squeezing task also interfered with the discrimination of large numbers in magnitude judgments, but this incongruency effect was only observed for the palm grip. The dissociated effects of the two grips in graspability and numerical judgments indicate that sensorimotor input may affect the perceived ability to grasp objects, independently of response congruency, by modifying the representation of the hand in action.

So you think you can read? Generalized metacomprehension in younger and older adults

ABSTRACT This study explored whether age differences in task-specific metacomprehension accuracy are partly explained by age differences in generalized metacomprehension (GM) or the use of GM as a task-specific judgment anchor. GM was measured before and after a summarization and metacomprehension judgment task and then correlated with prediction judgment magnitude to assess anchoring, and correlated with comprehension and task-specific metacomprehension accuracy to assess GM accuracy. Age differences in these relationships were then tested. GM was related to judgment magnitude but despite age differences in GM ratings, age did not moderate anchoring or GM accuracy. Age differences in task-specific metacomprehension accuracy do not seem to be explained by age differences in GM accuracy or its use as a judgment anchor. However, results are the first to show that older adults anchor task-specific metacomprehension judgments on their GM, providing unique evidence for the Anchoring and Adjustment Model of Metacomprehension in advanced age.

Why Salespeople Avoid Big-Whale Sales Opportunities

Contrary to the intuition that salespeople gravitate toward big-whale sales opportunities, in reality they often avoid them. To study this phenomenon, the authors integrate contingent decision-making and conservation-of-resources theories to develop and test a framework of salespeople's decision making when prospecting. Study 1 reveals that the performance impact of salesperson initial judgment of opportunity magnitude follows an inverted U-shape, indicating that salespeople's avoidance of large opportunities results from rational benefit–cost analyses due to their conservation of resources. Interestingly, salespeople use a calibration decision-making strategy (i.e., calculating expected benefits by accounting for conversion uncertainty) at the portfolio rather than prospect level, in solution- but not product-selling contexts. Ignoring this calibration effect can lead to under- or overestimation of conversion rates of up to 100%. Study 2 shows that salespeople's past performance success and experience bias this calibration. Simulations reveal that when high performers or inexperienced salespeople believe their portfolio magnitude is large and conversion uncertainty low, they are less concerned about resource conservation and improve their quota attainment by 50%. Study 3 confirms the theoretical mechanism. These findings shed new light on salespeople's decision making and suggest ways for sales professionals to improve effectiveness when prospecting.

Flawed stimulus design in additive-area heuristic studies

In a series of recently published studies purportedly on the “additive-area heuristic,” Yousif & Keil (2019, 2020) argue for a systematic distortion in the perception of the cumulative area of an item array and further claim that previous findings of numerical cognition and magnitude perception in general are “at risk” (Yousif & Keil, 2021). This commentary describes serious stimulus design flaws present in all of Yousif and colleagues experiments that prevent from making such conclusions. Specifically, item arrays used in those studies demonstrate a skewed correlational structure between selected magnitude dimensions and exhibit unbalanced ranges across different magnitude dimensions of interest. Because the perception of magnitude dimensions interferes one another and because our perceptual system is sensitive to the statistical regularities of the sensory input, such a biased design makes it difficult, if not impossible, to interpret the choice behavior of an observer making magnitude judgments. By re-introducing the mathematical framework for a systematic construction of dot array stimuli (DeWind et al., 2015) and by re-analyzing the data from another recent study on area perception (Tomlinson et al., 2020), this paper explains—and introduces a MATLAB code for—an optimal method for designing and constructing dot arrays for magnitude perception studies.