Metaphor Strength (Up = More & Down = Less)

Abstract

The Metaphor Strength (Up = More & Down = Less) scale is a psychometric instrument designed to measure individual differences in the strength, accessibility, and cognitive endorsement of the primary conceptual metaphor mapping vertical spatial position to quantitative magnitude. Grounded in Conceptual Metaphor Theory and embodied cognition frameworks, the instrument captures the degree to which an individual systematically links upward verticality with abundance, higher numerical value, or greater physical magnitude, and downward verticality with scarcity, lower numerical value, or diminished physical magnitude. Originally developed and empirically validated within consumer psychology and behavioral decision research by Michael J. Barone, Keith S. Coulter, and Xingbo Li (2020), this measurement tool plays a pivotal role in explaining why visual, spatial, and environmental cues alter human judgments of magnitude, retail pricing, risk assessment, and resource allocation.

The scale consists of a multi-item psychometric battery evaluated across continuous subjective endorsement intervals, commonly implemented via 7-point Likert-type response formats ranging from strongly disagree to strongly agree, alongside semantic differential and spatial association tasks. Structurally, the instrument captures two closely coordinated conceptual dimensions: Upward-Augmentation Association (the mental mapping of upper physical bounds to elevated quantities, gains, and increases) and Downward-Diminution Association (the mental mapping of lower physical bounds to reduced quantities, discounts, and decreases). Empirical investigations reveal strong psychometric integrity, featuring high internal consistency (Cronbach’s alpha coefficients routinely exceeding .82, with composite reliability estimates surpassing .85), robust test-retest reliability across multiple measurement intervals, and clear evidence of convergent, discriminant, and predictive validity. Factor-analytic assessments confirm a coherent latent structure that moderates how spatial positioning on retail packaging, digital interfaces, and promotional signage systematically influences consumer price evaluations and perceived savings.

Keywords

Conceptual Metaphor Theory, Embodied Cognition, Spatial Verticality, Metaphor Strength, Numerical Cognition, Price Perception, Visual Merchandising, Spatial Cognition, Psychometrics, Magnitude Representation, Consumer Psychology

Authors

The conceptualization, operationalization, and empirical validation of the Metaphor Strength (Up = More & Down = Less) assessment protocol were established by a prominent team of researchers in marketing, consumer behavior, and cognitive decision sciences:

• Michael J. Barone, Ph.D. — Professor of Marketing, College of Business, University of Louisville, Louisville, Kentucky, United States. Dr. Barone is an internationally recognized scholar in consumer psychology, behavioral pricing, advertising effects, and retail strategy, with extensive publications in leading academic journals such as the Journal of Marketing Research, Journal of Consumer Research, and Journal of Retailing.
• Keith S. Coulter, Ph.D. — Professor of Marketing, Graduate School of Management, Clark University, Worcester, Massachusetts, United States. Dr. Coulter specializes in consumer numerical cognition, pricing psychology, non-conscious visual processing, and advertising communication strategies.
• Xingbo Li, Ph.D. — Associate Professor of Marketing, Department of Marketing, College of Business, University of Louisville, Louisville, Kentucky, United States. Dr. Li’s research focuses on sensory marketing, spatial perception, visual heuristics, and consumer inference-making processes in retail contexts.

Inquiries regarding the theoretical development and research applications of the scale may be directed to the corresponding authors through institutional affiliations or via publications in the Journal of Retailing.

Purpose

The primary purpose of the Metaphor Strength (Up = More & Down = Less) scale is to quantify individual variation in the cognitive binding between physical vertical space and abstract numerical magnitude. For decades, cognitive linguists, neuroscientists, and developmental psychologists have noted that human beings do not process abstract concepts in isolation; rather, they ground intangible conceptual targets (such as price, volume, prestige, and numerical value) in tangible sensory experiences (such as height, gravity, vertical accumulation, and physical level). While Conceptual Metaphor Theory posits that metaphors like “MORE IS UP” and “LESS IS DOWN” are universal across human languages and cultures, empirical research reveals meaningful variance in the chronic cognitive accessibility, functional strength, and situational activation of these metaphorical associations across individuals.

Understanding this individual heterogeneity is critical for multiple disciplines:

• Consumer Psychology and Retail Merchandising: The scale enables researchers to assess how visual layout configurations—such as placing a discount price at the bottom versus the top of an advertisement or product package—interact with an individual’s latent metaphor strength to alter price magnitude perceptions, perceived savings, deal evaluation, and purchase intentions.
• Behavioral Economics and Financial Decision-Making: The tool facilitates investigation into how investors and consumers interpret graphical displays of financial assets, wealth accumulation, portfolio volatility, and budget burn-rates based on visual coordinate axes.
• Human-Computer Interaction (HCI) and User Experience (UX) Design: The scale allows interface architects to understand whether vertical slider controls, dashboard gauges, and navigational hierarchies align with cognitive mental models, thereby reducing cognitive load and error rates in digital environments.
• Cognitive and Educational Psychology: The instrument serves as a diagnostic metric to analyze how children and adult learners develop spatial-numerical associations (e.g., mental number lines and vertical magnitude scaling) and how these cognitive architectures facilitate or hinder formal mathematical reasoning.

By providing a standardized, psychometrically rigorous instrument, researchers are empowered to move beyond universalist assumptions regarding spatial-semantic metaphors and treat metaphoric endorsement as an operationalized, quantifiable individual-difference variable. This paradigm provides rich explanatory power when determining who is susceptible to spatial framing effects, under what processing conditions spatial heuristics dominate rational computation, and how multi-sensory marketing displays interact with embodied mental structures.

Psychological Construct

The psychological construct operationalized by the Metaphor Strength (Up = More & Down = Less) scale is situated at the intersection of cognitive linguistics, sensory processing, and psychophysics. At its foundation, the construct reflects the psychological representation of quantitative magnitude through vertical spatial orientation. Rather than treating “up” and “down” merely as physical coordinates, human cognition systematically maps spatial coordinates onto abstract qualitative and quantitative domains.

The Dual Poles of the Construct

The construct encompasses two theoretically integrated, bidirectional mental mappings that operate simultaneously within an individual’s conceptual schema:

• Upward-Augmentation Alignment (MORE IS UP): This facet reflects the cognitive disposition to associate elevated physical positions, upward directional movements, and high vertical coordinates with concepts of enlargement, numerical superiority, expansion, increased expense, and premium value. For individuals high in this dimension, an upward spatial cue triggers an automatic spreading activation in semantic memory toward concepts denoting magnitude, wealth, gain, and heightened scale.
• Downward-Diminution Alignment (LESS IS DOWN): This facet captures the cognitive tendency to link lower physical positions, downward directional trajectories, and bottom vertical coordinates with ideas of reduction, numerical inferiority, scarcity, economic discounting, and diminished volume. A strong alignment in this dimension leads individuals to instinctively evaluate stimuli placed in lower spatial fields as physically or monetarily smaller, lighter, or less impactful.

Cognitive Mechanisms: Polarity Correspondence and Cross-Modal Mapping

The construct relies heavily on the psychological principle of polarity correspondence. In spatial cognition, “up” and “down” are not neutral endpoints; “up” represents the plus-polarity endpoint (+polar) characterized by perceptual dominance, visibility, and physical effort against gravity, whereas “down” represents the minus-polarity endpoint (-polar). Concurrently, in numerical cognition, “more” is +polar while “less” is -polar. Metaphor strength captures the subjective tightness of this cross-modal polarity congruence. When a person possesses high metaphor strength, the cognitive system exhibits high processing fluency when encountering congruent pairings (e.g., an expensive luxury price placed high on a visual display, or a discount price placed low) and cognitive friction or disfluency when encountering incongruent pairings.

Moreover, the construct is conceptualized as an individual difference trait that remains relatively stable across moderate periods of time, yet remains sensitive to situational priming. Individuals with high chronic metaphor strength do not merely acknowledge the linguistic idiom; they utilize the vertical coordinate system as a perceptual heuristic to infer value, weight, frequency, and magnitude when explicit semantic information is ambiguous, rapidly presented, or processed under high cognitive load.

Theoretical Framework

The theoretical architecture of the Metaphor Strength scale synthesizes several seminal paradigms from cognitive psychology, linguistics, and neuroscience.

Conceptual Metaphor Theory (CMT)

The foundational bedrock of this measurement tool rests upon the pioneering work of George Lakoff and Mark Johnson in their classic treatise Metaphors We Live By (1980). Lakoff and Johnson posited that human thought processes are predominantly metaphorical. According to CMT, humans understand abstract conceptual domains (target domains, such as quantity, morality, time, and emotional states) by mapping them onto concrete, sensorimotor domains (source domains, such as physical space, verticality, temperature, and weight).

The metaphor “MORE IS UP / LESS IS DOWN” is classified as an orientational metaphor. Lakoff and Johnson argued that this metaphor arises organically from universal physical experiences encountered in early developmental infancy: whenever one pours water into a glass, stacks books on a table, or adds wooden blocks to a tower, the rise in the physical level of the substance directly correlates with an increase in quantity. Through millions of repeated sensorimotor pairings, physical verticality and quantitative accumulation become co-activated in the neural architecture, forming enduring cognitive conduits. The Metaphor Strength scale directly measures the residual strength and psychological dominance of these neural mappings in adult decision-makers.

Embodied Cognition and Perceptual Symbol Systems

Complementing CMT is Lawrence Barsalou’s theory of Perceptual Symbol Systems (1999) and the broader doctrine of embodied cognition. Embodied cognition asserts that knowledge is not stored as amodal, abstract propositions in a central processing unit; rather, semantic retrieval and conceptual thinking involve the mental reactivation of sensory, motor, and affective states. When an individual processes numerical data, the brain re-enacts physical perceptions of height, volume, and gravitational resistance. The Metaphor Strength scale operationalizes the extent to which an individual’s cognitive architecture relies on these sensory re-enactments to interpret mathematical and economic parameters.

A Theory of Magnitude (ATOM)

In cognitive neuroscience, Vincent Walsh (2003) proposed A Theory of Magnitude (ATOM), which hypothesizes that space, time, and quantity are processed by a shared, generalized magnitude system localized in the parietal cortex—particularly within the intraparietal sulcus. According to ATOM, spatial representations and numerical values share common neural metric mechanisms designed to facilitate action planning. Barone, Coulter, and Li (2020) integrate this perspective by demonstrating that because spatial coordinates and numerical evaluations draw upon overlapping neural substrates, individuals with tightly bound spatial-numerical mappings demonstrate measurable shifts in quantitative evaluation when stimuli are vertically displaced.

Validity

The Metaphor Strength (Up = More & Down = Less) scale has undergone rigorous empirical validation across multiple experimental and psychometric investigations, demonstrating exceptional construct, convergent, discriminant, and predictive validity.

Construct Validity

Construct validity was established through confirmatory modeling assessing whether the scale’s items appropriately reflected the underlying latent construct without multidimensional distortion. Across exploratory factor analyses (EFA) and confirmatory factor analyses (CFA) conducted on independent consumer samples, items consistently loaded onto their hypothesized latent factors with high statistical significance (all standard factor loadings > .70, p < .001). The scale demonstrated high average variance extracted (AVE), regularly exceeding .60, which surpasses the classic benchmark of .50 articulated by Fornell and Larcker (1981), confirming that the items capture substantial variance attributable to the latent construct rather than measurement error.

Convergent Validity

Convergent validity has been substantiated through significant correlations with established measures of spatial-numerical association, embodied conceptual accessibility, and visual-spatial processing styles:

• Spatial-Numerical Association of Response Codes (SNARC Effect): Individuals scoring higher on the Metaphor Strength scale exhibit stronger vertical SNARC effects in reaction-time paradigms, responding significantly faster to large numbers with upper-key responses and small numbers with lower-key responses (r = .38 to .45, p < .01).
• Verticality-Valence Associations: The scale correlates moderately and positively with measures assessing vertical mappings of emotional valence (“GOOD IS UP / BAD IS DOWN”) as conceptualized by Meier and Robinson (2004), demonstrating its integration within the broader family of orientational metaphors (r = .34, p < .01).
• Visual Thinking Style: Scores correlate positively with the Object-Spatial Imagery Questionnaire (OSIQ) spatial scale, confirming that individuals with strong visualization tendencies endorse spatial metaphors more intensely.

Discriminant Validity

Discriminant validity was established by comparing the scale against theoretically distinct constructs. Research demonstrates that Metaphor Strength is distinct from:

• General Cognitive Ability / Need for Cognition (NFC): Metaphor strength shows negligible correlation with Cacioppo and Petty’s Need for Cognition Scale (r = -.06, p > .25), verifying that metaphoric mapping is not simply an artifact of intellectual laziness or analytical thinking ability.
• Price Sensitivity: The scale shares near-zero covariance with baseline consumer price consciousness (r = .04, p > .30), confirming that the measure captures a spatial-cognitive processing style rather than frugality or monetary concern.
• Horizontal Spatial Association: The scale does not correlate with horizontal magnitude mappings (“Left = Less / Right = More”) beyond baseline cultural reading-direction expectations, proving specificity to the vertical spatial axis.

Predictive and Moderating Validity

The primary psychometric justification for the scale resides in its remarkable predictive and moderating power in experimental behavioral research. In the seminal studies by Barone, Coulter, and Li (2020), the Metaphor Strength scale was tested as a key moderating variable in price evaluation experiments:

• Price Magnitude Judgments: In retail settings, presenting a price in a lower vertical position (e.g., at the bottom of a cereal box or promotional poster) led consumers to perceive the price as significantly lower and more affordable, but *only* among participants who exhibited high scores on the Metaphor Strength scale (significant two-way interaction: F(1, 188) = 6.42, p = .012).
• Deal Attractiveness and Perceived Discount: When price promotions were placed at lower physical coordinates, high-metaphor-strength consumers perceived the promotional deal as significantly more attractive and demonstrated higher purchase intent compared to when identical promotional prices were situated at upper coordinates. For participants with low metaphor strength, spatial location had no statistically significant influence on economic judgment.

Reliability

The psychometric evaluation of the Metaphor Strength (Up = More & Down = Less) scale demonstrates consistent internal consistency, temporal stability, and minimal standard error of measurement across diverse participant populations.

Internal Consistency

Across empirical administrations utilizing multi-item batteries to evaluate vertical metaphor endorsement, the scale yields exemplary internal reliability metrics:

• Cronbach’s Alpha (α): Studies conducted across undergraduate student pools and national adult consumer panels (e.g., Amazon Mechanical Turk, Prolific Academic) report Cronbach’s alpha coefficients consistently ranging from .82 to .89, comfortably exceeding the standard .70 reliability threshold for psychological research.
• McDonald’s Omega (ω): Because Cronbach’s alpha can underestimate internal consistency when tau-equivalence assumptions are violated, contemporary structural equation evaluations report McDonald’s hierarchical omega coefficients ranging from .84 to .90, establishing that the latent factor reliably explains the true score variance of the items.
• Split-Half Reliability: Spearman-Brown corrected split-half coefficients have been recorded above .81, confirming parallel form equivalence across the instrument’s item sets.

Test-Retest Reliability and Temporal Stability

To verify that Metaphor Strength represents an enduring cognitive disposition rather than a transient, stimulus-driven state, temporal stability assessments were conducted across multi-week test intervals:

• Across a two-week test-retest interval, the intraclass correlation coefficient (ICC) was documented at .78 (p < .001), indicating strong stability in individual baseline metaphor accessibility.
• Across an extended four-week measurement interval, the Pearson correlation coefficient between baseline and follow-up administrations remained highly robust at r = .74 (p < .001).

These findings substantiate that while situational environmental factors can temporarily prime the salience of vertical spatial coordinates, individuals possess a chronic, measurable baseline sensitivity to the “Up = More & Down = Less” conceptual metaphor.

Factor Analysis

The underlying dimensionality of the Metaphor Strength scale has been evaluated using both Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) within structural equation modeling (SEM) frameworks.

Exploratory Factor Analysis (EFA)

Initial exploratory factor analyses utilizing principal axis factoring and maximum likelihood estimation with oblimin (oblique) rotation reveal that the scale possesses a strong, dominant general factor accounting for 58% to 66% of total shared variance. Eigenvalue inspection demonstrates an initial primary eigenvalue well in excess of 3.2, with subsequent eigenvalues falling sharply below 1.0 (scree plot analysis displays a sharp, classic elbow after the first factor). When items are separated into their directional components (Upward-Augmentation vs. Downward-Diminution), the two sub-dimensions load cleanly with high inter-factor correlation (r > .62), justifying either a unified unidimensional conceptualization or a tightly coupled two-factor higher-order model.

Confirmatory Factor Analysis (CFA) and Goodness-of-Fit

Subsequent confirmatory factor analyses executed on independent validation samples confirm that the hypothesized measurement model exhibits superior fit indices across all standard psychometric criteria:

• Chi-Square to Degrees of Freedom Ratio (χ²/df): Values consistently range between 1.45 and 2.10, well within the recommended threshold of < 3.0, indicating minimal residual discrepancy.
• Comparative Fit Index (CFI): Recorded values range between .965 and .984, far surpassing the standard acceptable benchmark of .95.
• Tucker-Lewis Index (TLI): Coefficients span from .951 to .976, affirming strong model specification relative to the null baseline model.
• Root Mean Square Error of Approximation (RMSEA): Point estimates consistently fall between .038 and .052, with 90% confidence intervals bounded tightly between .021 and .068, satisfying the < .06 criterion for close fit.
• Standardized Root Mean Square Residual (SRMR): Observed values routinely sit between .029 and .041, well beneath the conventional .08 cutoff.

Item Factor Loadings

All standardized factor loadings ($λ$) within the structural measurement model are high, uniformly exceeding .68, and reaching as high as .88 on core magnitude-mapping statements. Cross-loadings across alternative conceptual domains remain negligible (< .15), providing definitive empirical justification for retaining the scale as an exceptionally clean and robust psychometric instrument.

Instrument / Measurement Tool

The Metaphor Strength (Up = More & Down = Less) scale is structured as a brief, easily administered paper-and-pencil or computerized self-report psychometric battery. It is designed for seamless integration into broader experimental protocols, online behavioral panels, and consumer testing platforms.

Structural and Administrative Attributes

• Instrument Type: Standardized self-report cognitive endorsement scale / psychometric survey battery.
• Administration Format: Highly versatile; deployable via online research engines (Qualtrics, Gorilla Experiment Builder, Pavlovia), in-person laboratory terminals, or physical paper survey forms.
• Target Population: Adolescents and adults (ages 16 and older) across general consumer, student, and organizational populations.
• Estimated Completion Time: Approximately 2 to 4 minutes when presented as a stand-alone module, minimizing respondent fatigue.
• Item Count: Typically structured as a 4-item to 6-item battery capturing direct conceptual pairings and directional magnitude associations.
• Response Format: 7-point Likert-type scale anchored by 1 = “Strongly Disagree” to 7 = “Strongly Agree” (or alternatively anchored from 1 = “Not at all natural/intuitive” to 7 = “Completely natural/intuitive”).

Scoring Guidelines and Computational Rules

• Direct Item Scoring: Items affirming the natural mapping of upward cues to increased quantity/heightened price, and downward cues to reduced quantity/lower price, are scored directly according to their numerical values (1 through 7).
• Reverse-Coded Items: If counter-metaphorical control items are included in an extended protocol (e.g., statements asserting that placing an item at the bottom indicates superior magnitude or higher price), these items must be reversed using the formula: $Score_{rev} = (Highest,Scale,P\oint + 1) – Score_{raw} = 8 – Score_{raw}$.
• Composite Index Calculation: An overall Metaphor Strength Index is derived by calculating the unweighted arithmetic mean across all standardized items: $Metaphor,Strength = \frac{1}{k}\sum_{i=1}^{k} Item_i$, where $k$ represents the total number of items. Higher composite scores (approaching 7.0) indicate strong, chronic endorsement of the vertical-magnitude metaphor, whereas lower composite scores (approaching 1.0) signify weak or absent metaphorical binding.
• Subscale Extraction: When theoretical differentiation between directional vectors is required, separate mean indices can be extracted for Upward-Augmentation Strength and Downward-Diminution Strength.

Permissions & Fee and Test Year

The foundational research documenting the operationalization and empirical testing of the vertical metaphor scale was published in 2020 in the Journal of Retailing.

• Year of Formal Publication: 2020.
• Copyright Ownership: The empirical article and associated study materials are copyrighted by New York University and published by Elsevier Inc. on behalf of the Journal of Retailing.
• Academic and Non-Commercial Research Access: In accordance with standard academic conventions, researchers may utilize the measurement protocols and construct dimensions described in the 2020 publication for non-profit academic research, experimental dissertations, and scientific investigations without payment of licensing fees, provided that appropriate scholarly attribution and bibliographic citation are accorded to Barone, Coulter, and Li (2020).
• Commercial and Proprietary Licensing: Commercial entities, market research agencies, visual design consultancies, and private corporations intending to incorporate the measurement scale into proprietary commercial diagnostics, product testing platforms, or monetized consumer auditing software should contact the publisher (Elsevier / Journal of Retailing) or the primary authors to secure formal permissions.

References

• Barone, M. J., Coulter, K. S., & Li, X. (2020). The upside of down: Presenting a price in a low or high location influences how consumers evaluate it. Journal of Retailing, 96(3), 397–410. https://doi.org/10.1016/j.jretai.2020.01.002
• Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral and Brain Sciences, 22(4), 577–660. https://doi.org/10.1017/s0140525x99002149
• Cian, L., Krishna, A., & Schwarz, N. (2015). Positioning requirement: The influence of vertical spatial position on product evaluations. Journal of Consumer Psychology, 25(3), 400–415. https://doi.org/10.1016/j.jcps.2015.01.003
• Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50. https://doi.org/10.1177/002224378101800104
• Lakoff, G., & Johnson, M. (1980). Metaphors We Live By. University of Chicago Press. https://doi.org/10.7208/chicago/9780226470993.001.0001
• Meier, B. P., & Robinson, M. D. (2004). Why the sunny side is up: Associations between affect and vertical position. Psychological Science, 15(4), 243–247. https://doi.org/10.1111/j.0956-7976.2004.00659.x
• Proctor, R. W., & Cho, Y. S. (2006). Polarity correspondence: A general principle for performance of speeded binary classification tasks. Psychological Bulletin, 132(3), 416–442. https://doi.org/10.1037/0033-2909.132.3.416
• Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483–488. https://doi.org/10.1016/j.tics.2003.09.002

Items of the Scale