Raymond Cattell – 1905 1998

Biography

The history of twentieth-century psychological science is fundamentally characterized by an epistemological struggle between qualitative introspection and quantitative empiricism. Few scholars embodied this methodological transformation more completely or generated as vast an empirical architecture as Raymond Bernard Cattell (1905–1998). Over a career that spanned nearly seven decades, Cattell sought nothing less than the comprehensive mathematical systematization of human individuality, encompassing the disparate domains of human personality, cognitive capabilities, and dynamic motivational forces. Operating from the conviction that psychological phenomena must be discovered through rigorous multivariate analysis rather than invented through unconstrained clinical deduction, he developed an intricate taxonomy of traits, created novel statistical procedures, and formulated structural theories that continue to reverberate across differential psychology, psychometrics, and educational testing.

Cattell’s intellectual legacy is both colossal and uniquely polarizing. He was among the most prolific social scientists of his era, authoring or co-authoring more than fifty books, hundreds of research papers, and dozens of standardized psychological assessment instruments. His pioneering conceptualization of fluid and crystallized intelligence altered cognitive psychology permanently, providing a developmental paradigm that anticipated contemporary neurocognitive architectures. Concurrently, his sixteen-factor model of personality represented one of the earliest and most systematic attempts to reduce natural language descriptors of human behavior into an empirical, mathematically verifiable structural matrix. However, his unyielding commitment to extending empirical quantification into evolutionary ethics, human breeding, and socio-political organization through his philosophy of “Beyondism” alienated mainstream psychological institutions, generating controversies that shadowed his final years and complicated his historical reputation.

To evaluate Raymond Cattell is to examine the overarching evolution of multivariate behavioral research. From his early training in physical chemistry and psychometrics in London to his establishment of world-renowned laboratories in the United States, Cattell treated the human psyche not as a mysterious metaphysical entity, but as a lawful, multidimensional vector space amenable to precise mathematical prediction. This comprehensive monograph examines Cattell’s life, methodological innovations, substantive theoretical models, socio-political controversies, and enduring contributions to behavioral science, illustrating how his commitment to empirical measurement established both the immense power and the ethical complexities of modern psychological measurement.

1. Biographical Overview and Formative Years (1905–1937)

1.1 Early Childhood and Intellectual Awakening in Devon

Raymond Bernard Cattell was born on March 20, 1905, in West Bromwich, a manufacturing town in the Black Country near Birmingham, England. When he was approximately five years old, his family relocated to Torquay, Devon, a picturesque coastal town whose dramatic cliffs, maritime atmosphere, and open landscapes fostered in the young Cattell a profound appreciation for the natural world and solitary exploration. His father, Alfred Ernest Cattell, was a skilled mechanical engineer who designed steam engines and internal combustion mechanics, instilling in Raymond an early reverence for technical precision, functional efficiency, and rigorous empirical problem-solving. His mother, Mary Field Cattell, nurtured his literary and intellectual curiosities, encouraging wide reading across history, literature, and the physical sciences.

The pastoral calm of Cattell’s Devon childhood was shattered by the outbreak of World War I in 1914. Although too young for military conscription, the nine-year-old Cattell witnessed the grim realities of industrialized human conflict when local seaside hotels, public mansions, and civic halls were abruptly converted into convalescent hospitals for wounded soldiers returning from the Western Front. Cattell observed convoys of maimed, shell-shocked, and traumatized soldiers arriving daily from France, an experience that left an indelible mark on his adolescent psyche. The juxtaposition between humanity’s advanced technological mastery in chemistry and physics and its apparent moral and psychological backwardness struck him as a tragic civilizational paradox. He later recalled feeling that while the physical sciences had granted humanity unprecedented command over inanimate matter, our understanding of human nature, emotion, and societal organization remained primitive and superstitious.

In 1921, at the age of sixteen, Cattell enrolled at King’s College London on an academic scholarship, concentrating his studies in physical chemistry and physics. He excelled in the laboratory, mastering quantitative instrumentation, algebraic modeling, and the rigorous epistemology of the natural sciences. Yet, as he approached the completion of his Bachelor of Science degree—which he earned with first-class honors in 1924—Cattell experienced a growing intellectual dissatisfaction with the physical sciences. He became convinced that the most urgent challenges facing modern civilization were not chemical or mechanical, but psychological. Resolving to apply the measurement standards of the hard sciences to the chaos of human behavior, he made the perilous decision to abandon a promising career in chemistry to pursue the emerging discipline of experimental psychology, despite strong discouragement from professors and mentors who viewed psychology as an unscientific, intellectually suspect backwater.

1.2 Doctoral Training Under Charles Spearman

Upon his entry into graduate psychological studies at University College London (UCL), Cattell entered the orbit of Charles Edward Spearman, one of the founding fathers of psychometrics and the developer of factor analysis. Spearman had revolutionized cognitive psychology by demonstrating that performance across diverse mental tests was positively correlated, a mathematical regularity he operationalized as the general factor of intelligence, or g. At UCL, the dominant intellectual culture was the “London School” of psychology, an intellectual lineage characterized by an uncompromising commitment to mathematical modeling, individual differences, and psychometric operationalism.

Cattell immersed himself in Spearman’s quantitative methods, studying the matrix mathematics, correlation coefficients, and rudimentary factor-extraction methods then available. He was profoundly influenced by Spearman’s belief that unseen psychological constructs could be mathematically deduced from patterns of surface covariation among observable behaviors. Cattell’s doctoral dissertation, completed in 1929, focused on the objective measurement of intelligence and the examination of whether specific mental capacities could be isolated from Spearman’s omnibus general factor. During this period, Cattell began entertaining a theoretical ambition that went beyond Spearman: if factor analysis could illuminate the latent architecture of human cognitive abilities, could the same mathematical logic be applied to map the far more elusive, chaotic realm of human personality, temperament, and character?

The academic environment at UCL also exposed Cattell to the legacy of Sir Francis Galton and the biological orientation of Karl Pearson. This environment cultivated his lifelong belief that individual differences in cognitive capacity and personality were structural features of human biology that possessed deep evolutionary significance. While Cattell embraced Spearman’s statistical rigor, he gradually realized that Spearman’s two-factor cognitive theory (consisting of g and specific factors, s) was too restrictive. Cattell envisioned a far broader, multivariate framework capable of encompassing multiple cognitive abilities, dynamic motivational vectors, and emotional traits simultaneously, setting the stage for his subsequent methodological revolution.

1.3 Early Career and the Leicester Child Guidance Clinic

Completing a doctorate in psychology in 1929 coincided with the onset of the Great Depression, an economic catastrophe that severely restricted academic appointments across the United Kingdom. Unable to secure a permanent university professorship, Cattell was forced into a series of applied and administrative posts. From 1928 to 1931, he served as Director of the Department of Education in the City of Exeter, conducting educational assessments and advising on school curricula. In 1932, he was appointed to establish and direct the Leicester Child Guidance Clinic, one of England’s earliest municipal psychological clinics dedicated to diagnosing and treating behavioral, developmental, and emotional problems in children.

The Leicester clinic served as an invaluable empirical laboratory for Cattell. Confronted daily with practical diagnostic dilemmas—juvenile delinquency, emotional instability, learning disabilities, and neuroses—he quickly recognized the inadequacy of existing clinical tools. Traditional psychoanalytic and introspective approaches struck him as hopelessly subjective, unreliable, and unverifiable. Clinicians routinely applied qualitative labels to troubled children without any standardized baseline of normal developmental variation. Cattell responded by designing objective observational rating scales, standardized behavioral assessments, and early culture-reduced cognitive tests. He realized that effective diagnostic intervention required objective normative taxonomy: a comprehensive structural map of normal child personality and cognitive development against which pathology could be systematically indexed.

Despite his clinical successes in Leicester, this period was characterized by intense financial hardship, personal isolation, and chronic overwork. Cattell contracted a severe, chronic functional stomach ailment exacerbated by malnutrition and exhaustion, an illness that deepened his sense of the fragility of human existence and gave him an urgent sense of mortality. The British academic establishment remained conservative and hostile to quantitative multivariate psychology, viewing his statistical approaches with skepticism. Cattell watched his contemporaries secure elite chairs while he remained an applied clinician in the industrial Midlands. These experiences generated in him a persistent sense of professional marginalization, reinforcing an insular, self-reliant intellectual tenacity that would define his entire academic career.

2. Intellectual Foundations and Methodological Philosophy

2.1 Commitment to Inductive-Hypothetico-Deductive Spiraling

At the center of Cattell’s epistemology was his formulation of the scientific discovery process, which he designated as the inductive-hypothetico-deductive spiral. Cattell rejected what he characterized as the twin pathologies of twentieth-century psychology: pure armchair deductivism on the one hand, and mindless, atheoretical empiricism on the other. He directed sharp criticism toward classical psychoanalytic theorists like Sigmund Freud and Carl Jung, arguing that they formulated expansive, dogmatic deductive models of the human psyche without bothering to anchor their basic concepts in reproducible, objective measurement. Conversely, he criticized narrow behaviorists who accumulated disparate empirical observations without attempting to integrate them into comprehensive mathematical models.

Cattell proposed that scientific inquiry must operate as an iterative, ascending spiral. An investigator begins not with an untested a priori hypothesis, but with systematic, unbiased inductive observation of natural phenomena. Through the multivariate analysis of these broad observational matrices, latent structural patterns are identified. From these empirical regularities, the researcher constructs mathematical hypotheses regarding underlying causal mechanisms (the hypothetico-deductive phase). These hypotheses are then translated into specific empirical deductions, which are tested against fresh, independent datasets using confirmatory methods. If the deduced relations fail to hold, the model is refined, leading to another iteration of inductive exploration and confirmatory verification. For Cattell, psychology could achieve the status of a mature physical science only if it relinquished narrative storytelling in favor of this rigorous mathematical spiral.

This epistemological perspective was foundational to his defense of exploratory factor analysis as a discovery engine. Cattell maintained that in an immature science like psychology, researchers lacked the theoretical maturity required to formulate precise confirmatory models from pure intuition. Exploratory multivariate methods were essential for clearing away subjective semantic confusion and uncovering the true functional unities of the nervous system. Once these functional unities (source traits) were empirically isolated, hypothesis testing could proceed with mathematical precision.

2.2 Multivariate Analysis as the Scientific Standard

Cattell’s most profound methodological critique was directed against the uncritical importation of the classical “bivariate” experimental paradigm into psychological science. Derived from Newtonian physics and popularized in biological research, the classical experimental method involves manipulating a single independent variable while holding all other variables artificially constant in a controlled laboratory environment, subsequently measuring the effect on a single dependent variable. Cattell argued passionately that while this paradigm was appropriate for simple physical systems, it was fundamentally flawed when applied to complex, living biological and social organisms.

He argued that human behavior is inherently multivariate, multidetermined, and functionally integrated. When an experimenter tears an organism out of its natural socio-ecological context, places it in an artificial laboratory environment, and artificially holds constant variables that normally fluctuate dynamically, the functional integrity of the psychological phenomenon under study is destroyed. The resulting laboratory artifacts, Cattell insisted, offer little predictive utility regarding how human beings operate in the natural world. Instead of the artificial laboratory controls of bivariate design, Cattell championed multivariate naturalism. In this paradigm, the psychologist does not attempt to manipulate the organism artificially, but instead measures multiple variables simultaneously across large, naturalistic populations, relying on advanced statistical procedures—such as multiple regression, canonical correlation, and factor analysis—to achieve statistical control over confounding variables.

For Cattell, personality traits and cognitive structures were not metaphysical constructs, but functional unities represented mathematically as structural covariance matrices. The true laws of psychology could be discovered only by observing the simultaneous, lawful co-variation of dozens, or even hundreds, of biological, behavioral, and environmental indicators in real-world contexts. Multivariate analysis was therefore not merely an auxiliary data-analytic tool for Cattell; it was an epistemological worldview that preserved the systemic complexity of human nature while subjecting it to the rigorous discipline of matrix algebra.

2.3 The Covariation Chart (Data Box)

To systematically organize the universe of psychological data collection and clarify the methodological relationships between different experimental designs, Cattell conceptualized the Covariation Chart, which he later expanded into the famous three-dimensional Data Box (or Basic Data Relation Matrix). Cattell observed that any empirical psychological observation can be conceptualized as an entry within a three-dimensional coordinate system whose orthogonal axes represent Persons (individual organisms), Variables (measured behavioral traits, physiological states, or test performances), and Occasions (time points or environmental situations).

By systematically slicing and transposing this three-dimensional matrix, Cattell demonstrated that there exist ten distinct methodological designs for empirical psychological research, far beyond the traditional cross-sectional correlation study:

• R-technique: The classic nomothetic design in which a large sample of diverse persons is measured across multiple variables on a single occasion, correlating variables across individuals to uncover universal trait structures.
• P-technique: An idiographic design pioneered by Cattell, in which a single person is measured across multiple variables repeatedly across numerous occasions over time, factoring variables across time to map dynamic motivational fluctuations, state shifts, and internal structural conflicts within a single individual (cf. Birney & Beckmann, 2022).
• Q-technique: A design where correlations are computed between persons across multiple variables at a single occasion, identifying typological groupings or clusters of similar individuals.
• O-technique: Correlating occasions across multiple variables for a single individual to evaluate situational contexts.
• S-technique: Correlating persons across multiple occasions for a single variable, assessing interpersonal stability.
• T-technique: Correlating occasions across persons for a single variable, assessing situational profiles across groups.

The formulation of the Data Box resolved long-standing methodological disputes between nomothetic (group-level) and idiographic (individual-focused) approaches to personality. Cattell proved that the idiographic profiling championed by clinicians (P-technique) and the nomothetic factor architectures championed by psychometricians (R-technique) were not mutually exclusive philosophies, but complementary geometric projections of the same underlying multidimensional data space.

3. Data Modalities: The Tripartite Assessment Framework

3.1 Life Record Data (L-Data)

To prevent personality research from degenerating into semantic solipsism, Cattell insisted that any comprehensive psychometric taxonomy must triangulate personality constructs across three distinct, epistemologically diverse data modalities: Life Record Data (L-data), Questionnaire Data (Q-data), and Objective Test Data (T-data). Cattell viewed Life Record Data (L-data) as the primary empirical anchor for discovering fundamental personality dimensions. L-data consists of objective, observable behaviors occurring in real-world, naturalistic settings throughout the individual’s lifespan. These include institutional records—such as school grades, criminal arrests, employment stability, vehicular accidents, and marital status—as well as systematic, quantified behavioral ratings provided by objective peer observers, coworkers, supervisors, or teachers.

The primary virtue of L-data is its ecological validity. It captures how an individual actually functions and is perceived within the social matrix of everyday life, entirely free from the artificial demands of a testing laboratory. However, Cattell was acutely aware of the severe psychometric vulnerabilities inherent in observational ratings. L-data is notoriously susceptible to observer bias, halo effects (where a general positive or negative impression skews ratings across distinct behavioral categories), central tendency biases, and the varying observational opportunities available to raters. To overcome these limitations, Cattell developed standardized, multi-rater behavior-rating keys, requiring multiple independent raters who knew the subject intimately to rate them on carefully defined behavioral poles across extended timeframes.

In Cattell’s systematic research program, L-data served as the foundation of his personality research. He believed that the English language had evolved over centuries to encapsulate the significant observable behavioral interactions among individuals. Consequently, factor analysis of comprehensive L-data rating matrices provided the baseline taxonomy of human surface and source traits, which would subsequently need to be cross-validated and replicated within introspective and laboratory experimental modalities.

3.2 Questionnaire Data (Q-Data)

Questionnaire Data (Q-data) represents the internal, introspective dimension of personality assessment. Q-data is gathered through self-report inventories, structured personality questionnaires, and clinical surveys in which individuals respond to standardized queries regarding their own internal thoughts, emotional states, subjective preferences, behavioral tendencies, and bodily sensations. Cattell recognized that an individual has access to a vast repository of internal phenomenological experiences—such as inner anxieties, existential dread, somatic perceptions, and covert fantasies—that external observers cannot directly detect in L-data.

However, Cattell maintained a profound skepticism regarding the direct face validity of self-report instruments. He drew an uncompromising theoretical line between Q-data proper (which he viewed as self-perception mediated by subjective bias) and what he designated as Q’-data (unverified introspective claims treated as literal objective reality by naive researchers). Cattell warned that self-reports are perpetually contaminated by conscious faking, social desirability response sets, impression management, and response acquiescence (the tendency to agree with items regardless of content). Therefore, Cattell argued that self-report responses must never be assumed to reflect objective fact; rather, they must be treated as behavioral acts in their own right, the empirical meaning of which can be determined only when correlated with external criteria.

To construct psychometrically sound Q-data instruments, Cattell introduced sophisticated correction scales, indirect question phrasing, and mathematical factor-matching protocols. He insisted that a self-report scale was valid only if its factor structure demonstrated high mathematical congruence with the source traits previously identified in naturalistic L-data ratings. This rigorous cross-modal validation was central to the creation of his flagship personality instrument, the Sixteen Personality Factor (16PF) Questionnaire, which was explicitly designed as a Q-data operationalization of L-data source traits.

3.3 Objective Test Data (T-Data)

Recognizing the inherent vulnerabilities of observer ratings in L-data and the inescapable self-presentation biases in Q-data, Cattell devoted decades of laboratory research to the development of what he termed Objective Test Data (T-data). For Cattell, a psychological test is “objective” if and only if the research subject is unaware of which trait or psychological construct is actually being measured, thereby rendering conscious manipulation, faking, or defensive self-presentation virtually impossible.

T-data consists of miniature situational tests, physiological measurements, behavioral motor tasks, and cognitive-perceptual challenges administered under standardized laboratory conditions. For instance, rather than asking a subject whether they are “cautious” or “anxious” on a questionnaire (Q-data), a T-data protocol might measure the subject’s baseline physiological tremor when anticipating a loud noise, their willingness to guess on difficult cognitive items under risk of severe point penalties, their rate of optical dark adaptation, their perceptual speed in detecting hidden figures, or their unconscious physiological pupillary dilation when exposed to specific emotional stimuli. In each instance, the subject believes they are performing a neutral perceptual or motor task, while the experimenter is measuring latent emotional, temperamental, or dynamic vectors.

Cattell’s efforts in this domain culminated in the creation of the Objective-Analytic (O-A) Test Batteries, an enormous compendium comprising hundreds of objective behavioral apparatuses and psychomotor tasks designed to measure dozens of fundamental personality source traits (cf. Primi et al., 2014). Although Cattell regarded T-data as the absolute scientific future of differential psychology—because it mirrored the objective instrumentation of physics and chemistry—it faced severe practical impediments. The O-A batteries were mechanically cumbersome, extremely time-consuming to administer, expensive to manufacture, and proved difficult for other independent laboratories to replicate reliably, leading to their eventual commercial eclipse by simpler self-report instruments.

4. The Trait Stratification Model and Structural Hierarchy

4.1 Surface Traits versus Source Traits

At the theoretical heart of Cattell’s personality architecture lies the crucial distinction between surface traits and source traits. Cattell observed that when psychologists observe human behavior, they initially encounter correlations among visible, everyday manifestations of behavior. A group of individuals might simultaneously exhibit sociability, talkativeness, optimism, and an interest in social gatherings. Cattell termed such observable constellations surface traits: descriptive clusters of covarying characteristics that appear together on the surface of behavior, but do not necessarily share a single, underlying, causal neurobiological or psychological origin.

Surface traits are often the product of overlapping causal influences, temporary social circumstances, or environmental accidents. They describe what behavior looks like phenomenologically, but they lack stable explanatory and predictive power. In contrast, source traits are the underlying, unified, latent causal influences that produce the surface trait correlations. A source trait is a true functional unity—an irreducible, foundational structural dimension of the nervous system or socio-cultural learning that accounts for variance across a broad spectrum of overt behaviors. Source traits cannot be observed directly; they must be mathematically discovered and isolated through the procedures of factor analysis.

Cattell demonstrated that when correlation matrices derived from hundreds of diverse behavioral indicators are factored using oblique (correlated) rotational methods, the resulting primary factors represent these underlying source traits. Because source traits represent the basic, stable building blocks of personality, they demonstrate significantly greater longitudinal stability across the lifespan, higher cross-situational generalizability, and superior predictive power in mathematical equations compared to unstable, descriptive surface traits.

4.2 Constitutional versus Environmental-Mold Traits

Having established the structural reality of source traits, Cattell addressed their etiology, dividing source traits into two fundamental ontological categories: constitutional traits and environmental-mold traits. Constitutional traits are those foundational personality dimensions that originate primarily from the biological, physiological, and genetic architecture of the organism. Although influenced by post-natal physiological events, disease, and developmental biology, their variation across a population reflects inherited differences in neuroanatomy, neurotransmitter sensitivity, endocrine functioning, and autonomic reactivity. Examples include temperamental surgency, basic autonomic reactivity, and fluid cognitive efficiency.

Conversely, environmental-mold traits are structural patterns impressed upon the individual’s personality by the continuous, institutional learning pressures of the physical and socio-cultural environment. These traits represent the structural internalization of cultural norms, family socialization patterns, religious dogmas, educational systems, and socio-economic expectations. An individual’s degree of religious orthodoxy, work ethic, professional etiquette, or specific ideological sentiments constitute environmental-mold traits; they are lawful, stable personality configurations formed through continuous reinforcement and cultural conditioning.

To mathematically disentangle the relative contributions of genetic and environmental influences on these source traits, Cattell formulated an advanced biometric methodology known as Multiple Abstract Variance Analysis (MAVA). Unlike traditional twin studies, which merely compared identical twins reared together with fraternal twins reared together, MAVA utilized complex structural equations that incorporated data from identical twins reared together, identical twins reared apart, fraternal twins reared together, fraternal twins reared apart, unrelated children reared together (adoptive siblings), and ordinary siblings reared together. By factoring out common family environments and socio-economic variables, MAVA allowed Cattell to calculate sophisticated nature-nurture ratios for every major source trait, demonstrating that traits such as emotional stability and intelligence possessed high heritability coefficients, while dynamic sentiments and conscientiousness were predominantly shaped by environmental molds.

4.3 Ability, Temperament, and Dynamic Traits

To encompass the full spectrum of human individuality, Cattell categorized all source traits into a tripartite taxonomy based on their functional role in the execution of behavior: ability traits, temperament traits, and dynamic traits. This structural division allowed Cattell to account for human action comprehensively by answering three fundamental questions: How effectively does the person perform? With what stylistic energy and emotional tempo do they act? And what drives them to act in the first place?

• Ability Traits: These traits determine the functional efficacy and capability with which an individual pursues and accomplishes goals in the face of complex cognitive, perceptual, or motor demands. Ability traits dictate how effectively a person processes information, solves abstract problems, memorizes material, and adapts to novel challenges. General intelligence, spatial ability, and numerical aptitude fall into this category.
• Temperament Traits: These traits define the intrinsic stylistic tempo, fundamental emotional reactivity, pervasive mood state, and energetic speed with which an individual behaves. Temperament traits do not determine what an individual does or how successfully they do it, but rather how they do it. Whether a person approaches a problem with impulsive enthusiasm, calm deliberation, irritable tension, or social boldness is governed by their temperament traits, which Cattell found to be heavily biological and constitutional in origin.
• Dynamic Traits: These traits govern the motivational engines, energetic drives, and goal-directed teleology of the organism. Dynamic traits explain why a person initiates action, which directions their behavior takes, and what specific states they strive to achieve or avoid. Cattell subsequently divided dynamic traits into innate, biological drives (ergs) and environmentally learned motivational structures (sentiments and attitudes).

This tripartite division formed the computational foundation of Cattell’s predictive models. He maintained that no human act could be mathematically predicted or understood without simultaneously incorporating parameters from all three trait domains into a single predictive behavioral equation.

5. The 16 Personality Factor (16PF) Architecture

5.1 The Lexical Hypothesis and Reductionist Extraction

Cattell’s development of the Sixteen Personality Factor (16PF) model represents a classic implementation of the lexical hypothesis: the proposition that the most important individual differences in human transactions will inevitably become encoded into single descriptive words within natural language over evolutionary history. Working from the monumental lexical compendium compiled by Gordon Allport and Henry Odbert in 1936—which cataloged 17,953 English terms describing human behavior and internal states—Cattell initiated a systematic psychometric reduction to uncover the fundamental latent structure of human personality.

Recognizing that an 18,000-term dictionary was mathematically intractable for factor-analytic algorithms in the 1940s, Cattell executed a series of reductions. First, he eliminated temporary states (such as “furious” or “intoxicated”), purely evaluative physical characteristics, and obscure metaphorical designations, reducing the corpus to approximately 4,500 stable trait terms. Next, through extensive semantic analyses, synonym pairings, and antonym groupings, Cattell consolidated this unwieldy vocabulary into 171 distinct bipolar trait clusters. He then administered these 171 trait scales to large samples of normal adults, having trained peer raters observe and score the subjects over extended periods to generate naturalistic L-data correlation matrices.

Through visual and computational factor analyses of these intercorrelation matrices, Cattell consolidated the 171 traits down to 35 core surface trait clusters. Finally, Cattell subjected these 35 surface trait dimensions to factor analysis using oblique rotational methods. Through this procedure, he discovered that the correlation matrices could be accounted for by sixteen oblique, primary source traits. These sixteen factors were not arbitrary creations of the researcher, Cattell insisted, but the fundamental, mathematically irreducible building blocks of human personality.

5.2 The Primary Factors: Structure, Polarities, and Semantics

To avoid the misleading cultural connotations, moral evaluations, and semantic biases embedded in existing psychological vocabulary, Cattell took the controversial step of inventing a precise neologistic nomenclature for his primary source traits. He utilized technical Latinate terms and assigned alphabetic labels (Factors A through Q) to designate the extracted dimensions, seeking to establish a neutral taxonomic system akin to the periodic table of elements in chemistry. The sixteen primary factors, defined across their opposing bipolar dimensions, comprise the following:

• Factor A: Warmth (Sizothymia vs. Affectothymia). Reflects the degree to which an individual is reserved, detached, and aloof versus warmhearted, outgoing, and emotionally participating in interpersonal relationships.
• Factor B: Reasoning (Lower vs. Higher Mental Capacity). The primary cognitive ability factor embedded within the 16PF, indexing general intelligence and abstract problem-solving facility.
• Factor C: Emotional Stability (Low Ego Strength vs. High Ego Strength). Measures susceptibility to emotional upset, reactivity to frustration, and neurotic instability versus dynamic resilience, realistic emotional management, and ego strength.
• Factor E: Dominance (Submissiveness vs. Dominance / Submissiveness vs. Dominance). Differentiates accommodating, submissive, deferential behavior from forceful, assertive, competitive, and authoritative inclinations.
• Factor F: Liveliness (Desurgency vs. Surgency). Captures the dimension between sober, serious, taciturn, and prudent caution versus enthusiastic, spontaneous, cheerful, and talkative optimism.
• Factor G: Rule-Consciousness (Low Super-Ego Strength vs. High Super-Ego Strength). Measures expedience, non-conformity, and disregard for moral standards versus dutiful conscientiousness, high moral standards, and perseverance.
• Factor H: Social Boldness (Threctia vs. Parmia). Contrasts autonomic threat-sensitivity, shyness, and social timidity with stress-resistant autonomic boldness, adventurousness, and social uninhibitedness.
• Factor I: Sensitivity (Harria vs. Premsia). Reflects tough-minded self-reliance, utilitarian realism, and emotional stoicism versus tender-minded sensitivity, aesthetic orientation, and emotional vulnerability.
• Factor L: Vigilance (Alaxia vs. Protension). Contrasts trusting, adaptable, and accepting interpersonal orientations with suspicious, hyper-vigilant, skeptical, and paranoid projections.
• Factor M: Abstractedness (Praxernia vs. Autia). Measures practical, grounded, conventional reality-orientation versus imaginative, absent-minded, bohemian, and internal idea-absorption.
• Factor N: Privateness (Naivete vs. Shrewdness). Differentiates genuine, unpretentious, transparent openness from socially shrewd, calculating, private, and polished diplomacy.
• Factor O: Apprehension (Untroubled Adequacy vs. Guilt-Proneness). Contrasts confident, placid, self-assured serenity with vulnerable, self-blaming, insecure, and anxious guilt-proneness.
• Factor Q1: Openness to Change (Conservatism vs. Radicalism). Reflects adherence to established traditional methods and social dogmas versus progressive experimentation, skepticism, and openness to socio-intellectual reform.
• Factor Q2: Self-Reliance (Group Adherence vs. Self-Sufficiency). Differentiates social dependency, conformist affiliation, and group orientation from autonomous, self-sufficient, and solitary decision-making.
• Factor Q3: Perfectionism (Low Integration vs. High Self-Sentiment). Measures tolerance for internal disorder, impulsivity, and careless informality versus high self-discipline, meticulous organization, and structural willpower.
• Factor Q4: Tension (Low Ergic Tension vs. High Ergic Tension). Captures relaxed, tranquil, satisfied contentment versus driven, overwrought, restless, frustrated, and somatic drive tension.

5.3 Second-Order and Global Factors

Because Cattell utilized oblique (correlated) rotational techniques rather than forcing factors into artificial orthogonal (90-degree) relationships, the resulting sixteen primary source traits were themselves intercorrelated. Rather than viewing this covariation as a statistical defect, Cattell recognized it as an empirical opportunity. In accordance with his hierarchic structural philosophy, Cattell factored the intercorrelation matrix among the sixteen primary factors, extracting what he termed second-order factors (subsequently termed Global Factors in modern editions of the 16PF).

Factor analysis of the primary traits consistently revealed four to five robust higher-order dimensions. The two most prominent second-order factors were Extraversion (driven primarily by the convergence of primary Factors A, F, H, and inverted Q2) and Anxiety (driven by low C, high L, high O, and high Q4). Additional higher-order factors included Tough-Mindedness (low A, low I, low M), Independence (high E, high H, high Q1), and Self-Control (high G, high Q3). Cattell demonstrated that these second-order dimensions provided a parsimonious, bird’s-eye overview of the individual’s global personality organization (cf. Boyle et al., 2016).

Intriguingly, the second-order factors isolated by Cattell correspond structurally to the domains of the contemporary Five-Factor Model (“Big Five”): Extraversion, Neuroticism (Cattell’s Anxiety), Agreeableness (inversely related to Tough-Mindedness/Independence), Conscientiousness (Cattell’s Self-Control), and Openness/Intellect. However, Cattell strongly opposed collapsing the 16PF down exclusively into these five broad dimensions. He argued that doing so obscured the critical, high-fidelity predictive power of the primary source traits. Two individuals might register identical global Extraversion scores while possessing completely disparate primary profiles: one could be socially bold but interpersonally cold (high H, low A), while the other could be deeply warm and accommodating but shy and socially fragile (high A, low H). For Cattell, broad global factors were useful for coarse grouping, but clinical diagnosis, vocational selection, and behavioral prediction required the fine-grained resolution of the sixteen primary factors.

5.4 Clinical, Educational, and Industrial Applications

The 16PF was rapidly adopted across clinical psychology, psychiatry, industrial-organizational psychology, and educational counseling. In industrial settings, the instrument became a cornerstone of vocational selection, leadership assessment, and corporate recruitment. Industrial psychologists utilized empirical 16PF criterion-matching profiles to identify the personality configurations associated with success in specific occupations, from commercial airline pilots—who required high Emotional Stability (C), elevated Self-Control (Q3), low Apprehension (O), and moderate Dominance (E)—to creative researchers, who consistently scored high on Abstractedness (M), Openness to Change (Q1), and Self-Sufficiency (Q2).

In clinical psychology, Cattell developed dynamic diagnostic equations capable of identifying pathological configurations. While the 16PF was normed on non-clinical populations, extreme deviations across specific primary profiles reliably differentiated general neuroses from psychotic decompensation. Severe neurotic distress manifested as a combination of extremely low Ego Strength (C), elevated Guilt-Proneness (O), elevated Ergic Tension (Q4), and high Vigilance (L). Cattell later constructed specialized clinical supplements, such as the Clinical Analysis Questionnaire (CAQ), to measure depressive and psychotic source traits directly alongside the foundational sixteen factors.

In marriage, family, and relational therapy, Cattell utilized dyadic profile matching to assess marital stability and interpersonal compatibility. By comparing the 16PF vector matrices of romantic partners, clinicians could calculate mathematical indices of structural personality conflict, predicting areas of domestic friction, dominance struggles, and emotional alienation. Over the decades, the 16PF underwent multiple technical revisions (Forms A, B, C, D, and E), culminating in the modern 16PF Fifth Edition, which retained Cattell’s original sixteen primary source traits while updating psychometric scoring algorithms, modernizing language, and formalizing the reporting of the five Global Factors.

6. Cognitive Theories: The Investment Theory of Gf and Gc

6.1 Deconstruction of Spearman’s General Factor (g)

While Cattell was Spearman’s intellectual heir, he fundamentally challenged his mentor’s most celebrated theoretical construct: the monolithic, unitary nature of general intelligence, g. Spearman had maintained that a single biological energy or cognitive capacity underlay all intellectual operations, accounting for the positive manifold observed across mental performance tests. In the late 1930s and early 1940s, while examining cognitive performance data across diverse age cohorts and patients recovering from neurological trauma, Cattell noticed systematic empirical anomalies that Spearman’s unitary g model could not accommodate.

Cattell observed that different subtests within omnibus intelligence batteries followed completely divergent developmental trajectories across the human lifespan. Tests requiring rapid pattern recognition, abstract inductive reasoning, and spatial manipulation peaked in early adulthood (around age twenty) and showed steady, biological decline throughout late adulthood. Conversely, tests measuring vocabulary breadth, numerical problem-solving, and general cultural knowledge remained stable, often continuing to grow and accumulate well into the sixth and seventh decades of life. If intelligence were truly a unitary biological capacity (g), it would be mathematically impossible for different segments of an intelligence test to demonstrate diametrically opposed developmental trajectories across age cohorts (cf. Brown, 2016).

In a historic paper delivered at the 1941 meeting of the American Psychological Association, Cattell formally deconstructed Spearman’s g into two distinct second-order cognitive dimensions: Fluid Intelligence ($Gf$) and Crystallized Intelligence ($Gc$). Working in close collaboration with his most brilliant doctoral student, John L. Horn, Cattell expanded this conceptual breakthrough into what became known as the Cattell-Horn Theory of Fluid and Crystallized Intelligence, altering the trajectory of cognitive psychology and providing the first empirically viable developmental model of human intellectual aging.

6.2 Fluid Intelligence (Gf): Neurobiological Processing

Cattell defined Fluid Intelligence ($Gf$) as an individual’s innate, fundamental potential for abstract reasoning, relation-perceiving, and inductive problem-solving, operating entirely independent of formal educational exposure or acculturation. $Gf$ represents the physiological efficiency, neuroplasticity, and raw processing power of the central nervous system. It is manifested when an individual is confronted with completely novel cognitive problems that cannot be solved using previously memorized facts, automated verbal heuristics, or cultural scripts.

Because $Gf$ is tied to neurobiology, its performance correlates with structural brain metrics, including prefrontal cortical volume, white matter integrity, and neural transmission speed. Cattell noted that $Gf$ is vulnerable to neurological trauma, cerebral anoxia, toxic insult, and normal biological senescence. It follows a classic developmental trajectory: it rises rapidly throughout childhood and early adolescence, reaches its developmental plateau between ages 18 and 22, and subsequently undergoes a steady, biologically mediated decline throughout the remainder of adulthood.

Cattell operationalized the measurement of Fluid Intelligence through non-verbal, abstract matrix reasoning tasks, visual series completions, topological classifications, and geometric analogies. In these tasks, the individual must discern complex logical relations between novel geometric shapes, requiring rapid working memory manipulation, mental rotation, and dynamic pattern abstraction. Under this operationalization, $Gf$ constitutes the biological engine of cognition, representing the ceiling of an individual’s immediate problem-solving capacity when stripped of all acquired cultural tools.

6.3 Crystallized Intelligence (Gc): Culturally Acquired Acuity

In contrast to the biological nature of fluid ability, Cattell defined Crystallized Intelligence ($Gc$) as the secondary cognitive structure that arises from the experiential application, education, and cultural exposure of an individual over time. $Gc$ comprises the vast repository of acquired, semantic knowledge, linguistic proficiencies, conceptual frameworks, mathematical procedures, and learned cognitive heuristics that an individual internalizes from their socio-cultural environment (cf. Postlethwaite, 2011).

Crystallized ability is mediated through the institutions of formal schooling, vocational training, reading, social interaction, and deliberate practice. Consequently, while $Gf$ shows early biological decline, $Gc$ demonstrates remarkable longitudinal resilience across the adult lifespan. Because crystallized competencies are preserved within distributed semantic networks in long-term memory, an individual can continue to expand their crystallized vocabulary, domain-specific wisdom, and technical judgment well into their seventies and eighties, provided they remain cognitively engaged and free from severe neurodegenerative pathology.

Psychometrically, $Gc$ is measured through standardized tests of verbal comprehension, vocabulary breadth, mechanical information, formal arithmetic reasoning, and general cultural literacy. Cattell demonstrated that although $Gc$ manifests as an independent cognitive factor in adult cross-sectional factor analyses, it does not arise in a developmental vacuum. Rather, its ultimate magnitude and complexity within any given individual are heavily conditioned by the historical amount of Fluid Intelligence the person had to invest throughout their developmental history.

6.4 The Investment Theory and Culture Fair Intelligence Tests

To explain the developmental and structural relationship between $Gf$ and $Gc$, Cattell formulated the Investment Theory. The central hypothesis of the Investment Theory posits that an individual’s current level of Crystallized Intelligence ($Gc$) is the historical product of their initial, innate Fluid Intelligence ($Gf$) invested into specific learning experiences, formal educational curricula, and vocational opportunities across the lifespan. A child with high fluid ability learns abstract concepts more rapidly, comprehends complex texts with greater ease, and internalizes cultural heuristics more efficiently; consequently, over years of academic and cultural exposure, that child will accumulate higher levels of crystallized knowledge.

However, Cattell explicitly emphasized that the transformation of $Gf$ into $Gc$ is heavily moderated by non-cognitive factors, including motivational drive (dynamic traits), personality characteristics (such as conscientiousness and intellectual curiosity), and, crucially, access to environmental and educational resources. A person endowed with exceptional fluid capacity who is raised in severe environmental poverty, denied formal schooling, or afflicted by chronic emotional dysfunction may fail to develop corresponding levels of crystallized competence. Conversely, a person with modest fluid capacity who possesses exceptional drive, emotional stability, and continuous educational enrichment can achieve high levels of crystallized expertise through sustained, deliberate practice.

Recognizing that conventional, verbally loaded intelligence tests (such as the early Stanford-Binet and Wechsler batteries) were heavily contaminated with crystallized cultural artifacts—penalizing individuals from disadvantaged socio-economic backgrounds, immigrants, and non-native language speakers—Cattell developed the Culture Fair Intelligence Test (CFIT) (cf. Holden & Tanenbaum, 2023; Nicolas et al., 2011). The CFIT was deliberately designed to measure pure Fluid Intelligence ($Gf$) by utilizing non-verbal, perceptual, and abstract geometric puzzles—such as progression matrices, classifications, and topological conditions—thereby neutralizing the confounding influences of cultural knowledge, linguistic proficiency, and formal educational advantage.

Decades later, Cattell’s $Gf$–$Gc$ dichotomy merged with the cognitive processing models of John L. Horn and the Three-Stratum hierarchical framework developed by John Bissell Carroll, culminating in the contemporary Cattell-Horn-Carroll (CHC) theory of cognitive abilities, which stands today as the foundation of modern psychometric intelligence testing.

7. Dynamic Lattice, Ergs, and Motivational Structural Equations

7.1 Ergs: Innate Drive Mechanisms

Dissatisfied with personality models that focused solely on static cognitive abilities and stylistic temperament, Cattell devoted a significant portion of his research at the University of Illinois to the quantitative modeling of human motivation. He rejected the psychoanalytic model of the unconscious as unscientific, while simultaneously dismissing radical behaviorism’s denial of internal goal-directed dynamics. To replace these models, Cattell introduced the concept of the Erg (derived from the Greek ergon, meaning work or physical energy), which he defined as an innate, biologically anchored psychophysical drive mechanism that impels an organism toward specific survival and reproductive endpoints.

An erg is a constitutional dynamic source trait. When stimulated by environmental or physiological triggers, an erg produces an emotional appetite, directs perceptual attention toward relevant environmental cues, initiates behavioral strategies, and finds consummatory satisfaction in a specific biological goal state. Drawing upon the instinct theories of William McDougall and ethological observations, Cattell utilized P-technique and R-technique factor analyses of physiological and objective dynamic indicators to isolate ten distinct primary human ergs:

• Mating (Sex): The biological drive toward sexual reproduction, romantic attraction, and erotic consummation.
• Gregariousness: The evolutionary urge toward social affiliation, herd cohesion, and avoiding isolation.
• Fear (Escape): The survival drive toward self-preservation, safety, and threat evasion.
• Assertion: The competitive drive for social dominance, status recognition, achievement, and mastery.
• Exploration (Curiosity): The exploratory drive toward novelty, investigation, and understanding environmental dynamics.
• Pugnacity (Combat): The protective aggressive drive toward overcoming destructive impediments and hostile rivals.
• Parental Care (Protectiveness): The altruistic drive toward nurturing, protecting, and raising offspring.
• Appeal: The distress drive toward seeking aid, comfort, and sympathy when helpless.
• Narcissism (Sensory Pleasure): The biological pursuit of bodily comfort, sensory enjoyment, and self-indulgence.
• Rest (Sleep): The physiological drive toward exhaustion reduction and restorative inactivity.

Cattell separated himself from traditional motivational theorists by developing objective, physiological metrics to quantify the operational tension of these ergs. Using T-data methods—such as galvanic skin response (GSR), pupillometric dilation, blood pressure shifts, and projection tasks—Cattell was able to mathematically quantify the magnitude of ergic tension operating within an individual at any given moment.

7.2 Meta-Ergs: Sentiments and Attitudes

While ergs represent the innate biological motivational foundation of human nature, Cattell recognized that human behavior in complex civilizations is rarely expressed through raw, unmediated biological impulses. Instead, evolutionary ergs are channeled, conditioned, and elaborated through lifelong socio-cultural learning into complex, acquired motivational structures that Cattell termed Meta-Ergs. Meta-ergs represent environmental-mold dynamic source traits. Cattell divided meta-ergs into two distinct, hierarchically related categories: Sentiments and Attitudes.

A Sentiment is a major, enduring, culturally organized dynamic structure centered upon a significant socio-ecological object, institution, or domain of social life. Sentiments represent the stable, structural investments of emotional energy that an individual develops through socialization. Prominent examples isolated in Cattell’s factor-analytic investigations include the Sentiment toward Family, the Sentiment toward Career/Profession, the Sentiment toward Religion, the Sentiment toward one’s Nation/Country, and the foundational Self-Sentiment (the psychological ideal of self-regard and integrity, which coordinates and regulates all other dynamic systems). Sentiments develop slowly over years of experiential immersion, forming stable cognitive-emotional systems that organize long-term commitments and values.

An Attitude, within Cattell’s technical vocabulary, is not a vague verbal opinion, but a highly specific behavioral impulse directed toward a discrete object within a defined situational context. Cattell formalized the mathematical structure of an attitude as an operational proposition: “In these specific circumstances, I desire so much to do this particular action with this specific object.” For example, the statement “I want to study psychological statistics at university tonight to advance my scientific career” represents a discrete attitude. Attitudes are numerous, highly contextualized, and transient. Within Cattell’s hierarchy, dozens of specific attitudes are organized beneath and driven by a single enduring sentiment, which in turn derives its primary motivational energy from underlying biological ergs.

7.3 The Dynamic Lattice and Behavioral Specification Equation

To graphically and topologically map the pathways through which raw biological energy is transformed into concrete human behaviors, Cattell invented the Dynamic Lattice. The Dynamic Lattice is a complex, branched network diagram representing the motivational architecture of an individual. On the far right of the lattice sit the innate, biological Ergs (the ultimate sources of motivational power). On the far left of the lattice sit the thousands of concrete, situational Attitudes (the overt actions of the individual). In the intermediate strata sit the organizing cultural Sentiments.

The interconnecting lines linking these strata represent relationships of subsidiation—the psychological principle whereby one motivational structure serves as the instrument or means to achieve a higher-order end. Cattell demonstrated that a single overt attitude (e.g., working long hours at an office) is subsidized by multiple sentiments (e.g., devotion to one’s career and dedication to providing for one’s family), which are in turn subsidized by foundational ergs (e.g., Assertion, Parental Care, and Fear of poverty). The Dynamic Lattice mathematically models motivational ambivalence, dynamic conflict, and structural frustration when subsidiation pathways cross or become blocked by external reality.

The mathematical culmination of this conceptual framework was Cattell’s legendary Behavioral Specification Equation. Cattell maintained that any human response ($R$) in a given situation ($s$) could be mathematically predicted using a comprehensive linear vector equation:

$$R = \sum b_a A + \sum b_t T + \sum b_e E + \sum b_m M + \sum b_s S$$

In this equation, the individual’s predicted behavioral response is a function of their measured Ability traits ($A$), Temperament traits ($T$), Ergic drive tensions ($E$), Meta-ergic sentiments ($M$), and temporary internal physiological or emotional States ($S$). Critically, each trait score is weighted by an empirically calculated situational coefficient ($b$, or behavioral index), which represents the degree to which that specific trait is stimulated or required by the immediate environmental context. Through the Behavioral Specification Equation, Cattell attempted to realize his scientific dream: unifying the dynamic motivational physics of the human psyche with the predictive precision of matrix algebra.

8. Factor Analytic Innovations and Psychometric Inventions

8.1 The Scree Test for Factor Extraction

During the mid-twentieth century, the application of factor analysis was fraught with subjective ambiguity, particularly concerning the fundamental question: How many factors should be extracted from a correlation matrix? Extracting too few factors (under-factoring) resulted in the loss of critical psychological constructs, blending distinct psychological phenomena into uninterpretable amalgams. Conversely, extracting too many factors (over-factoring) capitalized on chance, introducing random sampling noise, unreplicable error variance, and statistical artifacts into the scientific literature.

Prior to Cattell, researchers relied primarily on arbitrary mathematical heuristics, such as the Kaiser-Guttman criterion, which suggested retaining all factors with an eigenvalue greater than 1.0. Cattell demonstrated that the Kaiser criterion was flawed, routinely leading to severe over-factoring in large matrices, sometimes extracting dozens of meaningless noise factors. In 1966, Cattell introduced the Scree Test, an elegant geometric and visual-mathematical solution to the factor-retention problem that rapidly became a standard diagnostic tool across the social sciences.

The term scree was borrowed by Cattell from geological terminology, referring to the loose, broken rock debris that accumulates at the base of a steep cliff or mountain slope. Cattell observed that when the eigenvalues of successive factors extracted from a correlation matrix are plotted sequentially along a descending line graph, the plot exhibits a distinct visual topography. The initial, substantial common factors account for large amounts of variance, producing a steep, rapidly falling cliff. Eventually, however, the curve flattens out into an asymptotic, linear slope of small, uniform eigenvalues that represent random measurement error, sampling noise, and residual unreliability—the statistical “scree.” Cattell demonstrated that the true number of common factors in the data is demarcated precisely at the inflection point where the steep cliff meets the straight debris slope. While subsequently complemented by modern computational procedures like Horn’s Parallel Analysis, Cattell’s Scree Test provided a simple and enduring method for identifying factor structures.

8.2 Oblique Rotation and Simple Structure

A second major methodological battleground in psychometrics concerned the mathematics of factor rotation. After extracting an initial factor matrix, the factor coordinate axes must be rotated within multidimensional space to achieve psychological interpretability. The dominant American methodological school, led by Louis Leon Thurstone and later championed by researchers who favored algorithms like Henry Kaiser’s Varimax rotation, insisted on orthogonal rotation. Orthogonal methods maintain a strict 90-degree angle between factor axes, mathematically forcing the extracted personality or cognitive traits to be completely uncorrelated ($r = 0.00$).

Cattell waged a relentless methodological campaign against the arbitrary imposition of orthogonal rotation, condemning it as an unscientific, procrustean bed. He argued that nature does not organize biological, social, and psychological systems into completely independent, non-interacting compartments. Human attributes—such as anxiety, intelligence, sociability, and emotional resilience—demonstrate lawful, natural covariations in real-world populations. Forcing personality traits to be mathematically uncorrelated merely to satisfy an aesthetic preference for rectangular geometric coordinates, Cattell asserted, distorted psychological reality and obscured the true causal architecture of the nervous system.

Instead, Cattell championed oblique factor rotation, which permits the factor coordinate axes to freely assume correlated, non-perpendicular angles if the empirical data naturally demand it. Cattell refined Thurstone’s principle of Simple Structure—which seeks to rotate factor axes until each variable has high loadings on only one factor and near-zero loadings on all others—by developing computational algorithms that iteratively searched for maximum simple structure hyperplanes. Cattell’s commitment to oblique rotation led directly to the development of modern rotation software programs, including Oblimin and Promax (which begins with an orthogonal solution and raises factor loadings to powers to achieve oblique resolution), forever establishing correlated factor modeling as a foundational standard in psychometrics.

8.3 The Procrustes Program and Profile Similarity Coefficients

Long before the advent of modern structural equation modeling (SEM) and formal confirmatory factor analysis (CFA) programs like LISREL, Cattell recognized the need for mathematical techniques that could confirm specific theoretical hypotheses against empirical data. To achieve this, Cattell and his associates formulated the Procrustes Program, one of the earliest algorithmic methods designed to execute targeted factor rotations.

Named after the rogue smith of Greek mythology who physically stretched or amputated travelers to fit his iron bed, the Procrustes algorithm operated by taking an empirical, unrotated factor matrix and rotating it mathematically to achieve the closest possible least-squares fit against a pre-specified, theoretical “target” matrix populated by hypothesized ones and zeros. If the empirical data could be rotated to match the target matrix without severe statistical distortion, the investigator obtained quantitative confirmation of their theoretical model. Although Cattell was mindful of the danger of forcing data to fit an arbitrary model (capitalization on chance), the Procrustes program was a direct precursor to modern hypothesis-driven confirmatory factor analysis.

Additionally, Cattell made lasting contributions to psychodiagnostic pattern matching by inventing the Coefficient of Profile Similarity ($r_p$). Standard Pearson correlation coefficients were inadequate for comparing psychological profiles because they indexed only the shape of the profile, ignoring differences in absolute level (elevation) and scatter (variability). Cattell’s $r_p$ was an algebraically rigorous distance metric that incorporated profile elevation, scatter, and shape simultaneously, allowing clinicians and researchers to calculate precise probabilities regarding whether an individual’s multifaceted 16PF or cognitive test profile matched an empirical diagnostic prototype (e.g., clinical depression, creative scientific excellence, or specific learning deficits).

9. Major Academic Appointments and Institutional Influence

9.1 Transition to the United States: Columbia, Clark, and Harvard

By the mid-1930s, Cattell was intellectually stifled by the conservative climate of British psychology, which remained largely indifferent to large-scale multivariate psychometrics. His fortunes shifted in 1937, when he received an invitation from Edward Lee Thorndike, the pioneer of American educational psychology, to join Teachers College at Columbia University in New York City as Thorndike’s research associate. Cattell accepted, permanently emigrating to the United States at the age of thirty-two. The move marked his transition into an intellectual environment characterized by abundant computational resources, research funding, and institutional enthusiasm for psychometrics.

After a fruitful year collaborating with Thorndike on cognitive measurement and socio-economic variables, Cattell was appointed in 1938 as the G. Stanley Hall Professor of Psychology at Clark University in Worcester, Massachusetts. At Clark, Cattell began expanding his empirical studies of personality, but he found the institutional focus of the department leaning heavily toward developmental psychology and psychoanalysis. In 1941, he was recruited to Harvard University as a Lecturer in Psychology, entering an intellectually vibrant environment where he engaged with leading figures of American psychology, including Gordon Allport, Henry Murray, and Edwin Boring.

Cattell’s time at Harvard was marked by intense methodological debates, particularly with Gordon Allport. While both men were committed to establishing traits as the primary units of personality, they occupied opposing methodological poles. Allport championed a humanistic, idiographic approach, arguing that each personality was a unique, unquantifiable constellation that defied universal dimensionalization. Cattell argued that Allport’s approach was literary and unscientific, asserting that human individuality could be measured via universal nomothetic dimensions through multivariate matrix algebra. These Harvard debates solidified Cattell’s determination to establish an independent, well-funded research institute dedicated exclusively to the multivariate exploration of human behavior.

9.2 The Illinois Laboratory of Personality Assessment (1945–1973)

In 1945, Cattell accepted a research professorship at the University of Illinois at Urbana-Champaign (UIUC), an institution that offered him an extraordinary environment: generous state funding, large laboratory facilities, freedom from heavy undergraduate teaching responsibilities, and access to the world’s most advanced computational technology, including the early ILLIAC supercomputers. At UIUC, Cattell established the Laboratory of Personality Assessment and Group Behavior, which he directed for nearly three decades until his retirement in 1973.

The Illinois laboratory became the world capital of multivariate psychological research. Cattell secured massive research grants from the United States Office of Naval Research, the National Institute of Mental Health (NIMH), and the Rockefeller Foundation. The scale of his empirical operation was staggering. Cattell coordinated teams of psychometricians, computer programmers, physiological technicians, and field observers, administering batteries of hundreds of L-data, Q-data, and T-data measures to thousands of military recruits, university students, schoolchildren, and psychiatric patients. The computational infrastructure of UIUC allowed Cattell to execute complex matrix inversions and factor extractions that were impossible elsewhere.

During his Illinois tenure, Cattell’s academic productivity was virtually unprecedented in the behavioral sciences. He published dozens of major books, including Description and Measurement of Personality (1946), Factor Analysis (1952), Personality and Motivation Structure and Measurement (1957), and the two-volume encyclopedic opus Handbook of Multivariate Experimental Psychology (1966). Furthermore, Cattell trained generations of doctoral students, post-doctoral fellows, and visiting psychometricians who went on to populate chairs of quantitative psychology across North America and Europe, cementing his influence across the discipline.

9.3 Founding of the Society of Multivariate Experimental Psychology (SMEP)

Throughout the 1940s and 1950s, Cattell grew frustrated by the institutional dominance of the American Psychological Association (APA), which he believed was controlled by narrow laboratory behaviorists who favored bivariate animal experiments on the one hand, and clinical practitioners who lacked quantitative training on the other. Multivariate researchers frequently found their complex factor-analytic papers rejected by mainstream APA journals, whose editors and peer reviewers often lacked the mathematical competence to evaluate matrix algebra, oblique rotations, and structural equations.

In response to this institutional marginalization, Cattell organized a gathering of quantitative researchers in 1959, leading to the formal incorporation in 1960 of the Society of Multivariate Experimental Psychology (SMEP). SMEP was established as an elite, computationally rigorous scientific society dedicated to advancing multivariate mathematical methodologies across the behavioral sciences. Cattell served as its inaugural president, gathering prominent figures such as Lyle Jones, John Horn, Ledyard Tucker, and Chester Harris into its ranks.

To provide a publishing outlet for advanced quantitative psychometrics, Cattell and SMEP founded the flagship academic journal Multivariate Behavioral Research (MBR) in 1966. Under Cattell’s guidance, MBR became the premier venue for groundbreaking developments in exploratory and confirmatory factor analysis, structural equation modeling, profile similarity analysis, and multivariate analysis of variance. SMEP and MBR transformed psychological training globally, playing an indispensable role in institutionalizing advanced multivariate statistics as an mandatory requirement within doctoral psychology curricula.

10. Socio-Political Controversies and the ‘Beyondism’ Ideology

10.1 Formulation of Beyondism as an Evolutionary Ethics

While Cattell’s mainstream scientific fame rested upon his psychometric and cognitive architectures, he harbored a lifelong, messianic ambition to formulate a comprehensive, scientifically derived ethical and religious system. Deeply influenced by his adolescent encounters with the horrors of World War I, Cattell believed that humanity’s traditional revealed religions—such as Christianity, Islam, and Judaism—were obsolete dogmatic systems incapable of preventing civilizational collapse. In their place, Cattell sought to construct an objective morality derived from evolutionary biology and differential genetics, a system he christened Beyondism.

Cattell articulated this socio-political philosophy in two major volumes: Beyondism: Religion from Science (1972) and The Beyondist Goal (1987). The fundamental ethical premise of Beyondism is that evolutionary survival and adaptive advancement constitute the supreme moral goods of the universe. Cattell asserted that humanity does not exist as an undifferentiated, universal collective; rather, evolution proceeds through natural selection operating between distinct cultural, socio-political, and biological groups. Therefore, Cattell argued, humanity must actively foster inter-group diversity and cultural differentiation, allowing different societies to experiment with disparate socio-political institutions and genetic profiles.

Crucially, Cattell insisted that this inter-group evolutionary competition should not be conducted through violent warfare, military conquest, or physical destruction—which he condemned as dysgenic and catastrophic. Instead, he advocated for peaceful “co-operative competition,” in which distinct societies would remain culturally and biologically separate, allowing natural selection to reward societies that demonstrated superior intelligence, emotional stability, altruism, and social organization, while allowing maladaptive, dysfunctional societies to undergo peaceful demographic decline. Cattell launched fierce philosophical attacks against egalitarianism, universalism, and international welfare systems, arguing that subsidizing dysfunctional societies interfered with evolutionary selection and courted collective civilizational degeneration.

10.2 Eugenics, Racial Variations, and Academic Backlash

Cattell’s socio-political philosophy was inextricably bound to his unwavering commitment to the principles of eugenics, an intellectual lineage tracing directly back to Francis Galton, Leonard Darwin, and the British Eugenics Society (of which Cattell was an active member in the 1930s). Throughout his career, Cattell argued that general cognitive ability ($Gf$–$Gc$) and dynamic emotional traits possessed high biological heritability. Consequently, he warned that modern industrialized societies were undergoing demographic decay due to differential birth rates: individuals with lower cognitive capacity and higher impulsivity were having more children than highly intelligent, conscientious individuals.

To halt what he perceived as a biological decline in national intelligence, Cattell advocated for both “positive eugenics” (providing financial incentives, social honors, and institutional rewards to encourage individuals of high intellectual and moral capacity to reproduce at higher rates) and “negative eugenics” (discouraging or restricting reproduction among individuals afflicted with severe genetic disorders, low intellectual capacity, and chronic antisocial pathology). In his 1930s publications, such as The Fight for Our National Intelligence (1937), Cattell offered speculative policy proposals regarding selective reproductive incentives that alienated liberal and egalitarian scholars.

Furthermore, Cattell extended his differential psychometrics into controversial investigations of racial, national, and socio-economic differences. While he occasionally noted that intra-group individual differences were vastly larger than inter-group differences, his writings repeatedly suggested that distinct racial and national populations possessed different mean levels of fluid cognitive efficiency and temperamental traits, shaped by disparate evolutionary selection pressures across geographic histories. He advocated for strict national immigration controls designed to prevent the cultural and genetic disruption of host populations. These sociopolitical assertions generated severe academic backlash. Throughout the 1970s and 1980s, anti-racism organizations, civil rights groups, and critical scholars condemned Cattell, labeling his Beyondist philosophy as an ideological justification for scientific racism, eugenics, and social Darwinism, casting a shadow over his empirical factor-analytic achievements.

10.3 The 1997 APA Gold Medal Controversy

The simmering tensions between Cattell’s towering psychometric contributions and his controversial socio-political writings exploded into a national academic crisis in the summer of 1997. The American Psychological Foundation (APF), an affiliate of the American Psychological Association, voted to bestow upon the 92-year-old Cattell the prestigious Gold Medal Award for Lifetime Achievement in Psychological Science. The award was designed to honor his lifetime of empirical discoveries, his pioneering work on fluid and crystallized intelligence, and his creation of multivariate measurement tools.

Days before the formal presentation was scheduled to take place at the APA annual convention in Chicago, an intense public protest erupted. Led by Barry Mehler, a professor of history at Ferris State University and director of the Institute for the Study of Academic Racism, critics presented the APA leadership with extensive dossiers containing excerpts from Cattell’s writings on Beyondism, eugenics, and racial differences, accusing Cattell of having spent decades promoting racist, anti-Semitic, and quasi-fascist ideologies. Prominent civil rights organizations, media outlets, and factions within the APA demanded that the award be immediately rescinded.

Caught in a public relations crisis, the APA and APF leadership decided to postpone the presentation of the Gold Medal, announcing the formation of an official blue-ribbon committee of historians, psychometricians, and ethicists to review Cattell’s lifetime writings. Cattell, frail and in failing health at his home in Honolulu, Hawaii, was deeply wounded by the accusations. On August 13, 1997, Cattell took the initiative and formally withdrew his name from consideration for the award, issuing a passionate public open letter defending his life’s work. In his letter, Cattell wrote:

“I abhor racism and discrimination based on race. Any other impression from my writings is a heinous distortion… My life has been dedicated to the pursuit of objective truth through science. Beyondism was an attempt to formulate an evolutionary framework for the survival of human culture, not an instrument of hatred.”

The controversy laid bare the irreconcilable divide between Cattell’s technical methodological brilliance and the provocative socio-political speculations he had pursued in parallel. Cattell died less than six months later, with the historical judgment of his legacy permanently entangled with this bitter public dispute.

11. Methodological Critiques and the Factor Structure Replicability Debate

11.1 The Replicability Crisis in the 16PF Matrix

Despite the widespread practical adoption of the 16PF, Cattell’s structural model faced sustained mathematical and methodological critiques from within quantitative psychology. The most damaging line of attack emerged from independent researchers who attempted, and repeatedly failed, to replicate Cattell’s foundational sixteen-factor solution from his raw correlation matrices. Beginning in the late 1950s and accelerating through the 1960s and 1970s, investigators found that when they subjected Cattell’s data to independent factor analysis, the sixteen distinct primary factors consistently failed to emerge.

In a historic series of re-analyses conducted by Ernest Tupes and Raymond Christal (1961) for the United States Air Force personnel laboratory, followed by influential investigations by Warren Norman (1963) and John Digman, researchers demonstrated that the complex correlation matrices derived from Cattell’s lexical and L-data variables yielded only five robust, replicable orthogonal factors. These five dimensions—Extraversion, Agreeableness, Conscientiousness, Emotional Stability (Neuroticism), and Culture/Openness—proved invariant across demographic samples, raters, and test instruments, planting the empirical seeds for what would eventually dominate personality psychology as the “Big Five” model.

Critics argued that Cattell’s extraction of sixteen primary factors was the result of subjective biases in his factor-rotation procedures. Before the advent of fully automated rotational algorithms, Cattell utilized manual, visual rotations using a “rotoscope” (a manual mechanical projecting device), visually shifting factor hyperplanes on two-dimensional graph paper. Critics contended that Cattell’s manual rotations were guided by subjective theoretical expectations rather than purely objective mathematical criteria, leading him to capitalizes on local, sample-specific error variance and extract far more factors than were objectively present in the data. Cattell vigorously rebutted these criticisms, publishing scathing counter-critiques arguing that Tupes, Christal, and Norman had severely under-factored the data by stopping their rotational iterations prematurely, applying crude orthogonal constraints, and lacking the technical expertise required to identify subtle, oblique simple-structure hyperplanes.

11.2 Mathematical Objections to Extreme Multi-Trait Modeling

Beyond the empirical replicability disputes, Cattell’s methodological philosophy was subjected to sustained theoretical critique by competing psychometric giants, most prominently his longtime British contemporary and intellectual rival, Hans J. Eysenck. Eysenck, operating from the Institute of Psychiatry in London, championed the principle of scientific parsimony (Occam’s razor). He argued that Cattell’s hyper-complex sixteen-factor model was mathematically unstable, excessively detailed, and practically unmanageable for clinicians and researchers.

Eysenck championed a radically simplified three-factor model—the PEN model (Psychoticism, Extraversion, and Neuroticism)—arguing that these three broad, orthogonal superfactors accounted for the vast majority of reliable behavioral variance. Eysenck pointed out that Cattell’s sixteen primary traits were significantly intercorrelated, which Eysenck viewed as a fatal defect: if primary traits correlated heavily with one another, they were not truly distinct, independent dimensions of personality. Eysenck contended that Cattell was reifying descriptive behavioral nuances and semantic redundancies as if they were distinct neurological structures.

Furthermore, mathematical statisticians raised technical objections regarding the degrees of freedom in Cattell’s complex dynamic specification equations. With dozens of ability traits, temperament dimensions, ergic states, and meta-ergic sentiments entering into a single linear regression model, the equations required hundreds of parameters to be estimated simultaneously. Critics pointed out that with a sufficient number of predictor variables and situational indices ($b$-weights), a regression equation could fit almost any empirical data set post hoc, while possessing zero genuine predictive power when applied to fresh, independent samples. Modern quantitative psychology eventually settled on a hierarchical compromise: accepting that human personality is organized hierarchically, with broad domains (like the Big Five or Eysenck’s superfactors) sitting at the apex of the hierarchy, subsuming narrower, specific facet traits (similar to Cattell’s primary factors) beneath them.

11.3 Ecological Validity and Psychometric Over-Complication

In applied settings, Cattell’s expansive measurement batteries encountered substantial resistance from clinical, educational, and organizational practitioners. While academic researchers admired the theoretical elegance of Cattell’s tripartite framework (L-data, Q-data, and T-data), the practical reality of administering these instruments presented significant logistical barriers. The primary casualty was Cattell’s most prized invention: the Objective-Analytic (O-A) Test Batteries (T-data).

The O-A battery required clinical practitioners to maintain rooms filled with complex, specialized mechanical equipment: finger-tremor devices, tachistoscopes, dark-adaptation viewers, galvanic skin response apparatuses, and dozens of paper-and-pencil perceptual tasks. Administering the full O-A battery to a single patient took several hours, required specialized laboratory training, and imposed significant physical and cognitive fatigue on both the clinician and the subject. Furthermore, the psychometric scoring was opaque; clinicians were presented with abstract mathematical factor indices that bore no intuitive relationship to the concrete clinical complaints—such as panic attacks, marital infidelity, or major depression—that patients brought into the consulting room.

Because the T-data batteries were logistically burdensome and expensive, the clinical and commercial markets largely abandoned them, opting instead for simpler, self-administered self-report questionnaires (such as the MMPI, the Beck Depression Inventory, and simple Big Five inventories). Cattell viewed this practical abandonment of objective testing as a tragedy, lamenting that clinical psychology had surrendered scientific measurement in favor of the cheap convenience of introspective self-reports. Nevertheless, the tension between Cattell’s hyper-systematic taxonomy and the demands of clinical practice highlighted the limits of importing the laboratory standards of physical chemistry directly into psychological assessment.

12. Enduring Legacy and Modern Impact on Contemporary Psychology

12.1 The Cattell-Horn-Carroll (CHC) Cognitive Framework

Despite the controversies that surrounded his socio-political writings and the debates regarding his personality taxonomy, Cattell’s structural model of human cognitive abilities stands as one of the most successful and enduring scientific paradigms in the history of psychology. The conceptual breakthrough he initiated in 1941—deconstructing general intelligence into Fluid Intelligence ($Gf$) and Crystallized Intelligence ($Gc$)—permanently dismantled the assumption of a monolithic cognitive efficiency.

Following Cattell’s initial formulation, John L. Horn substantially expanded the $Gf$–$Gc$ architecture throughout the 1960s, 1970s, and 1980s, adding specialized second-order cognitive factors, including Visual Processing ($Gv$), Short-Term Memory ($Gsm$), Long-Term Retrieval ($Glr$), Processing Speed ($Gs$), and Auditory Processing ($Ga$). In the late 1990s, psychometrician Kevin McGrew spearheaded the formal mathematical integration of the Cattell-Horn model with John B. Carroll’s landmark Three-Stratum theory, officially synthesizing them into the unified Cattell-Horn-Carroll (CHC) Theory of Cognitive Abilities.

Today, CHC theory is recognized globally as the gold-standard theoretical taxonomy for human intellectual capabilities. It provides the psychometric architecture and factor structure for the world’s most widely utilized standardized cognitive assessment instruments, including the Woodcock-Johnson IV Tests of Cognitive Abilities, the Wechsler Adult Intelligence Scale (WAIS-IV), the Wechsler Intelligence Scale for Children (WISC-V), the Stanford-Binet Intelligence Scales (Fifth Edition), and the Kaufman Assessment Battery for Children (KABC-II). Modern structural and functional neuroimaging studies have validated Cattell’s original developmental deductions: fluid reasoning tasks activate dynamic, distributed frontoparietal neural networks that undergo age-related neurobiological decline, while crystallized tasks rely upon established, consolidated temporal and cortical networks that remain structurally resilient across the lifespan.

12.2 Precursor to Big Five and Contemporary Trait Taxonomy

In personality psychology, contemporary researchers recognize Raymond Cattell as an indispensable architect of modern trait taxonomy. While modern personality research coalesced around the Five-Factor Model (FFM) popularized by Paul Costa, Robert McCrae, and Lewis Goldberg, this modern consensus was built directly upon the foundation of Cattell’s lexical reduction research. Cattell was the first to take Allport and Odbert’s unwieldy 18,000-term dictionary and demonstrate that natural language personality descriptors could be mathematically condensed into an interpretable, multidimensional factor space.

The structural congruence between Cattell’s second-order global factors and the contemporary Big Five domains is an established historical reality: Extraversion mirrors Cattell’s Second-Order Extraversion; Neuroticism directly reflects Cattell’s Second-Order Anxiety; Agreeableness aligns inversely with Cattell’s Tough-Mindedness; Conscientiousness matches Cattell’s Self-Control; and Openness reflects his Openness to Change/Abstractedness vectors. Cattell’s pioneering advocacy for oblique (correlated) factor rotation laid the mathematical foundation for contemporary structural equation modeling (SEM) and hierarchical factor models, which routinely allow higher-order factors to explain the correlations among lower-order scales.

Furthermore, contemporary clinical, forensic, and organizational psychometrics has witnessed a renewed appreciation for Cattell’s insistence on primary, narrow-facet traits. Personality researchers have increasingly recognized that while five broad domains are adequate for broad epidemiological studies, they lack the diagnostic specificity required for real-world clinical and vocational decision-making. Modern inventories—such as the NEO-PI-3, the HEXACO Personality Inventory, and the Personality Inventory for DSM-5 (PID-5)—rely on multifaceted lower-order trait scales that echo Cattell’s original argument: understanding the true multidimensional complexity of an individual requires profiling the specific, nuanced primary source traits that underpin general human behavior.

12.3 Final Reflections on a Century of Psychometrics

Raymond Bernard Cattell passed away on February 2, 1998, at his home in Honolulu, Hawaii, at the age of 92, and was buried in the Valley of the Temples Memorial Park. In his final years, despite declining physical health, he continued to write, analyze matrices, and publish, serving as an emeritus professor at the Hawaii School of Professional Psychology. By any objective bibliometric standard, Cattell was an intellectual giant of the twentieth century; a comprehensive empirical study published in the Review of General Psychology ranked Cattell as the 16th most eminent and frequently cited psychologist of the twentieth century, placing him in the company of Sigmund Freud, B.F. Skinner, Jean Piaget, and Carl Rogers.

Cattell’s life and career serve as both an inspiration and a cautionary tale within the history of science. His inspirational legacy lies in his uncompromising methodological dedication: his refusal to accept arm-chair philosophical speculation, his development of sophisticated factor-analytic tools (such as the Scree test and oblique Simple Structure algorithms), and his bold unification of cognition, personality, and motivation into a single mathematically integrated framework. He demonstrated that the human psyche—viewed by traditionalists as too elusive and subjective for quantitative measurement—could be subjected to the rigorous empirical discipline of matrix algebra and multivariate statistics.

The cautionary dimension of his legacy resides in the hubris of attempting to extract a complete socio-political and moral philosophy from unverified evolutionary interpretations of differential genetics. His Beyondist ideology stands as a reminder of the historical dangers of overstepping the boundaries between empirical psychometric description and speculative social engineering. Yet, when stripped of his ideological excursions, Cattell’s core scientific contribution remains monumental. He permanently transformed psychology from a qualitative, speculative offshoot of philosophy into a quantitative, multivariate natural science, leaving behind an empirical legacy that will continue to shape our understanding of human individuality for generations to come.

References

• Birney, D. P., & Beckmann, J. F. (2022). Intelligence IS Cognitive Flexibility: Why Multilevel Models of Within-Individual Processes Are Needed to Realise This. Journal of Intelligence, 10(3), 49. https://doi.org/10.3390/jintelligence10030049
• Boyle, G. J., Stankov, L., Martin, N. G., Petrides, K. V., Eysenck, M. W., & Ortet, G. (2016). Hans J. Eysenck and Raymond B. Cattell on intelligence and personality. Personality and Individual Differences, 103, 29–40. https://doi.org/10.1016/j.paid.2016.04.029
• Brown, R. E. (2016). Hebb and Cattell: The Genesis of the Theory of Fluid and Crystallized Intelligence. Frontiers in Human Neuroscience, 10, 606. https://doi.org/10.3389/fnhum.2016.00606
• Holden, L. R., & Tanenbaum, G. J. (2023). Modern Assessments of Intelligence Must Be Fair and Equitable. Journal of Intelligence, 11(6), 126. https://doi.org/10.3390/jintelligence11060126
• Nicolas, S., Gras, D., & Seguí, J. (2011). Alfred Binet et le laboratoire de Psychologie de la Sorbonne. L’Année psychologique, 112(2), 291–318. https://doi.org/10.3917/anpsy.112.0291
• Postlethwaite, B. E. (2011). Fluid ability, crystallized ability, and performance across multiple domains [Doctoral dissertation, University of Iowa]. https://doi.org/10.17077/etd.zopi8wvs
• Primi, R., Ferreira-Rodrigues, C. F., & Carvalho, L. de F. (2014). Cattell’s Personality Factor Questionnaire (CPFQ): Development and Preliminary Study. Paidéia (Ribeirão Preto), 24(57), 29–37. https://doi.org/10.1590/1982-43272457201405
• Woyciekoski, C., & Hutz, C. S. (2009). Inteligência emocional: teoria, pesquisa, medida, aplicações e controvérsias. Psicologia: Reflexão e Crítica, 22(1), 1–11. https://doi.org/10.1590/s0102-79722009000100002