Journal cj Educational Piyckoloiy1963, Vo! 54, No. 1, 1-22

THEORY OF FLUID AND CRYSTALLIZEDINTELLIGENCE:

A CRITICAL EXPERIMENT1

RAYMOND B. CATTELLUniversity of Illinois

The theory of fluid and crystallired intelligence propounded 20 years agoby the author has since accumulated support. However, the crucial is-sue of whether 1 or 2 general factors subtend intellectual performanceshas lacked an experiment adequately designed for accurate, determinate,simple-structure rotation at the 2nd order. By factoring culturally em-bedded with culture-fair intelligence measures on a background of purepersonality primaries (N = 277 7th and 8th grade boys and girls), it isshown that 2 general factors indeed exist. A review, with some mathe-matical formulations, is given of the theory's implications for the nature-nurture ratio, brain injury, standard deviation of the IQ, growth curves,the concept of a relational difficulty hierarchy, test standardization, andthe relative validities of traditional and culture-fair intelligence tests

PRESENT TRENDS IN INTELLIGENCE

CONCEPTS

Since Spearman's demonstration ofthe general ability factor (g) first putintelligence testing in the framework ofscientific research, the field has experi-enced three major theoretical develop-ments, which, however, have not hithertobeen interrelated.

1. Thurstone's (1938) proof that anycomprehensive array of ability measureswill factor uniquely into a set of simple-structure, oblique, primary abilities,from which g can be obtained as asecond-order factor, more uniquely de-terminable than by the first-orderapproach.

2. The notion, most frequently asso-ciated with the name of Piaget (1947)

1 The research reported herein was per-formed pursuant to a contract with the UnitedStates Office of Education, Department ofHealth, Education, and Welfare. We are alsoindebted to D. W. Dunnan, and the schoolteachers of Springfield, Illinois, and to C. C.Newman, and the school teachers of Paxton,Illinois.

but widely surmised, and stated veryclearly by Ferguson (1956), for example(see also the review by Hunt, 1961),that the formal structure of abilities ispartly developmental^ determined bywhat might be called "generalized solu-tion instruments" (i.e., habits the acqui-sition of which becomes a key, openingthe way to rapid advance in some gen-eral area of cognitive problem solving).These we shall briefly call "aids."

3. The theory of "fluid and crystal-lized general abilities," which states thatwith more refined analytical methods thegeneral ability factor now measured byintelligence tests will be found to be notone factor but two. In spite of markedcooperativeness of loading pattern (Cat-tell, 1952), which makes them difficultto separate, they have properties differ-ing in vital ways for educational andclinical prediction.

This article puts forward entirely newevidence specifically on the theory offluid and crystallized g factors, but inte-grates all three of the above and hasimplications for practical testing interms of culture-fair intelligence tests.

l

RAYMOND B. CATTELL

THEORY OF FLUID AND CRYSTALLIZED

GENERAL ABILITY

Although the theory of fluid and crys-tallized general ability was first stated20 years ago (Cattell, 1941, 1943),and since developed more precisely(Cattell, 1950, pp. 477-491; Cattell,1957a, pp. 871-879; Cattell, 1957b), themomentum of custom among intelligencetesters, and the absence of sufficientlysustained research on the theory, havehitherto denied to practical test con-struction and use the advantages in un-derstanding that might be expected toacrue from such dual measurement. Themain problem in research advance isone of organization, since, as the fol-lowing summary of the theory willshow, coordination is necessary amongspecialists and practitioners in severaldifferent fields. Parts of the followingtheory have been stressed by certaininvestigators, e.g., in Ferguson's (1956)use of "ability" and "learning set,"Hebb's (1942) notion of A and B com-ponents in ability, Newland's2 (1962)use of process and product, and Hayes'(1962) notion of "experience-producing-drives" (though the last joins cognitiveand dynamic components here kept sep-arate). But the necessary experimentalconditions for constructive conclusionsare possible only if the total theory iskept in focus, as is happily the case in,for example, the recent work of Horn(unpublished). The interrelated aspects

2 In communicating to nonpsychologist teach-ers, for example, the particular aspect of thefluid and crystallized ability theory expressedin Newland's "process" and "product" provesto be readily conveyed by these terms. In anymore precise and comprehensive context theterms mislead, however, for the capacity tolearn is not only a function of the process(fluid ability) but often of the product, aswell as of personality and motivation. Particu-larly when aids have been acquired, the rateof learning is a function not only of fluidability but of the crystallized products of for-mer application of process.

of the theory may be briefly stated asfollows:

1. That among the primary abilitiesin the area semantically designated "in-telligence" in our culture (and which, asGuilford points out, is not totally gen-eral to cognitive performance) there isnot one "general ability" second-orderfactor, as in the Spearman-Thurstoneresolution (Cattell, 1943), but more.Two of these are highly cooperative(Cattell, 1952) in the sense that theyagree in loading positively most of thegeneral ability primaries and havelargely zero loadings outside the intelli-gence field. Being cooperative they arevery difficult to separate, and most pre-vious ability factorings have been satis-fied to recognize the joint factor as onefactor. This conglomerate has been madethe basis of IQ measurement and hasbeen called "general intelligence." Tech-nical reasons for this confusion are dis-cussed in the section "Implications forExperimental Checks on the Theory."

2. The two factors, which will becalled fluid (f) and crystallized (c)general ability, gf and gc, and indexed8

as U.I. (T) 1 and U.I. (T) 2, havedifferent properties, as follows:

a. Crystallized ability loads morehighly those cognitive performances inwhich skilled judgment habits have

8 In the Universal Index (VI.) system pro-posed elsewhere (Cattell, 1957c; Cattell &Warburton, 1963), to preserve factor identi-fication during changing explanatory devel-opment, U.I. (T) 1 was assigned to generalability and UJ. (T) 2 to flexibility of closure,in French's (1951) series. However, as pointedout elsewhere (Cattell, 1957a, p. 830), there isincreasing evidence that flexibility of closureis really the Personality Factor UJ. (T) 19,outcropping in ability when ability tests onlyare used. Accordingly it preserves the his-torical importance of order in the index muchbetter if the U J. (T) 2 niche—flexibility goingto UJ. (T) 19—is now allocated to crystallizedgeneral ability, and flexibility removed to UJ.19.

FLUID AND CRYSTALLIZED INTELLIGENCE

become crystallized (whence its name)as the result of earlier learning appli-cation of some prior, more funda-mental general ability to these fields.Thurstone's Verbal and Numericalprimaries, or achievement in geogra-phy or history, would be examples ofsuch products. Fluid general ability,on the other hand, shows more in testsrequiring adaptation to new situations,where crystallized skills are of no par-ticular advantage.

b. Before biological maturity (15-20 years of age) individual differencesin the difference of g, and gc will re-flect mainly differences in cultural op-portunity and interest. Among adultsthese discrepancies will reflect alsodifferences in age, since the gap be-tween gt. and gf will tend to increasewith experience and the time decayof g(. Although the speed of an intel-lectual performance is not a functionof U.I. 1 and U.I. 2 alone, (for ex-ample, U.I. 22, Cortertia, is a power-ful personality contributor; Cattell,1957a), performances at speed, in anycognitive field, will load gt more thangc, while tests without time limit (un-less they are absolutely new and adap-tive) , such as Thorndike called powertests, will have relatively large load-ings of gc.

c. Fluid and crystallized abilitieswill differ on their age trend plots forthe general population, gf reaching anearly maximum at 14—15 years, whileg0 increases to 18, to 28, or beyond,depending on the cultural learningperiod for the given subculture.Thereafter, whereas gf will declinefrom about age 22 continuously toold age, gc will show a later and lesserdrop. In all these comments on gc, itmust be understood that we are talk-ing about the general factor in a broadarray of crystallized abilities, not anysingle crystallized ability.

d. The standard deviation of theIQ calculated "classically" frommental ages, will be about 12-16points for gc and 24-25 points for g{(Cattell, 1937, 1955, 1957b). Thelatter will be more constant and bio-logically determined, whereas theformer will hinge on culture habits.For example, classroom systems whichslow the bright and press the dull willreduce the possible absolute individ-ual difference in gc at any age level,and therefore, gc standard deviationof IQ, when annual increment is con-stant. Culture may similarly influencethe sigma on gc in that a powerfuleducation, with larger annual meanincrements and, therefore, larger ageperformance sigma, will tend to re-duce IQ sigma. Parenthetically, sincetraditional intelligence tests are amixture of gc and gf, the standarddeviation of the IQ on such tests willbe a function as follows:

(p) . .

where p subscripts mean across peopleat one age, and a subscripts meanacross age (years), taken as the vari-ance of the means when 1 year sam-ples are included across an agreednumber of yearly age groups. As<7f(p, and af(6) can be assumed to bebiologically given, the IQ sigma on atraditional, culture-contaminated in-telligence test will in general becomesmaller (over school years only)where schools produce a large ageincrement in scholarship and whereopportunity is not highly adapted tonative ability differences, i.e., whenrCf(P) is small.

e. For any same-age group thenature-nurture variance ratio will bemuch higher for gt than gc on thehypothesis that gf is directly physio-

RAYMOND B. CATTEIX

logically determined whereas gc is aproduct of environmentally varying,experientially determined investmentsof gf. At present the only available,and still scant evidence, reached withthe new multiple abstract varianceanalysis method (Cattell, Stice, &Kristy, 19S7) for culture-fair tests(which we shall show are largelygt measures), does point to higherinheritance* for gf. However, al-though it is our hypothesis that gfis biologically and physiologically de-termined, as a function of total corti-cal cell count, this does not mean thatone would expect anything like com-plete hereditary determination. For en-vironment includes gestation period in-fluences and later physical trauma andphysiological change, all affecting gf.

f. The reversible, day-to-day ormonth-to-month fluctuations in levelwill be different in gf and gC) theformer varying only with generalphysiological efficiency (Pribram,1960) and the latter less with physi-ology and more with recent exerciseand interest.

g. The effect of general brain dam-age (e.g., arteriosclerotic) will besimilar in both but more pronounced

4 This conclusion requires some special tech-nical discussion for which we have little spacePrevious studies, such as those of Blewett(1954b) and Burks (1928), Freeman, Eysenck,and others used twin methods in which theenvironmental difference range (that betweentwins) is smaller than in the total family ofsibs, as in our studies. Since the actual ratioswe obtained with Culture Fair Tests are closeto the mean of those they obtained with tradi-tional tests, despite our environmental rangebeing larger, the Culture Fair Tests can beconcluded to have lower environmental deter-

mination. Our ratios were i ? M = ge-

netic contribution for twins, and J*-L5_= 90%90.0

for the genetic component in between-familyvariance in gt (Cattell et al., 1957, p. 154).

in gt. The effect of local brain dam-age will be always to lower gf in pro-portion to the magnitude of the dam-age, but the effect on the g,. score willonly be through the localized abilitychanges, e.g., verbal aphasia (Lans-dell, 1962). Consequently, if the gc

level happens to be estimated from aset of primaries which do not involvethe particular area, as a representa-tive, in the standard array of sampledareas in a traditional intelligence test,no significant fall in gc IQ will neces-sarily be detected following localinjury.

h. The implication in Part a above,that crystallized ability will be a gen-eral factor, i.e., covering a substantialtotal and variety of ability measures,needs to be examined. For such afactor to arise it is necessary thatpeople (a) compete in, i.e., be inter-ested and active over, the same seriesof experiential areas; and (b) experi-ence difference degrees of learningopportunity (to acquire skills) simul-taneously over all these areas. Evi-dence for the capacity of common in-struction and experience to generatesuch group or general factors comesfrom the pioneer researches of Anas-tasi (1936) and of Woodrow (1938);and later work by Greene (19S3),Fleishman (1954), and others. Onlywhen the common variance of experi-ence is considerable would we expectthe magnitude (mean variance con-tribution over a standard sample ofvariables) of gc factor to exceed thatof gf.

Since the present g( levels of a setof people are simple growth-plus-accident functions of their gt levelsobtaining a few years earlier, andsince their present gc levels are onlya somewhat more complex function ofgi levels over preceding years (seeEquation 3), one would theoreticallyexpect gf and gc to be substantially

FLUID AND CSYSTAUIZED IKTZLUGENCE

correlated. The conditions favorableto most substantial correlation prevailin subjects at school age with respectto g«. factor measured over school sub-jects. In adult life, though school sub-jects will continue to correlate by"remnant correlations" (see below), amore valid measure of gc will be madeby weighting a much wider range ofperformances, though any one is likelyto be less loaded than were schoolsubjects. The use of culture-fair tests,to measure gt, becomes, under theseadult conditions especially, the morereliable, valid, and intelligible intelli-gence measure.

i. The rate of learning in any par-ticular area will be a function, as faras cognitive components only are con-cerned, not only of gf, but also of gc,and the level of the specific abilityfactor in that area. In so far as gc

and the specific are concerned, we arethus saying that learning begets learn-ing capacity. Even so, the effect of gcas a general factor should prove to besmall relative to g{ in proportion asthe learning is in a completely newarea. And in old areas the non-grpre-dicted variance is more likely to de-pend upon crystallized group factorsthan the general factor, namely, thoseassociated with what we have calledaids. The demonstration of such ac-tion in learning increments, however,involves complex and refined statisti-cal treatment, as discussed by Hum-phreys (19S9), Lord (1956), Tucker(19S9), Woodrow (1939), and others.

IMPLICATIONS FOR EXPERIMENTALCHECKS ON THE THEORY

The original theory of fluid and crys-tallized general ability has just beenbriefly recapitulated in the form of ninepropositions integrating quite diversefields of psychological observation, andindicating a possible array of tangible

experimental research checks. However,there are further implications which can-not be stated concentratedly in the ninepropositions and which require freer dis-cussion, before the need for certain fea-r

tures in our own experimental designcan be clear.

A first major implication is that theform of fluid ability—as a pattern ofexpressions and loadings—is due to aninfluence present and operative at thetime of the experiment, whereas crystal-Iked ability has a form determined by,and representing, history. Further, oneis biologically, the other culturally deter-mined. Our earlier analogy for ge (Cat-tell, 1943) of the shape of a dead coralformation, representing the propertiesand accidental history of once livingcoral organisms, and Newland's (1962)recent use of "process" and "product"(or Guttman's "analysts" and "achieve-ment") for gf and gc, bring out thismeaning figuratively, in simple meta-phors, but not quite as precisely or com-pletely as the real scientific model needsto do.

In behavioral terms, the theory of gfis that it is "a capacity to perceive rela-tions and educe correlates" in Spear-man's (1932) original sense. Furtherthe theory postulates that relations, be-ginning with those between sensory ele-ments, can be arranged objectively in ahierarchy5 of increasing abstraction and

5 The present writer's definition of intelli-gence proceeds to developments of Spearman'srelational theory which should be distinguishedfrom those for which Spearman would beresponsible. It assumes that the hierarchicalorganization of relationships among relation-ships will begin with sensory fundamentals.The special sense areas will therefore formsubsets, in the sense of mathematical set the-ory, and in a psychological sense, in largersets. From this one might be inclined to con-clude that the most complex relations mustnecessarily lie in the Cartesian space involvingall six sensory sets. This may be, but at leastfor the ordinary ranges of intelligence, suffi-cient complexity can be reached in the hier-

RAYMOND B. CATTEIA

complexity, and that the level of gf ofan individual at a given time is dennedby the position in the hierarchy at whichhis insight fails, as shown by the onsetof chance response behavior. It is a taskfor logicians (Braine, 1959), ecologists,and machine-simulation specialists todevelop bases for this hierarchy; but ourhypothesis would be that it will be foundto rest on sensory area fundaments, andtherefore, require for its genesis intactsensory neurological structure, as statedin Footnote 5. Meanwhile psychologistscan delineate a rough hierarchy bytrial-and-error item construction, or-dered by enlightened difficulty-levelanalysis (extremity-vector analysis;Cattell, 1957, p. 360) experiments.

Most attempts, operationally, tomeasure intelligence, even when it hasbeen conceived as some sort of constitu-tional, fluid-ability, relation-eduction ca-pacity, have been made, however,through first measuring crystallizedability (i.e., on fundaments and evenrelations upon which strong culturaltraining has already occurred). The newmovement which began with studyingrelation-education in perceptual tests(Cattell, 1931, 1940; El Koussy, 1938;Fortes, 1932; Line, 1931; Penrose &Raven, 1936) apparently supports thetheory, however, that quite complex in-telligence-demanding relations can besuccessfully set up in entirely new(and therefore perceptual, not memory-stored) material. Both experience andpsychological reasoning in this area of

archy within the relations arising from onesensory area, to reach the limen of failure ofinsight. This happens because there is a verylarge number of further subsets among whichcomplex relations can hold, even within onesensory area. The successful use of CultureFair Tests (involving largely spatial funda-ments) but transcending merely spatial rela-tions and ability, offers some proof of asufficiently high relational complexity beingattainable upon a limited (two sense) sensoryfoundation.

endeavor lead to the general conclusion,however, that to place individuals intheir proper rank order on gf it is nec-essary that the test fundament mate-rial should be either, (a) equally over-learnt by all, or {b) equally new toall (and therefore "perceptual" in thesense used in this particular field).Anything in between will contaminatethe variance with experiential variance.The sensory area, e.g., whether ananalogies test is visual or by sound,seems unimportant. However, the ap-proach through a—equally overleamt—is risky unless certain conditions arewatched, and even though it ranks per-sons correctly, it gives no correct accountof absolute level. Moreover, there isalways the risk that individuals highlyfamiliar with and trained in a field willknow by rote the correct answers to rela-tional decisions into which they do nothave, and have never had, any insight.For example, many people can respondthat Einstein's famous formula is e —me2, not e=wc8 .

With these introductions to the gen-eral theoretical position we are ready tobring it to precise formulation, and toask what the implications are for acrucial factor analytic experiment. Atthis level of precision it can no longer beassumed, at least in the ordinary cir-cumstances of experimental testing of anintellectual performance, that perform-ance level is going to be determined onlyby fluid and crystallized general ability.The specification equation must putthese hypothesized two general abilitiesin the full context of specific abilities andtemperamental and dynamic traits, asfollows:

PJ = SjiFj + s j2F2+sJnFN +

s jtTT+s,ITi+SjFj [2]

where Fx and F2 are g( and gc, respec-tively (as in the U.I. factor index);the Subscripts T, I, and J represent

FLUID AND CKYSTAIXIZED INTELLIGENCE

temperament, interest (dynamic, moti-vation) , and local area (specific) abilityfactors, respectively, and FN representsa factor of strength of immediate mem-ory (for if, as in senility, the capacity tohold the material is deficient the ana-lytical capacities cannot act upon it).

Actually these latter, in a fully ex-panded formula, would each be severalfactors, but that expansion is unneces-sary for our present statement of essen-tials. If, moreover, the performance (pj)is made a highly intellectual one, andthere is good, uniform, experimental mo-tivation, and sheer speed is not so im-portant that it brings in temperamentfactors, the analysis of the variance inPJ can be restricted largely to the threecognitive factors.

To understand better what would bethe theoretically expected outcome of afactor analysis of purely cognitive vari-ables (i.e., of "intellectual" performancemeasured under such conditions) let us,however, pry more closely into the na-ture of F,. This is our specificationequation notation for gc which, accord-ing to Propositions e and i, should itselfbe resolvable historically into other fac-tors. In fact, any variable likely to behighly loaded on gc might, by specialfactor analysis directed to splitting F2,be expected to yield factors consistentwith the Equation 3. This equationstates that a crystallized ability perform-ance (pjC) is a function of previous time(T) and interest (I) invested in theapplication of fluid ability; memory;and specific, problem solving aids.

[sjiF,e + sJMFMe+sJAFAe] + Q [3 ]where:

Te represents the time given earlier(e) to applying one's abilities ina whole field of intellectual per-formances—i.e., to pjc, Pki and

the numerous other performancescovered by F2;

Tej is time specifically given only to

Ic represents the mean strength ofinterest in learning at that earliertime which, like T, is assumedcommon to several pjc's—e.g.,those in school work;

IeJ is interest specific to p j c only;Fie is the level of fluid general ability

over this earlier (not the pres-ent) learning period;

FMe is a memory capacity factor, alsoat its earlier level at that time;

FAe is an aid, i.e., a discovered "in-strument for problem solving"mentioned earlier9 which oper-ates as a group factor over somearea less wide than the generalability factors;

Cj is a statement of the change, anincrement or deterioration by

8 An aid is a term for the generalizable habit,discussed by Piaget (1947), Hunt (1961),Hayes (1962), Forgus (1955), Ferguson (1956),and others which opens up faster learning ina whole region, e.g., the infant's grasping thepossibilities of babble, the kindergartener's dis-covery that doing to others as one would liketo have done to oneself is an avenue to socialgoodwill, the junior high school student's reali-zation that a triangle drawn on the boardmeans not that particular triangle but a classof triangles, or that letters in algebra canstand for numbers, and so on. Such a pieceof mental equipment stands in the class ofachievement-attainment measures, as the useof FA is intended to remind us. In the last re-sort, it is itself a product of Fi, Fu, etc., andbelongs to that subclass of attainments whichhave the special property of aiding furtherattainment. As such it has an independenceof these other terms and a characteristic fieldof operation, probably as a group factor like aThurstone Primary Ability. In view of thelength of time which Piaget and his followershave been discussing such action it is surpris-ing that there are still no multivariate experi-mental studies demonstrating their existence,and their nature and position among abilitiesgenerally; but they seem a reasonable specu-lation.

RAYMOND B. CATTELL

"forgetting" since the originallearning experience, due to timeand changing interests, retroac-tive inhibitions, etc. (In thescholarship area one may thinkof the effect upon a foreignlanguage area of neglect for adecade.)

The s's are the usual situational in-dices showing by weights specific to thetime, interest, ability, etc., how muchintelligence, memory, etc., contribute toperformance, pJc. The w's are weightssimilarly given to number of repetitions(time of exercise) and strength of in-terest, e.g., w^ is the rate at which in-creased time expenditure brings increasein p jc score.

Two statements in this formula needespecial comment: (a) Whereas in apresent performance the specificationequation for the factor analytic modeladds factors of ability and interest toestimate the performance, we have heremultiplied ability, memory, etc., by inter-est and by the time, recognizing therebya different quality in them from addi-tive influences within the organism.Neither the rather hollow science oflearning theory (still helpless wherehuman higher abilities are concerned)nor the degree of precision of factoranalysis (Tucker, 19S9), permit deci-sion yet as to whether an additive orproduct model is better. But the prod-uct formulation is consistent with ourformulations of motivation in the dy-namic calculus, elsewhere (Cattell,1957a) and is contingently adopted forthese accumulative learning effects, (b)The T and I terms as indicated by theirappearance outside the bracket, are notgiven separate values for the gc, memoryfactor and aid factors, though in an ex-panded formulation they might be givendifferent weights. By the nature of thelearning situation intelligence, memory,etc., would normally operate together so

they are gathered within the bracketswith T and I outside. (The TI, if onewishes, is an integration of interest overtime.) The introduction of the memoryterm (FM) recognizes, as pointed outearlier, that a subject's correct judg-ment, even on a test item of a highlyintellectual kind, may depend on good-ness of rote memory, operating over thecourse of exposure to an intellectual edu-cation. For example, a correct decision ingeometry may depend on rememberingthe formula for the area of a circle, orsolving a crossword puzzle on good rotememory for Greek. As Cohen (1957)shows, the variance in intelligence per-formances from this memory componentbecomes large in older adults.

Now our problem is to ask to whatkind of a factor structure the theoretical,psychological formulation in Equation 3would be expected to lead. Should weexpect distinct factors for T and I? Theanswer seems to be that although veryspecially planned and exceptionally exe-cuted factor analyses might express aproduct relation like TeIeFie as an addi-tion of three factors, the normal preci-sion and choice of variables would yielda single general factor loading mosthighly the variables which have simul-taneously shared high interest, muchtime and much involvement of fluidability. However, because they are mul-tiplied by the same TJ.e the intelligence,memory, and aid factors would tend tobe cooperative (Cattell, 1952) (i.e.,loading the same variables). And if thevariance in TJ* were great, we shouldexpect a powerful second-order factoramong them defined by TeIe. Thus thereare really two possible definitions of thecrystallized general ability factor: (a)As the first-order factor TJeFie , repre-senting the past areas of investment offluid ability, and (b) as the second-order factor—strictly a general achieve-ment factor—corresponding to the in-

FLUID AND CRYSTALLIZED INTELLIGENCE

vestment of Tele in fluid ability expres-sion, memory, and various aids and spe-cial primary abilities.

The situation is further complicatedby the fact that skills not only increasebut decay, and a common history ofchange or decay after the pattern hasbeen reached as in the first part of Equa-tion 3 could also lead to a common fac-tor structure. This, with some over-condensation, we have represented bythe term Cj in the latter part of Equa-tion 3. For example, if Cj is a timefunction and our sample is scatteredfrom 30 to 60 years of age, a generalfactor would tend to appear over allschool subjects due to their all beingforgotten to the same degree, as a func-tion of the time lapse. Such considera-tions have been grossly overlooked intraditional adult intelligence tests, aswell as the fact that a new general crys-tallized ability factor, distinct from thescholastic one, is likely to arise throughcommon learning by the application TeIc

to whatever common areas of gf useexist for adults in our culture. Hereonly culture-fair, but not traditional,intelligence tests seem to recognize thatin the majority of our population whichproceeds to "nonverbal" occupations(e.g., garage mechanics, farmers, etc.) asubstantial decay of the attained crys-tallized ability levels in vocabulary andsimilar areas supervenes (Burt, 1955).Further, the normal adult intense invest-ment of skills in relatively narrow occu-pations will tend to make the appear-ance of a second "adult" crystallizedability factor, superseding the schoolcurriculum crystallized general abilityfactor, a relatively poor substitute, oflower variance and poorer predictivepower.

In summary, one must face the com-plication that the crystallized generalability factor is for various reasons Pro-tean. Strictly the term crystallized in-

telligence (Symbol gc) should be re-stricted to the first of the two factorsmentioned three paragraphs above,namely, to the Expression TeIeFie. Thesecond-order factor covering TeIc[Fic+Fiie+FAe] is in any sense of the word ageneral achievement factor, though itmust be confessed that a substantial partof traditional intelligence test scores de-rive from this source. Both of thesefactors are at the mercy of culture, andeven before one encounters the difficultyof cross-cultural comparisons thereon,one gets entangled in the shift whichoccurs in them between the schoolingage and the adult activity age. The Pro-tean character is thus at best reducibleto four concepts, corresponding to fourcrystallized general ability factorpatterns.

1. School age crystallized intelligence(gcs)—common to gf expressions pow-ered by time and interest within theculturally set framework of the schoolcurriculum.

2. School age crystallized achieve-ment (acg)—a second-order factor acrossintelligence, memory, special abilityareas, etc., corresponding purely to theeffect of common time, interest, memory,and curriculum. It will differ markedlyfrom gca in being predictive of achieve-ments (e.g., athletics, foreign languages,and rote areas of school learning) inwhich gt has never had any appreciableimportance or role.

3. Adult activity crystallized intelli-gence (gca)—representing whateverskills develop strictly from fluid intelli-gence being applied in whatever activityareas receive common time and interestfrom adults, i.e., TaIaFia.

4. Adult activity crystallized achieve-ment (aca)—representing whatever gen-eral factor is produced in adult achieve-ments through their common expendi-tures of time and interest. Except inmixed samples from different cultures

10 RAYMOND B. CATTELL

this would be a very tenuous factor oflittle practical predictive use.

Only in the case of Concept 1 wouldwe expect the correlation of fluid andcrystallized intelligence factors to bereally substantial, and the term intelli-gence is best eschewed completely forConcepts 2 and 4. Also the terms "schoolpractised" and "non-school-practised"abilities are misleading for gc and gf,for the first would describe both Con-cepts 1 and 2 and the second could beeither Concepts 3 or 4, or gf. Any com-bination from decay influences is omittedfrom this reduction to four general fac-tor concepts.

DESIGN OF THE EXPERIMENT INRELATION TO EXPECTATIONS

Testing the theory of fluid and crys-tallized intelligence requires not one ex-periment but a comprehensive organiza-tion of experiments. Yet one whichneeds to be performed before all others,as crucial to further work, is a factoranalysis to check whether one factor ortwo runs through most intellectual per-formances.

Technically, two questions need carein planning such a factor analytic experi-ment:

1. Are we going to aim at abstractingTeIeFjo as a single factor or at splittingit? Theoretically it is not beyond thepower of fine factor analysis to split apresently operating whole into the com-ponents which historically produced it.A product relation would be approxi-mated by additive factors as the plas-mode studied by Bargmann (1955),Cattell and Dickman (1962), Cattelland Sullivan (1962), and Thurstone(1947) sufficiently demonstrate. But inthe present case Te, Ie, and F l e wouldbe cooperative, because by the necessarychoice of tests for intelligence they wouldbe variables also on which common Te

and Io have been expended. Besides

there is much to suggest that productrelations are often revealed by coopera-tive factor patterns. Consequently, sincecooperative factors are hard to rotatecorrectly, it would seem best at thisstage not to attempt such finesse but toaccept variables sufficient to reveal crys-tallized intelligence as a "factor inbeing," if it so exists. When such deeperanalysis is eventually undertaken itwould be well to keep in mind that Ie

might split again into a number of per-sonality and dynamic factors (e.g., superego strength, emotional stability) affect-ing the investment of fluid intelligence incrystallized intelligence skills. Essen-tially this has recently been powerfullyargued by Hayes (1962). Decay factorswill also need consideration.7

2. Provisions must be made for defi-nition by rotation of factors possiblygeneral to every cognitive test employed.One reason why the present theory,rather than the Spearman-Thurstone-Thomson theory of a single general in-telligence factor, has not hitherto re-ceived due and serious consideration isthat most workers in the cognitive fieldhave included only cognitive tests andthus rendered quite impossible any reve-lation of a distinctly rotatable second

7 A summary of the main influences nowposited in any performance in the area se-mantically designated Intelligence might beconvenient at this final step: (a) a fluidgeneral intelligence factor; (6) a crystallizedgeneral intelligence factor; (c) one or morecrystallized auxiliaries, corresponding to timeand application acting with sheer capacitiesto memorize at the former among time (e.g.,knowledge of vocabulary as distinct from nicejudgment of meaning among familiar basicEnglish words); (d) factors corresponding toany general patterns of change or decay sincelearning; (e) existing personality and dynamic(motivation) factors helping application to anintellectual test.

Here b, c, and d have structure in virtue ofhistory, while a and to some extent e are struc-tures due to present organismic functionalunities.

FLUID AND CRYSTALLIZED INTELLIGENCE 11

general factor. The procedures of Burt(1955) and Vernon (1950) for example,neither permit unique determination ofthe alleged general intelligence entity norseparation of a possible second generalfactor.

The technical failure in factor analysishere, by which investigators have failedto see the wood for the trees, is onlya special case of ignoring a generalprinciple in scientific method—namely,the figure-ground principle, according towhich, if we wish to define X adequatelywe must introduce data which is not X.In this case to rotate with any approachto precision a factor expected to be gen-eral to all abilities one must include awide framework of nonability factors(not merely variables) as hyperplanestuff (Cattell, 1952). Indeed, in spiteof the immense importance of the intelli-gence concept to education, the second-order general ability factors appear neverto have been so rotated, in any researchdiscoverable by the writer, to a compre-hensively determined simple structureposition.8

In the present study we planned toreach the second-order analysis withonly nine ability measures—a bare butsufficient minimum for testing the maincognitive hypotheses—but with 13 non-ability measures. The latter were chosen(a) to outnumber abilities, {b) to be

8 In many cases investigators have shown acurious inconsistency in believing that first-order factors should be rotated but secondorders should be left where they fall! (TheSchmidt-Leiman determination of loadings ofvariables on second orders, for example, as-sumes this.) In other cases, the explanationseems to be the usual exhaustion phenomenon,in which, by the time the investigator gets tothe second order of a long factor analysis,neither time nor energy remains to press on toa determinate second-order resolution. Mainly,however, it seems that like early climbers onEverest, they have not dragged along at theearly stages of the expedition the equipmentwhich foresight might have indicated to beessential at the last stage of ascent.

well-known factors, not merely variables,so that they would fan out into a maxi-mum number of dimensions to give sta-bility of rotation of the ability factorswith respect to many reference points,and (c) themselves to have a knownsecond-order structure, the emergence ofwhich in the present blind rotation wouldgive a check on its general correctness.These requirements9 we felt to be bestmet by taking Personality Factors Athrough Q4 (having the same meaning ason the 16 PF Test) on the High SchoolPersonality Questionnaire (HSPQ; Cat-tell & Beloff, 1959).

The nine ability variables consistedof five Thurstone Primary Abilities—Verbal, Spatial, Reasoning, Number, andFluency—and four subtests from theInstitute of Personality and Ability Test-ing (IPAT) Culture Fair IntelligenceTest, Scale 2a—namely, PerceptualSeries, Perceptual Classification, Ma-trices, and Topology. If our hypothesis iscorrect all the Thurstone primaries, withthe exception of Spatial and possiblyFluency preformances should load on acrystallized ability factor (as also shouldbe the case with each specific aid fac-tor).10 On the other hand, the Culture

°This procedure of entering the ability re-search with more personality than abilitymeasures, may seem quixotic to conservativeresearchers, but in addition to the reasonsgiven above it is actually strategically neces-sary in terms of demonstrating that second-order ability factors are in fact distinct frompersonality factors. This can by no means betaken for granted, since some "primary abili-ties," e.g., flexibility of closure, now appear(Cattell, 1957a) as outcroppings of personalityfactors "in disguise" in the cognitive realm.

10 A small note on a large issue is necessaryhere in connection with the notion raised abovethat an accumulation of separate aid develop-ments might constitute a general factor. Themagnitude of the aid factor, F*1 is a joint func-tion of Fi and some environmental "accident"A1, though whether it should be written as(a) Fi = Fx X A, or, (6) FA = Fi •+• A is un-certain. In either case A would be operating as

12 RAYMOND B. CATTEIX

Fair subtests, being purely perceptualand lacking even pictorial reference tothe not-present should load only a fluidgeneral ability factor. However, sinceeven the Verbal item decisions involvesome immediate adaptive performance,the fluid factor should extend to somedegree (in the rotation position denned

a group factor covering from two or three toa large number of performances.

In the early stages of the operation of an aid,as suggested above, it should be detectable ineither case as a group factor. In later stages,it would be possible for an accumulation ofoverlapping group factors to be resolved as ageneral factor, indeed, they would constitutepart of the crystallized general ability. That aset of overlapping small group factors couldalternatively appear as a general factor haspuzzled factor analysts since the early debatesof Thomson and Spearman on the interpreta-tion of g as a "sampling of bonds" versus a"single power." This factor analytic prob-lem can be kept clear only by invoking theprinciple of organismic setting.

This principle states that although each ofa set of separate covariational entities may ap-pear as a separate group factor, yet, if theyall have some quality in common, so that theycan appear as part of a larger organization,then, by simple structure resolution, their sumwill also appear as a single factor, in the con-text of several other, qualitatively different,such accumulations. Thus although each leaf ina heap of leaves is a separate entity and (if itsvariation, e.g., in perception from variousangles, were considered, a separate factor) yetthe heap also has its dimensions, as an entity,among other heaps. Similarly for cells in anorganism or people in a team. What one getsfactor analytically depends upon the organis-mic level at which measurements and rotationsare made.

Even before one gets a shift of organismiclevel, a mere change of scale, from microscopic,or, in terms of psychological variables, fromlow to high density of representation of vari-ables, can convert the resolution from a mul-tiple group factor outcome to a general factoroutcome. Pending further experiment our hy-pothesis is that the variance produced bycummulative action of distinct aids will, exceptfor what is left in the truncated group factors(Cattell, 1962) become part of the crystallizedgeneral ability factor, i.e., Fi and F* in Equa-tion 3 will both go into its variance. Thisstates an important difference from Hunt's(1961) theory.

by the wider realm of personality meas-ures) into such performances as Verbal,Spatial, etc., primaries.

The choice of sample was made on theassumption that Horn's (unpublished)research would use adults. For a com-plete answer on the above hypothesisrequires a check on the expectation thatthe crystallized intelligence factor willbehave very differently (as go, and gca)with children and adults. There is someadvantage in beginning with, say, 12-year-old children, because we may ex-pect less complication from any decayterm (Q in Equation 3). Also one mightexpect the gCB factor, based on so uni-form an area of earlier application, tobe larger than with adults (about thesame variance as the gr) and thus easierto locate in a first study.

DATA AND ITS ANALYSIS

The sample consisted of 124 eighthgrade boys and girls from Paxton, Illi-nois, and 154 from the seventh andeighth grades of a junior high school inSpringfield, Illinois, a total of 277 (i.e.,one dropped) being carried forward tothe analysis. The Thurstone Primaries(except for Fluency) were given in bothforms, and HSPQ was similarly givenin separate A and B scores for eachprimary personality factor; but the Cul-ture Fair Intelligence Test used onlyone form (which must be remembered inappraising later saturations). Testingtook about 3 hours and was under oneexaminer.

The first order analysis requiredproduct-moment correlations11 for 44

1 1 The correlation matrix, centroid, lambdatransformation, and final simple structurematrix have been deposited with the Ameri-can Documentation Institute. Order DocumentNo. 7381 from ADI Auxiliary PublicationsProject, Photoduplication Service, Library ofCongress; Washington 25, D. C, remitting inadvance $1.25 for microfilm or $1.25 for photo-copies. Make checks payable to: Chief, Photo-duplication Service, Library of Congress.

FLUID AND CRYSTALLIZED IKTTT.UGE.NCE 13

variables (9 Thurstone abilities, 4 Cul-ture Fair subtests, and 28 HSPQ per-sonality variables), i.e., in all 41 plus 3random variables for hyperplane testing.Since they consisted mainly of pairedmarkers for factors, it was not surprisingthat the Tucker (Thurstone, 1938) andGuttman (Cattell & Sullivan, 1962)tests (separately applied) pointed to20-24 factors to be extracted. We settledon 22 as the limit for determinate, con-verged, iterated communalities and iter-ated four times to reasonable stability.

The rotation for simple structure wascarried out with extreme care, since aswill now become apparent, all conclu-sions in the second order hinge upon theangle values settled upon in the first.Simple structure reached, after fouroverall rotations, the very high value of82% of all variables lying within the±.10 hyperplane. At this point in the

blind rotations an inspection showed thatthe usually accepted structure for boththe Thurstone Primary Abilities andHSPQ primary personality factors hademerged, independently, with excellentclarity. The two prescribed markers,and virtually nothing else, loaded eachnamed factor. Although only one markerhad been inserted for Fluency and eachCulture Fair subtest, these five picked upenough on other variables, e.g., classifi-cation had loading on HSPQ Factor B,for each to appear as a nonspecific fac-tor, though they are in the usual widersense, specifics.

The CR matrix for this carefully ro-tated study was now inverted to givethe correlations among the 22 factors(CF=DCE"1D) and this was again fac-tored. The advantage of proceeding tothe second order from the CB insteadof from correlations of actual batterymeasures of the factors is that we elimi-nate distortions from the unreliabilitiesand imperfect validities of actual scales.In exchange we pick up whatever un-certainties remain in the simple structure

rotation, but with at least 20 variables todefine the hyperplane, this should bea lesser risk and offer a better design.

Centroid factoring of the first-order22-factor matrix yielded, by the samepair of criteria as before, 8 factors. Theirsimple structure rotation is shown inTable 1, together with Cp of their cor-relations (see Footnote 11). The simplestructure here is no longer quite as cleanas at the first order. If the oddity ofFactor 7 is omitted (with which we arenot much concerned) the count is, how-ever, still 59%, which is high amongreported studies and at any rate theessential maximum or plateau attainableamong present possible rotations.

The structure of Table 1 reveals un-mistakeably the distinctness of the fluidgeneral ability pattern, which is Factor 1(loading the four subtests of the CultureFair, the Thurstone Spatial, and theHSPQ Ego Strength, C, factor), and thecrystallized general ability factor, Fac-tor 2, which loads Verbal ability, Rea-soning, and Number most highly. Thatthese two ability factors, roughly orthog-onal to the remaining six, are essenti-ally in the right position is attestedfurther by the correctness of the second-order factors emerging among these lat-ter personality factors. Factor 3 is thetypical U.I. Q. I. (Cattell, 1957a) sec-ond-order extraversion factor (Carrigan,1960) covering the primaries A, D( —),F, H, Q 2 ( - ) . Factor 4 is the generalAnxiety versus Adjustment factor—C( - ) , 0 , and Q,( - ) , (with Q3 slightlyanomalous); and Factor 5 continuesthese previously recognized second-orderfactors to include that indexed as U.I. Q.I l l (Cattell, 1957a). Although theseare to be remarked here only as confir-mation of the "setting" for the two mainability factors, it is possible that Factor6—"super-ego-good-upbringing" or Con-trol—has also some interaction withcrystallized ability.

Let us for the moment postpone ex-

14 RAYMOND B. CATTELL

TABLE 1

SECOND-ORDER FACTORS AND THEIR INTERCORRELATIONS

Part A: Factor

First order factorvariable

Thurstone primariesVerbalSpatialReasoningNumberFluency

IPAT Culture Fair subtestsSeriesClassificationMatricesTopology

IPAT HSPQA CyclothymiaC Ego StrengthD ExcitabilityE DominanceF SurgencyG Super Ego StrengthH ParmiaI PremsiaJ CoastheniaQ TimidityQ. Self-SufficientQ» Self-Sentiment ControlQ. High Ergic Tension

% in ± 1 0 hyperplane

1. Fluid general ability2. Crystallized general ability3. Extroversion versus In via4. Anxiety versus Adjustment5. UJ. Q. HI6. Control7. ?8. ?

loadings

F,g<

.15

.32

.08

.OS

.07

.35

.63

.SO

.51

- . 0 4.21

- . 0 4- . 1 5- . 0 5- . 1 4

.21- . 0 9- . 1 0

.16- . 0 6

.05- . 0 4

.51

Part B

1.00.47.29.35.09.21

- . 0 1- . 1 5

(in reference-vector correlation

F,ge

.46

.14

.50

.59

.09

.43- . 0 2

.10

.09

.52- . 0 7- . 4 4- . 0 1

.09

.08- . 0 4- . 2 9- . 0 4- . 0 1

.05- . 0 2

.37

.60

F.Exvia-Invia

- . 1 7- . 0 2

.08- . 0 4- . 5 2

.05- . 0 5- . 2 3

.16

.31- . 0 4- . 4 4-.OS

.39- . 0 1

.55- . 0 5

.01

.01-37

.06

.03

.60

FiAnxiety

— .03- . 0 3

.02

.OS- . 1 8

- . 1 2-.OS

.04

.12

- . 2 3- . 5 2- . 0 9- . 0 0- . 0 7- . 1 0- . 1 7

.2639.73

- . 0 5.00.45

.51

: Factor correlations

.471.00

.17

.15- . 0 3

.28

.03-20

.29

.171.00.17

- . 0 1.10

- . 2 4- . 0 5

35.15.17

1.0024.06.14

- . 1 2

F,UJ.Q.in

.04- . 0 3- . 0 2- . 0 7

.12

.06

.00- . 0 1

.03

.05- . 0 8

.09

.61

.06- . 1 0

.00- . 5 4— .12

.09- . 4 3

31- . 0 0

.73

.09- . 0 3- . 0 1

.241.00

- . 4 6.06.26

form)

F,Control

.07

.OS

.02- . 0 5

.26

.10

.14- . 0 8- . 0 3

.11- . 0 9

.04- . 0 4- . 4 0

.43

.13-.OS

.45- . 0 4- . 0 4

35-37

.55

.21

.28.10.06

- . 4 61.00.07

- . 7 0

F7

?

-.OS-27

38- . 1 0

.13

.24

.16-25- . 1 4

.20- . 4 9

.14- . 0 2- . 2 0

.41

.03

.43

.01

.10- . 0 4

.56— .14

32

- . 0 1.03

— .24.14.06.07

1.00- . 1 1

F.?

- 1 2.04

- . 1 4.03

- . 0 7

.04

.06

.42- . 0 0

.03

.12- . 2 7- . 1 7- . 0 9

.OS- . 0 3- . 0 1

.16

.17

.05

.11

.05

.60

- . 1 5-20-.OS- . 1 2

.26- . 7 0— .11

1.00

perimental examination of our assump-tions about the inherent modes of ex-pression of these two factors as shownby loadings and pause to examine theirmutual relation as shown in Tables 1and 2. The substantial positive corre-lation, + .47, shown in Table 1, Part B,is what would be expected from our

theory, on the grounds that both mustbe highly related to an entity whichexisted a few years earlier, and which wehave symbolized (Equation 3) by Fie

(or gfe)—the fluid ability level earlier.The present crystallized ability level—F2 (or gc)—is a function of F t e and thetime and interest applied at that time.

FLUID AND CRYSTALLIZED INTELLIGENCE 15

The present fluid ability level—F2 (orgf)—is an organic continuation of Fie,falling short of perfect correlation withit only because different times haveelapsed for different people and the in-terlude has treated them more or lesskindly in terms of brain damage, etc.

If next we ask what this correlationimplies in terms of a third-order analysis,different theories will give different an-swers. Our theory would posit that Fjand F2 (g<; and g() should come togetherin a single higher order factor, becausehistorically a single influence, Fu, is re-sponsible for them both. It has, so tospeak, fathered Fj out of time (as "thechild is father of the man") by simplematuration, and F2 out of experience byinterest and learning investment.Whether the third-order F]e should loadhigher on Fj or F2 depends on manythings. High similarity of experiences(including time length) and interestshould raise the loading on F2, whereasheterogeneity of the group in this respectshould lower it. Heterogeneity of thegroup in age and time lapse since theformative period of gc should lower theloading in F L In a group of schoolchildren such as the present, in themidst of their growth period, the Fie

loading in Fj should be quite high andthat in F2 a little short thereof. In adultsor children more heterogeneous for age,the loadings should both be lower.

The third-order analysis designed totest these hypotheses again had, by rea-son of the initial planning, enough hyper-plane stuff to determine the rotation ofthis still broader general ability factor.Further, the rotation was again madewith pure factor measures, not error-contaminated actual battery scores, forsimple structure was attained in the ref-erence vector matrix underlying CFshown in Table 1. In this CF four factorswere indicated by the Tucker test and asatisfactory 63% in the hyperplane was

T A B L E 2

THIRD-ORDER FACTORS AND INTERCORRELATIONS

Second-order factorsThird-order primary factors

I. 2. 3. 4.

Fluid intelligence .69 .02 —.07 .00Crystallized intelligence .63 —.04 .07 .32Extraversion versus Invia

(U I. Q. I) .18 .03 .38 .23Anxiety versus Adjustment

(U.I. Q. II) - . 0 1 .01 00 .79U.I. Q III .09 —.51 —.07 .32Control .01 .99 —.03 —.05FT .06 .03 —.74 .04Fs .02 —.69 08 —.06% in it 10 byperplane

Primary factor correlations at third order

1.2.3.4.

1.00.38.14.25

.381.00

.00

.10

.14.00

1.00—.16

.25

.10—.161.00

obtained after five overall rotations, withresults shown in Table 2.

If our hypotheses is correct it wouldnot be right to conclude from Table 2that "fluid and crystallized generalability form a single third-order factor,"but rather that a single influence, whichis fluid ability as it stood during theformative period of crystallized ability,is causative to the present levels of both.That this "formative fluid ability" influ-ence is in fact Fi in Table 2 could bechecked by preserved records of thesubjects' earlier fluid ability scores. Itis noteworthy in Table 2 that this fluidability factor has no significant loadingon any personality factor, but stands asa measure of pure ability. On the otherhand, it has slight, significant correla-tions as a factor with control and anxietyof a kind we have come to expect fromthe linking of intelligence with otherfactors through the natural selection ofsocial status (Cattell, 1945; Fisher,1958). The factor contingently dubbedControl here has, on the other hand,significant relations to crystallizedability in Table 1 and must be consid-ered one of the personality factors con-tributing, partly by aiding school memo-

16 RAYMOND B. CATTEIX

rizing, to crystallized ability, via FM,etc., in Equation 3 above.

NATURES OF FLUID AND CRYSTALLIZED

INTELLIGENCE

With concepts denned and checked atthe experimental level we can now pro-ceed to broader formulations. The state-ments so far are:

1. That intelligence test and schoolperformances must be considered, morecomprehensively than hitherto, to be de-termined, at the moment, by personalityand motivation factors as well as by twodistinct second-order general factors,(fluid and crystallized intelligence) assymbolized in Equation 2. Equation 2is primarily an expression for perform-ance in a timed test, but with trivialadjustments, is also an expression forrate of learning.

2. As a result of this mechanism oflearning operating uniformly acrossschool subjects, and other areas, for timeintervals differing for different people,third-order general factors of schoolachievement (for children) and adultactivity achievement (for adults) arecreated. (There is no space to discusstheir relation here, but they should beslightly positively correlated.) The termcrystallized intelligence, however, is se-mantically better reserved for thesecond-order factor in such performancesas derive their positive correlations onlyfrom the action of fluid ability, not frommemory and various special abilitiesoperating in the school (or adult) set-tings. Crystallized intelligence andachievement are thus not identical gen-eral factors, the former being narrowedin manifestation to the handling of com-plex relations, whereas the latter couldcover whatever the breadth of the cul-tural schooling curriculum embraces.

A special logical complexity ariseshere, however, in that rate of learning incomplex fields is assisted both by fluid

and crystallized general abilities, as wellas by such aids (usually primary, groupfactor patterns) as are relevant to theparticular field (Equation 3). Conse-quently, crystallized ability must be con-sidered to be begotten by crystallizedability as well as by fluid ability. Thismay seem to contradict the conceptabove that crystallized ability is aconsequence and function of fluid abilitylevels, but it is not so if we consider (a)that fluid ability is so to speak put outat compound interest, and recognizealso that the rate of return may be dif-ferent over different periods of learning,depending on interest, etc.; and (b)that crystallized ability is not only afunction of fluid ability but also of per-sonality factors, etc. Thus personalityfactor "deposits" occur in what at thetime of learning is considered an ability—crystallized general ability—and alsoin aids. If space permitted, these rela-tions of earlier personality and motiva-tion factors, as operating in Equation 2to crystallized abilities as in Equation3, could be worked out in a fourth or"historical depth" equation.

As to the descriptive similarities anddifferences of gt and ge, both are verygeneral to complex, intellectual, rela-tion-perceiving performances, and evenin regard to the variables chosen to dis-criminate them one notices, in Figure 1,that each has some tendency to load thevariables set to mark the other. However,the slight loading of crystallized intelli-gence in say Pluency is not as great asthat of fluid ability in Verbal or Series.(Note with oblique axes the lines ofprojection are drawn parallel to the axesin Figure 1.) Parenthetically, it will benoted that if the experiment had beenundertaken without personality fac-tors, etc., as hyperplane substance, therotator would almost certainly havefallen into the false resolution of makingthese factors more highly correlated

FLUID AND CRYSTALLIZED INTELLIGENCE 17

CKVSTAUJZED t

FIG. 1. Culture-fair subtests and ThurstonePrimaries in relation to %t and ge. (Rotationassisted by 16 PF factors in hyperplane.)

(especially in the absence of D, I, A,and Q2) by going through the abilityvariables only, e.g., through Verbal andTopology.

Figure 1 also confirms the whole argu-ment of Equation 2 to the effect thatcrystallized intelligence, being partly theproduct of motivational and personalityhistory, will have more significant asso-ciation with personality factors. Thisassociation is not only statistically sig-nificant but makes psychological sense,for crystallized ability correlates sub-stantially positively with Cyclothymia(Factor A in HSPQ), and negativelywith Excitability (D), and Premsia (I)which other researches show to besimilarly related to general schoolachievement. Similarly in the motiva-tion realm (Connor, 1961), docility (lowself-assertion) and super ego strengthhave the highest correlation with totalschool achievement. Their correlationswith the Verbal (V) factor, the Rea-soning (R) factor, and the Culture Fairare, respectively, .20, .48, and .02; and.19, .41, and - .02 , (see Footnote 10)the Culture Fair (fluid ability) measuresconsistently being more free of associa-tion with personality factors affectingachievement. As stated above, this

greater freedom of the second-orderfluid ability from personality loadings,which supports our hypothesis, is notincompatible with its having correla-tions therewith at the third order, point-ing to genetic and social status ties.12

A word is necessary here to forestalla misunderstanding which will almostcertainly arise in the attempt of con-servatives to avoid any major restructur-ing of ideas. This will be the view thatgf is nothing more than the k or "prac-tical ability" factor, located by suchfactorizations as those of Vernon (1950)and Cohen (1957). There are three goodreasons for rejecting this. The first,comparatively trivial, is that k has al-ways shown decided associations withmasculinity and mechanical experiencewhereas in our mixed boy and girl sam-ple gc shows statistically no differenceand is actually a shade higher for thegirls. Secondly, and more systemati-cally, the whole mode of factor resolutionin the Burt-Holzinger-Vernon bipolarsystem is quite different from multiple-factor simple-structure resolution andnever yields a one-to-one matching. Theformer method puts verbal ability on oneside and practical-mechanical on theother. In the present writer's opinionthis is in any case a fallacious form offactor resolution, for since the first gen-eral factor is indeterminate, the wholehierarchy is fictitious. But, fallacious ornot, it is, except by some accidental

12 In looking for indications of some sep-arate action of the interest-personality factorsposited in Equations 1, 2, etc., one may notein Table 1 that Factors 6 and 7 admit of asingle factor being rotated from them whichloads the two Super Ego factors, G and Q»;Desurgency, F( — ) ; and positive performanceon Reasoning, Fluency, Series, and Classi-fication. It makes good psychological sense thatsuch cognitive performances should be aidedby such personality factors, but it suggeststhey are acting in the present test situation(as in Equation 1) rather than through help inpast performance as in Equation 3.

18 RAYMOND B. CATTELL

caricature, too different for gt ever tobe identified with k. Finally, however,gf is not particularly loaded on mechani-cal aptitude variables (the evidence isnot given here, but in Horn, unpub-lished), or in spatial ability measures, orone-sidedly in any of those performanceswhich have been included in this vagueand impractical practical ability artifact.

On the last issue—that of giving us afar more complete descriptive differenti-ation of gf and gc in the extent andnature of their loading fields—there isadmittedly a great deal still to be foundout. Considering the volumes of abilitycorrelating that have gone on over thepast 20 years it has been, to say theleast, theoretically uninspired. Espe-cially the hypothesis should be testedthat gc's loading pattern will alter withage, subculture, and culture whereas g('swill not. Already such studies as thatof Sisk (1940) point to the effect on theform of the crystallized intelligence pat-tern of such very local influences as an"interest in study" over particular col-lege courses shared by members of agroup. However, one unjustified as-sumption needs to be scotched whichhas been, among teachers, as obstructivein holding up the practical introductionof culture-fair tests, as the k illusion hasbeen in buttressing outworn theory. Thisis the "faith validity" judgment that be-cause such tests employ shapes theymust be testing spatial ability. As Fig-ure 1 shows, the loading of the fluidgeneral intelligence factor is not as greatin Spatial as in Matrices, Topology, andSeries tests, and though such tests de-pend on perception there is as yet noevidence that they load unduly Thurs-tone's perceptual factors.

If, as stated at the outset, the theo-retical aim of culture-fair intelligencesubtest construction is to require com-plex relation eduction in material thatis either completely new to or completely

overlearnt by all persons to be tested, itis of interest to discover what theseareas may be. A systematic attack onthis was begun some years ago in thework of Cattell (1940), Line (1931),Fortes (1931), and others and pointedto simple spatial perception, shade andpitch perception, and probably tactileexperience and awareness of the body,as being sufficiently overlearnt in mostcultures, but this exploration was nevercontinued. Meanwhile, from a practicalintelligence test construction standpointit is interesting to note that the Classi-fication, Topology and somewhat less,the Matrices tests are good measures offluid ability (at any rate as used in theCulture Fair Test) and Number, Rea-soning and Verbal primaries of crystal-lized ability. Incidentally, the evidenceof cultural learning in the Series testis a bit surprising.

While commenting on odd loadings inTable 1 one may note also the loadingwhich a factor, Number 8, outside thegeneral ability factors, has on the Ma-trices test. The present writer has else-where argued, on the theoretical likeli-hood of such a loading, against the le-gitimacy of using Matrices alone, formeasuring fluid general intelligence, in-stead of a complete Culture Fair batteryaveraging several subtests. This showsthat indeed appreciable specifics orextra factors are as likely to occur inperceptual as in traditional subtests. Itis possible they will not prove to be cog-nitive specifics, but, as the present analy-sis suggests, less than half of the variancein Matrices appears to lie in general in-telligence, and the rest is sheer unknownbias in the test measurement if Matricesalone is used as an intelligence test.

As to the present accuracy of estimateof Fi and F2 the loadings of the subtestsin the Culture Fair battery18 on the fluid

18 The search for further good subtests mightnow be guided by the emerging theory that

FLUID AMD CRYSTALLIZED INTELLIGENCE 19

ability factor are, in general, as good as,or a little better than, those of theThurstone primaries on the crystallizedability factor (mean=.40 as against.36).

NEEDED RESEARCH

At the present moment researches onthese theories are as vital in the appliedas in the basic field. For if the mainconcepts are correct, present routine test-ing practices in school, and still more invocational selection of adults, are wast-ing a lot of talent. The traditional in-telligence test, because it confounds fluidwith crystallized intelligence and evenwith the third-order general attainmentfactor, gives a speciously good correla-tion, at least in schools, with the crite-rion. A test in June predicts academicachievement in June (or even in thefollowing September) for the simplereason that it already surreptitiouslycontains in itself most of the criterion itis claiming to predict. In fact, if short-term correlation is all that is required itwould be sensible to abolish intelligencetests and predict from today's schoolachievement to tomorrow's.

But the idea of introducing intelli-gence tests has surely much broader ob-jectives. I t aims to give psychologicalunderstanding of causes of backwardness

fluid ability shows itself most highly, relativeto crystallized ability, in complex relation andcorrelate eduction performances where crys-tallized ability is eliminated either by (o) allsubjects being entirely untrained in the per-formance, or (6) aU subjects being com-pletely overlearnt in the fundaments (but notthe relations, else intelligence would disap-pear) ! Possibly Culture Fair Subtest Number4, Topology, is an example of the former andSpatial ability of the latter, since the latter isa common requirement of bodily movementfor people in all cultures. This definition ofone property of the fluid general ability needsto be experimentally pursued in relation to theother hypothesized properties above, nowthat the factor can be isolated.

or sources of high performance, to per-mit prediction of more remote perfojrm-ances in time and place, and to permit usto apply a psychological science viafunctional analytical concepts. Thewriter had a student who never went toschool till 17, who was soon gettingstraight A's as a junior in college, hedid splendidly on a culture-fair test at17 but would have been excluded fromcollege on his traditional intelligencetest or achievement performance. Thediscrepancy of gc and gt is, however,mostly small in the school years, so longas we have homogeneity of school, cul-tural subgroup, and social status. It isin the adult field, e.g., in selecting for anintelligence-demanding learning oppor-tunity among persons of different agesand distances from school activities, indifferent regions, that failure to measuregt and gc separately could lead to seriousmisdirection. How fair is the MillerAnalogies to engineering students com-peting for graduate school positionsagainst English majors, compared witha culture-fair test? It is well knownthat the norms of extensively standard-ized traditional intelligence tests areinvalidated within 2 or 3 years of theirproduction by changing (usually in-creased!) school and cultural educationlevels. Is this intergenerational "creep"of norms on crystallized intelligencetests avoided by culture-fair tests aspreliminary data (Cattell, 1957b) in-dicates? These are the problems whichapplied research should be facing.

In terms of basic research a realmof fascinating concepts and possibilitiesis opened up. Is it possible that gf

minus gc might be the best predictor oforganic brain damage? Can gt and gc

also be separated by intraindividual, Ptechnique factoring, demonstrating thefunctional unity of each in terms of sus-ceptibility to day-to-day changing con-ditions and stimuli? What clarity might

RAYMOND B. CATTELL

be brought to the vexed question of pre-school ability organization by these con-cepts? (There are important leads herein the work of Burt, 1955; Hebb, 1942;Hofstaetter, 1954; McNemar, 1940;Reitan, 1958.) Will nature-nurture ra-tios calculated on gf measures prove tobe altogether more highly geneticallydetermined than gc measures? Is the gf

IQ more constant?Is it possible that what Thurstone

called primary ability factors are psy-chologically the same as what we havecalled aids above? Probably both willconsistently appear as first-order factors,relative to gc and gf as second order, and,although some may well be genetic inorigin, the theory is worth exploringthat many first orders will prove to begrowths from a specific breakthrough(in the form of hitting upon a habit ofanalysis which becomes instrumental toa whole sequence of skill). In view ofthe elaborate writing of Piaget, and stillmore the speculations of his followers,regarding structures of this kind (seethe recent summary by Hunt, 1961) it ishigh time that more precise correlationalmethods should attempt to demonstratethese patterns and relate them to thethree types of formation here discussed.14

But perhaps good research strategyindicates that the first necessity today isthe checking of the existence of the twogeneral factors in groups of differingages, homogeneities, and cultural set-tings, in relation to the obvious differ-ences which would be expected from thetheory. For example, this experimentneeds repeating with age-homogeneous

14 In so far as the discovery of each aid (in-strument for further problem solving) mustbe partly a function of fluid ability level, apart of the variance of all aid developmentswill be absorbed in the general factor of crys-tallized ability. The F/s of Equation 3 wouldrepresent, therefore, only the narrow groupfactor variance left over after this absorptionin the general factor.

groups at 30 and 50 years of age; withadults heterogeneous as to age; and withmixed "normals" and known brain dam-aged cases. It needs to be tried withlarger ranges of variables, identicallyused with two or three different culturalgroups, to see whether the third-orderachievement general factor can be sepa-rated both from the second-order crys-tallized intelligence and fluid intelligencefactors, and especially we need age plotsof the differing course of these two fac-tors, each with and without speed limitsin testing.

SUMMARY

The theory of fluid and crystallizedgeneral intelligence factors has been ex-amined in regard to an array of implica-tions. A distinction has been drawn be-tween a general achievement factor andthe crystallized intelligence factor. Both,as distinct from fluid intelligence, willso change their pattern (a) with age,and (b) with culture as to constituterelatively poor predictors of other per-formances in groups of different agesand heterogeneous subcultures.

An experiment factoring 44 hypothe-ses-relevant variables measured on 277seventh and eighth grade boys and girls,with sufficient noncognitive variables topermit effective rotation of any generalcognitive factors which might appear,demonstrated the existence of two gen-eral ability factors. One fits the crystal-lized ability factor measured in tradi-tional intelligence tests and the other afluid general ability measured in culture-fair intelligence tests. Evidence is offeredthat the latter is neither a spatial abilityfactor nor the so-called "practicalability" (k) factor, but basic generalintelligence. These two general abilitiesappear in a single third-order factor hy-pothesized to express the "formativefluid ability" partly responsible for thepresent level of both of them.

FLUID AND CRYSTALLIZED INTELLIGENCE 21

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(Received April 20, 1962)