Spearman's Two-factor Theory of Intelligence Explained

He proposed that intelligence consists of two factors, i.e., the ”g” factor (general ability) and the ”s” factor (specific ability), where the ”g” factor is ... HomePsychologySpearman’sTwo-factorTheoryofIntelligenceExplained PrevArticle NextArticle     Whatisintelligence?ifyouaskthisquestiontodifferentpeople,everyonemaygiveyouadifferentanswer,accordingtotheirperspectives.Forsomepeople,apersonmaybeintelligentifhe/sheisquickatsolvingvariousproblemsoransweringquestions,whileforothers,itmayberelatedtothesuccessandachievementsoftheperson.Definingtheterm‘Intelligence’hasalwaysbeendebatableamongthefraternityofpsychologistsasdifferentpsychologistshavedifferentviewsonthetermintelligence.Generally,intelligenceisdefinedastheabilitytouseallthecognitiveprocessesinvolvingplanning,attention,learning,andsolvingday-to-dayproblems.Todefineintelligence,ameetingwasorganizedin1921,consistingof13renownedpsychologistsspecializedinthefieldofhumanintellectualabilities.Theproceedingofthismeetingwaspublishedinthe“JournalofEducationalPsychology”thatrevealedthateverypsychologistgaveadifferentdefinitionofintelligence.Someofthedefinitionsofintelligencegivenbythedifferentpsychologistsaregivenbelow, AccordingtoStern, Intelligence,thatistosay,reasoning,judgment,memory,andthepowerofabstraction” AccordingtoBinet, Intelligenceisageneralcapacityoftheindividualconsciouslytoadjusthisthinkingtonewrequirements” AccordingtoSpearman, Intelligenceisthecapacityoftheorganismtoadjustitselftoanincreasinglycomplexenvironment” Variousintelligencetheorieshavebeenproposedbydifferentresearchers,andSpearman’stwo-factortheoryofintelligenceisalsooneofthem.Wewilllearnaboutthistheoryinthisarticle. IndexofArticle(ClicktoJump) CharlesEdwardSpearmanSpearman’sTwo-factorTheoryofIntelligenceMathematicalExplanationofSpearman’sTheoryEducationalImplicationsofSpearman’sIntelligenceTheoryCriticismsofSpearman’sTwoFactorIntelligenceTheory CharlesEdwardSpearman CharlesE.SpearmanwasaBritishpsychologist,whowasbornon10September1863inLondon,England.Heisthepioneerofapopularstatisticalmethod‘factoranalysis’andisalsoknownforhisworkon‘Spearman’srankcorrelationcoefficient’andhis‘two-factortheoryofintelligence.’HedidhisschoolingatRoyalLeamingtonSpaCollege,U.K.In1883,hejoinedtheBritishArmyasanengineerofficer,andwhileservingintheRoyalMunsterFusiliersin1893,hewaspromotedtothepostofcaptain.Healwayshadagreatinterestinphilosophy,sohedecidedtopursuehisacademicsinphilosophy.Hence,afterservingfor15years,heresignedfromtheBritishArmyin1897.Hewantedtostudyphilosophy,butlater,herealizedthattheadvancementtotheconceptsofphilosophycanonlybedonethroughpsychology,whicheventuallymotivatedhimtostudypsychology.In1904,hepublishedhispaperon‘factoranalysisofintelligence’anddevelopedhistwo-factortheoryofintelligence.HecompletedhisPhDatLeipzigUniversity,Germany,whereheworkedwiththe‘ExperimentalPsychology’founder‘WilhelmWundt.’Later,heworkedasaprofessorintheUniversityCollege,London,andhediedon17September1945. Spearman’sTwo-factorTheoryofIntelligence CharlesEdwardSpearmanproposedhistwo-factortheoryofintelligencein1904.Hewasthefirstwhointroducedtheconceptofgeneralintelligencecalledthe”g”factor.Todevelophistheory,heanalyzeddifferentmentalaptitudeandcognitivetestsgivenbytheparticipants.Henoticedthatthescoresofthesameparticipantswerealmostsimilarineverytest.Thosewhohadagoodscoreinoneaptitudetesthadalsoscoredwellinotheraptitudetests,andthosewhoperformedbadlyinonetestalsoperformedsimilarlyinothertests,whichrepresentsthatthereexistsafactorthatiscommontoalltheintellectualandcognitiveabilitiesoftheperson.Usingthefactoranalysistechnique,atechniquethroughwhichvariouscorrelatedvariablesarereducedtothelowernumberoffactors,heexaminedthecognitivetestsandconcludedthatfactorsrelatedtointelligencecanbemeasuredandexpressednumerically,itsmathematicalexplanationisdiscussedfurtherinthisarticle.Spearmanstatedthatvariousmentaltraitsarenotindependentofeachother,andthereexistsacommonfactorinallthecognitiveabilitiesoftheperson,hecalledthiscommonfactorageneralfactoror”g”factor.Heproposedthatintelligenceconsistsoftwofactors,i.e.,the”g”factor(generalability)andthe”s”factor(specificability),wherethe”g”factorisinvolvedineverygeneralmentalabilitytaskoftheperson,andthe”s”factorisresponsibleforonlythespecificintellectualabilitiesoftheperson.Itistobenotedthatalthoughthenameofthistheoryistwo-factor,therearemorethanjusttwofactorsasthesfactorhasvarioussub-factors,dependinguponthenumberofspecificabilitiesineachtest.Itmeansthattherearetwodifferent‘kindsoffactors,’i.e.,ageneralfactorandspecificfactors.Thespecificabilitiesofapersonmaybedrawinginterference,codingabilities,mathematicalabilities,andsoon. AccordingtoSpearman,everyindividualisbornwithadifferentlevelofthe”g”factor,andthegreaterthe”g”factor,thegreaterarethechancesthatthepersonwillsucceedinvariousaspectsoflife,whereasthe”s”factorisnotinborn,peopleacquirethisfactorthroughexperiencesandfromtheirsurroundingenvironment.The”g”factorissharedwitheveryothercognitiveorintellectualactivityoftheperson,butthe”s”factorisnotsharedwithdifferentintellectualactivities,it’sspecifictoaparticularactivity.Letusunderstanditwithanexample,considertwotests,i.e.,‘numerical’and‘verbal,’whichhavethespecificfactor‘S1’and‘S2,’respectivelyandcommonfactor”g,”andconsideranothertwotests,‘spatial’and‘mechanical,’havingspecificfactors‘S3’and‘S4’respectivelyandcommonfactor”g.”Here,”g”representsthegeneralability,and”s”representsthespecificabilitiesoftheperson.Thiscanbeunderstoodfromthefiguregivenbelow,whichshowsthatthe”g”factoriscommoninallthespecificfactors.Spearmanstatedthatthemainpurposeofthepsychologicaltestsistomeasurethe”g”factoroftheindividualsbecauseitisthecommonfactorinallthecognitiveabilities,andeveryindividual’sintellectualabilitiesandperformancedifferbasedontheir”g”factor. Thisfigureshowsthatthe“g”factoriscommoninallthespecificfactors,i.e.,S1,S2,S3,andS4. In1927,Spearmanpublishedhisbook,“TheAbilitiesofMan,”inwhichhecalledthe”g”factoras‘mentalenergy,’andelaboratedtheconceptsofthe”g”and”s”factors.Hestatedthatthedegreesofthe”g”factororgeneralintelligencevaryineveryindividual,andthe”g”factorofthepersoncannotbeincreasedupontraining,but”s”factorscanbeimproved.Mathematically,Thetotalintelligencescoreoftheperson(I)isthesumofthe”g”factorand”s”factorsthatanindividualpossesses,i.e., I=g+S1+S2+S3+S4+… WhereS1,S2,andS3representthedifferentspecificabilitiesoftheperson,saymechanical,numerical,vocabulary,orspatialabilities. Spearman’sTwo-factortheoryofintelligencehasagreatcontributioninthefieldofpsychologyasitintroducedtheconceptoffactoranalyses,whichisnowwidelyusedbymanyotherresearchersintheirstudies.AnAmericanPsychologist,JoyPaulGuilford,whoispopularlyknownforhispsychometricstudyofhumanintelligence,hasstatedthat, NosingleeventinthehistoryofmentaltestinghasprovedtobeofsuchmomentousimportanceasSpearman’sproposalofhisfamoustwo-factortheory,1904.” MathematicalExplanationofSpearman’sTheory InSpearmans’two-factortheoryofintelligence,werepresentthegeneralfactorbytheletter”g”andoftentermitasthe“generalintelligence,”butitisamathematicalvaluethatisderivedfromthestatisticalprocessfromtheavailablequantitativedata.ItisdifficulttoarriveattheexactmathematicalproofofSpearman’stwo-factortheory,butitcanbeunderstoodbythemethodofthe”correlationmatrix”thatheusedinhistheory.Thecorrelationmatrixisatablethatconsistsofsystematicallyarrangedcorrelationcoefficientsofscoresobtainedbythepersoninvariousmentalaptitudetests.Thecorrelationmatrixisgivenbelow. Correlationmatrixshowingdifferentcorrelationcoefficientsvaluesofscoresobtainedbytheparticipantindifferenttests.Here,a,b,c,d,erepresentdifferenttests. J.PGuilford(1953)showedthattheproportionalitybetweendifferentvariablescanbecalculatedeasilywiththehelpofacorrelationmatrix,whichmakesiteasytocalculatethetetraddifferencebetweenthesubtests.Spearmanusedthe‘tetraddifference’methodtoanalyzeintelligence.Thismethodhasbeenwidelyusedinvariouspsychologicalinvestigations;itisrepresentedbythequantityF,anditisthedifferencebetweenthecrossproductsoftwooppositescoefficientsofanyfourcorrelationcoefficientsinasquareblock.Forexample,considerfourintellectualactivitiesthataremeasuredinthetest,havingcorrelationcoefficientsR13,R14,R23,R24inthecorrelationmatrix(nearbyfourinthecorrelationmatrix),thenthemathematicalexpressionoftetradequationwouldbe, F=(R13)(R24)-(R14)(R23) Spearmanobservedthatthecrossmultiplicationofanytwooppositecorrelationcoefficientsinthesquareblock(nearbyfourcorrelationcoefficients)inthecorrelationmatrixwasalmostequal,i.e.,thevalueofFapproximatelyequalszero.Hence,fortheaboveexpression, (R13)(R24)≈(R14)(R23) Thisimplies,F≈(R13)(R24)-(R14)(R23)≈0 Let’sconsiderthefollowingsquareblockfromtheabovecorrelationmatrix. FourNearbyCorrelationCoefficients(squareblock)fromtheaboveCorrelationMatrix. Here,thetetraddifference,i.e.,F=(.40)(.28)-(.32)(.35)=0.112–0.112=0 ThisexplainsthattheFvalue(tetraddifference)approximatelyorequalszeroinalmostalltheintellectualtests,i.e.,almostsimilarperformanceoftheindividualinthevariousmentalaptitudetests;thisrepresentsthe”g”factor.Thevariationinthetetraddifferenceorwecansaythatthemeasuredintelligencevariationindifferenttestsisduetothespecific”s”factoroftheindividual.Anindividualshowsdifferentspecificabilitiesindifferenttests.Hence,itprovesthatthe“g”factor,i.e.,thegeneralfactorisrequiredinalltheintellectualtests,andthehigherthecorrelationbetweenthetwocoefficients,thehigheristhesaturationofthesecoefficientswiththe“g”factor.Letusunderstanditwithgraphicalrepresentationsof“g”and“s”factorsdonebyJ.PGuilford(showninthefigurebelow).Here,thefactor“G”isrepresentedbythecentrallargecircle,andthedifferentspecificfactorsarerepresentedbythesmallcirclesaroundthecentrallargecircle.Eachellipserepresentsthedifferentmentalaptitudetests.Itisobservedfromthebelowdiagramthatdifferentellipsesoverlapwiththecentrallargecircle(Gfactor)todifferentextents.Thelargeoverlappingmeansthatparticulartestsarelargelyloadedwiththe“G”factorthantheothertests(teststhatmeasuremore“G”factor).Thecorrelationbetweenthetwomentalaptitudetestscanalsobeanalyzedthroughthisgraphicalrepresentationbylookingattheextentofoverlappingofthetwotestswiththecentralcircle(Gfactor).Here,itisclearlyseenthattestsaandbarehighlycorrelatedwitheachotherthantestsaandcbecauseaandbtestshavesimilarloadingswiththe“G”ascomparedtotheaandctests,similarlywithbandc. GraphicalrepresentationofGandSfactorsofSpearman’sTwo-FactorTheoryofIntelligence Spearman,alongwithhisstudents,alsoexplainedthatapartfromtheGfactor,therealsoexistssomethingcommoninsomeofthetestsbecauseitwasobservedthatsometestsshowmorecorrelationthanthatoftheGfactor,andthisextracommonfactoriscalledgroupfactorregardingwhichGuildford(1953)statedthat, Amongthegroupfactorsthatspearmanandhisassociatescametorecognizeareverbalability,numericalability,andpossiblefactorsofmentalspeed,mechanicalability,attention,andimagination” EducationalImplicationsofSpearman’sIntelligenceTheory Spearman’stwo-factortheorycanbeappliedintheeducationsectortoanalyzetheintellectualabilitiesofchildren.Aswehavediscussedinthisarticle,everypersonpossessesdifferentlevelsof“g”and“s”factors.Thestudentsneeddifferentdegreesof“g”and“s”factorstoperformwellindifferentacademicsubjects.Forexample,thestudent’sperformanceinmathematicscouldbeduetohisgeneralintelligenceandhisspecificnumericalabilities,i.e.,g+s1.Similarly,inliterature,itmaybebecauseofg+s2factors,andinscience,itmaybebecauseofg+s3,andsoon.Sincethe“g”factoriscommoninallspecificactivities,theperformanceofthestudentinacademicscanbeanalyzedthroughtheir“g”factor.The“g”factorofthestudentscanbecheckedthroughavarietyofintelligencequotientteststhathaveahigh“g”factorcorrelation.Aswediscussedearlier,the“g”factorisinbornandcan’tbeimproved,buttheperformanceofthestudentscanbeimprovedbydevelopingtheir“s”factors.Theschoolsshouldorganizevariousacademicsandsportsactivitiestoimprovethespecificabilitiesofthestudents. CriticismsofSpearman’sTwoFactorIntelligenceTheory ABritish-AmericanpsychologistnamedRaymondCattell,whowasalsoSpearman’sstudent,criticizedthetwo-factortheorybyarguingthatthenatureofintelligencecouldbebetterunderstoodbytheconceptof“fluidintelligence”(Gf)and“crystallizedintelligence”(Gc).Theamountofknowledge,experiences,skillsthatareaccumulatedinanindividual’sbrainthroughouthis/herlifeiscalledfluidintelligence,andtheabilitytoaptlyunderstandandreasontheavailableinformationorknowledge,andlearningnewskills,iscalledfluidintelligence.Cattellreferred“g”factormoreaccuratelyas“Gc”(crystallizedintelligence)andsaidthatteststhatincorporateonlythe“g”factorskiptheotherintelligencefactorsthatarecoveredwiththefluidintelligence. Spearman’stwo-factortheoryisalsocriticizedbecauseSpearmanhadonlyfocusedonthepsychometricapproach,i.e.,factoranalysistechniquetomeasureintelligence,andhedidnotfocusonthecognitionprocessesrelatedtointelligence.The“g”factorofspearman’stheorydoesnotincludethevariousotheractivitieslikeperception,emotional,andmotorabilities. TheAmericanDevelopmentalPsychologistHowardGardnerstatedthatapartfromacademicintelligence,otherdomainssuchasbody-kinesthetic,existentialintelligence,andmusicalintelligenceshouldalsobeconsideredasanimportantpartofintelligence.Thereareseveralexamplesofpeoplewhowerebadinacademics,buttheyacedinotherdomainslikemusic,sports,ordance.Hearguedthatthe“g”factoroveremphasizedacademicintelligence,suchasverbalandlogicalintelligence. 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