g factor (psychometrics) | Psychology Wiki - Fandom

When all correlations in a matrix are positive, as they are in the case of IQ, factor analysis will yield a general factor common to all tests. The general ... 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SignIn Advertisement in: Protectedtemplates,Pageswithbrokenfilelinks,Intelligence, and 3more Intelligencetests Psychometrics PagesusingISBNmagiclinks gfactor(psychometrics) Viewsource History Talk(0) HumanintelligenceAbilities,traitsandconstructs Abstractthought Communication Creativity Emotionalintelligence gfactor Intelligencequotient Knowledge Learning Memory Problemsolving Reactiontime Reasoning Understanding VisualprocessingModelsandtheories Cattell–Horn–Carrolltheory Fluidandcrystallizedintelligence Theoryofmultipleintelligences Threestratumtheory Triarchictheoryofintelligence PASStheoryofintelligenceFieldsofstudy Cognitiveepidemiology Evolutionofhumanintelligence Psychometrics HeritabilityofIQ Impactofhealthonintelligence Environmentandintelligence Neuroscienceandintelligence Raceandintelligence SexandintelligenceIntelligencemeasures WechslerAdultIntelligenceScale WechslerIntelligenceScaleforChildren Stanford–BinetIntelligenceScalesvte [create]Documentation Thegfactor(shortfor"generalfactor")isaconstructdevelopedinpsychometricinvestigationsofcognitiveabilities.Itisavariablethatsummarizestheconsistentfindingofpositivecorrelationsamongdifferentcognitivetasks,reflectedinthefactthatindividualswhoexcelatonetypeofcognitivetasktendtoexcelinotherkindsofcognitivetasks,too,whilethosewhodopoorlyononetasktendtodosoonalltasks,regardlessofthetasks'contents.Thegfactortypicallyaccountsfor40to50percentofthevarianceinIQtestperformance,andIQscoresarefrequentlyregardedasestimatesofindividuals'standingonthegfactor.[1]ThetermsIQ,generalintelligence,generalcognitiveability,generalmentalability,orsimplyintelligenceareoftenusedinterchangeablytorefertothecommoncoresharedbycognitivetests.[2] TheexistenceofthegfactorwasoriginallyproposedbytheEnglishpsychologistCharlesSpearmanintheearlyyearsofthe20thcentury.Heobservedthatchildren'sperformanceratingsacrossseeminglyunrelatedschoolsubjectswerepositivelycorrelated,andreasonedthatthesecorrelationsreflectedtheinfluenceofanunderlyinggeneralmentalabilitythatenteredintoperformanceonallkindsofmentaltests.Spearmansuggestedthatallmentalperformancecouldbeconceptualizedintermsofasinglegeneralabilityfactor,whichhelabeledg,andalargenumberofnarrowtask-specificabilityfactors.Today'sfactormodelsofintelligencetypicallyrepresentcognitiveabilitiesasathree-levelhierarchy,wheretherearealargenumberofnarrowfactorsatthebottomofthehierarchy,ahandfulofbroad,moregeneralfactorsattheintermediatelevel,andattheapexasinglefactor,referredtoasthegfactor,whichrepresentsthevariancecommontoalltests. Traditionally,researchonghasconcentratedonpsychometricinvestigationsoftestdata,withaspecialemphasisonfactoranalyticapproaches.However,empiricalresearchonthenatureofghasalsodrawnuponexperimentalcognitivepsychologyandmentalchronometry,brainanatomyandphysiology,quantitativeandmoleculargenetics,andprimateevolution.[3]Whiletheexistenceofgasastatisticalregularityiswell-establishedanduncontroversial,thereisnoconsensusastowhatcausesthepositivecorrelationsbetweentests. Behavioralgeneticresearchhasestablishedthattheconstructofgishighlyheritable.Ithasanumberofotherbiologicalcorrelates,includingbrainsize.Itisalsoasignificantpredictorofindividualdifferencesinmanysocialoutcomes,particularlyineducationandtheworldofwork.Themostwidelyacceptedcontemporarytheoriesofintelligenceincorporatethegfactor.[4]However,criticsofghavecontendedthatanemphasisongismisplacedandentailsadevaluationofotherimportantabilities. Contents 1Mentaltestingandg 2Theoriesofg 2.1Mentalenergyorefficiency 2.2Samplingtheory 2.3Mutualism 3Factorstructureofcognitiveabilities 4"Indifferenceoftheindicator" 5Populationdistribution 6Spearman'slawofdiminishingreturns 7Practicalvalidity 7.1Academicachievement 7.2Jobattainmentandperformance 7.3Income 7.4Othercorrelates 8Geneticandenvironmentaldeterminants 9Neuroscientificfindings 10Otherbiologicalassociations 11Groupsimilaritiesanddifferences 12Relationtootherpsychologicalconstructs 12.1Elementarycognitivetasks 12.2Workingmemory 12.3Piagetiantasks 12.4Personality 12.5Creativity 13Challengestog 13.1Gf-Gctheory 13.2Theoriesofuncorrelatedabilities 13.3Othercriticisms 14Seealso 15Notes 16References 17Externallinks Mentaltestingandg Spearman'scorrelationmatrixforsixmeasuresofschoolperformance.Allthecorrelationsarepositive,aphenomenonreferredasthepositivemanifold.Thebottomrowshowsthegloadingsofeachperformancemeasure.[5] Classics French English Math Pitch Music Classics - French .83 - English .78 .67 - Math .70 .67 .64 - Pitchdiscrimination .66 .65 .54 .45 - Music .63 .57 .51 .51 .40 - g .958 .882 .803 .750 .673 .646 Mentaltestsmaybedesignedtomeasuredifferentaspectsofcognition.Specificdomainsassessedbytestsincludemathematicalskill,verbalfluency,spatialvisualization,andmemory,amongothers.However,individualswhoexcelatonetypeoftesttendtoexcelatotherkindsoftests,too,whilethosewhodopoorlyononetesttendtodosoonalltests,regardlessofthetests'contents.[6]TheEnglishpsychologistCharlesSpearmanwasthefirsttodescribethisphenomenon.[7]Inafamousresearchpaperpublishedin1904[8],heobservedthatchildren'sperformancemeasuresacrossseeminglyunrelatedschoolsubjectswerepositivelycorrelated.Thisfindinghassincebeenreplicatednumeroustimes.Theconsistentfindingofuniversallypositivecorrelationmatricesofmentaltestresults(orthe"positivemanifold"),despitelargedifferencesintests'contents,hasbeendescribedas"arguablythemostreplicatedresultinallpsychology."[9]Zeroornegativecorrelationsbetweentestssuggestthepresenceofsamplingerrororrestrictionoftherangeofabilityinthesamplestudied.[10] Usingfactoranalysisorrelatedstatisticalmethods,itispossibletocomputeasinglecommonfactorthatcanberegardedasasummaryvariablecharacterizingthecorrelationsbetweenallthedifferenttestsinatestbattery.Spearmanreferredtothiscommonfactorasthegeneralfactor,orsimplyg.(Byconvention,gisalwaysprintedasalowercaseitalic.)Mathematically,thegfactorisasourceofvarianceamongindividuals,whichentailsthatonecannotmeaningfullyspeakofanyoneindividual'smentalabilitiesconsistingofgorotherfactorstoanyspecifieddegrees.Onecanonlyspeakofanindividual'sstandingong(orotherfactors)comparedtootherindividualsinarelevantpopulation.[11][12][10] SubtestintercorrelationsinasampleofScottishsubjectswhocompletedtheWAIS-Rbattery.ThesubtestsareVocabulary,Similarities,Information,Comprehension,Picturearrangement,Blockdesign,Arithmetic,Picturecompletion,Digitspan,Objectassembly,andDigitsymbol.Thebottomrowshowsthegloadingsofeachsubtest.[13] V S I C PA BD A PC DSp OA DS V - S .67 - I .72 .59 - C .70 .58 .59 - PA .51 .53 .50 .42 - BD .45 .46 .45 .39 .43 - A .48 .43 .55 .45 .41 .44 - PC .49 .52 .52 .46 .48 .45 .30 - DSp .46 .40 .36 .36 .31 .32 .47 .23 - OA .32 .40 .32 .29 .36 .58 .33 .41 .14 - DS .32 .33 .26 .30 .28 .36 .28 .26 .27 .25 - g .83 .80 .80 .75 .70 .70 .68 .68 .56 .56 .48 Differenttestsinatestbatterymaycorrelatewith(or"loadonto")thegfactorofthebatterytodifferentdegrees.Thesecorrelationsareknownasgloadings.Anindividualtesttaker'sgfactorscore,representinghisorherrelativestandingonthegfactorinthetotalgroupofindividuals,canbeestimatedusingthegloadings.Full-scaleIQscoresfromatestbatterywillusuallybehighlycorrelatedwithgfactorscores,andtheyareoftenregardedasestimatesofg.Forexample,thecorrelationsbetweengfactorscoresandfull-scaleIQscoresfromWechsler'stestshavebeenfoundtobegreaterthan.95.[14][10][1]ThetermsIQ,generalintelligence,generalcognitiveability,generalmentalability,orsimplyintelligencearefrequentlyusedinterchangeablytorefertothecommoncoresharedbycognitivetests.[2] Thegloadingsofmentaltestsarealwayspositiveandusuallyrangebetween.10and.90,withameanofabout.60andastandarddeviationofabout.15.Raven'sProgressiveMatricesisamongthetestswiththehighestgloadings,around.80.Testsofvocabularyandgeneralinformationarealsotypicallyfoundtohavehighgloadings.[15][16]However,thegloadingofthesametestmayvarysomewhatdependingonthecompositionofthetestbattery.[17] Thecomplexityoftestsandthedemandstheyplaceonmentalmanipulationarerelatedtothetests'gloadings.Forexample,intheforwarddigitspantestthesubjectisaskedtorepeatasequenceofdigitsintheorderoftheirpresentationafterhearingthemonceatarateofonedigitpersecond.Thebackwarddigitspantestisotherwisethesameexceptthatthesubjectisaskedtorepeatthedigitsinthereverseordertothatinwhichtheywerepresented.Thebackwarddigitspantestismorecomplexthantheforwarddigitspantest,andithasasignificantlyhighergloading.Similarly,thegloadingsofarithmeticcomputation,spelling,andwordreadingtestsarelowerthanthoseofarithmeticproblemsolving,textcomposition,andreadingcomprehensiontests,respectively.[18][19] Testdifficultyandgloadingsaredistinctconceptsthatmayormaynotbeempiricallyrelatedinanyspecificsituation.Teststhathavethesamedifficultylevel,asindexedbytheproportionoftestitemsthatarefailedbytesttakers,mayexhibitawiderangeofgloadings.Forexample,testsofrotememoryhavebeenshowntohavethesamelevelofdifficultybutconsiderablylowergloadingsthanmanyteststhatinvolvereasoning.[20][21] Theoriesofg Whiletheexistenceofgasastatisticalregularityiswell-establishedanduncontroversialamongexperts,thereisnoconsensusastowhatcausesthepositiveintercorrelations.Severalexplanationshavebeenproposed.[22] Mentalenergyorefficiency CharlesSpearmanreasonedthatcorrelationsbetweentestsreflectedtheinfluenceofacommoncausalfactor,ageneralmentalabilitythatentersintoperformanceonallkindsofmentaltasks.However,hethoughtthatthebestindicatorsofgwerethoseteststhatreflectedwhathecalledtheeductionofrelationsandcorrelates,whichincludedabilitiessuchasdeduction,induction,problemsolving,graspingrelationships,inferringrules,andspottingdifferencesandsimilarities.Spearmanhypothesizedthatgwasequivalentwith"mentalenergy".However,thiswasmoreofametaphoricalexplanation,andheremainedagnosticaboutthephysicalbasisofthisenergy,expectingthatfutureresearchwoulduncovertheexactphysiologicalnatureofg.[23] FollowingSpearman,ArthurJensenhasmaintainedthatallmentaltaskstapintogtosomedegree.AccordingtoJensen,thegfactorrepresentsa"distillate"ofscoresondifferenttestsratherthanasummationoranaverageofsuchscores,withfactoranalysisactingasthedistillationprocedure.[24]Hehasarguedthatgcannotbedescribedintermsoftheitemcharacteristicsorinformationcontentoftests,pointingoutthatverydissimilarmentaltasksmayhavenearlyequalgloadings.DavidWechslersimilarlycontendedthatgisnotanabilityatallbutrathersomegeneralpropertyofthebrain.Jensenhashypothesizedthatgcorrespondstoindividualdifferencesinthespeedorefficiencyoftheneuralprocessesassociatedwithmentalabilities.[25]Hehasalsosuggestedthatgiventheassociationsbetweengandelementarycognitivetasks,itshouldbepossibletoconstructaratioscaletestofgthatusestimeastheunitofmeasurement.[26] Samplingtheory Theso-calledsamplingtheoryofg,originallydevelopedbyE.L.ThorndikeandGodfreyThomson,proposesthattheexistenceofthepositivemanifoldcanbeexplainedwithoutreferencetoaunitaryunderlyingcapacity.Accordingtothistheory,thereareanumberofuncorrelatedmentalprocesses,andalltestsdrawupondifferentsamplesoftheseprocesses.Theintercorrelationsbetweentestsarecausedbyanoverlapbetweenprocessestappedbythetests.[27][28]Thus,thepositivemanifoldarisesduetoameasurementproblem,thatis,aninabilitytomeasuremorefine-grained,presumablyuncorrelatedmentalprocesses.[12] IthasbeenshownthatitisnotpossibletodistinguishstatisticallybetweenSpearman'smodelofgandthesamplingmodel;bothareequallyabletoaccountforintercorrelationsamongtests.[29]Thesamplingtheoryisalsoconsistentwiththeobservationthatmorecomplexmentaltaskshavehighergloadings,becausemorecomplextasksareexpectedtoinvolvealargersamplingofneuralelementsandthereforehavemoreofthemincommonwithothertasks.[30] Someresearchershavearguedthatthesamplingmodelinvalidatesgasapsychologicalconcept,becausethemodelsuggeststhatgfactorsderivedfromdifferenttestbatteriessimplyreflectthesharedelementsoftheparticulartestscontainedineachbatteryratherthanagthatiscommontoalltests.Similarly,highcorrelationsbetweendifferentbatteriescouldbeduetothemmeasuringthesamesetofabilitiesratherthanthesameability.[31] Criticshavearguedthatthesamplingtheoryisincongruentwithcertainempiricalfindings.Basedonthesamplingtheory,onemightexpectthatrelatedcognitivetestssharemanyelementsandthusbehighlycorrelated.However,somecloselyrelatedtests,suchasforwardandbackwarddigitspan,areonlymodestlycorrelated,whilesomeseeminglycompletelydissimilartests,suchasvocabularytestsandRaven'smatrices,areconsistentlyhighlycorrelated.Anotherproblematicfindingisthatbraindamagefrequentlyleadstospecificcognitiveimpairmentsratherthanageneralimpairmentonemightexpectbasedonthesamplingtheory.[32][12] Mutualism The"mutualism"modelofgproposesthatcognitiveprocessesareinitiallyuncorrelated,butthatthepositivemanifoldarisesduringindividualdevelopmentduetomutualbeneficialrelationsbetweencognitiveprocesses.Thusthereisnosingleprocessorcapacityunderlyingthepositivecorrelationsbetweentests.Duringthecourseofdevelopment,thetheoryholds,anyoneparticularlyefficientprocesswillbenefitotherprocesses,withtheresultthattheprocesseswillendupbeingcorrelatedwithoneanother.ThussimilarlyhighIQsindifferentpersonsmaystemfromquitedifferentinitialadvantagesthattheyhad.[33][12]Criticshavearguedthattheobservedcorrelationsbetweenthegloadingsandtheheritabilitycoefficientsofsubtestsareproblematicforthemutualismtheory.[34] Factorstructureofcognitiveabilities File:SpearmanFactors.svg AnillustrationofSpearman'stwo-factorintelligencetheory.Eachsmallovalisahypotheticalmentaltest.Theblueareascorrespondtotest-specificvariance(s),whilethepurpleareasrepresentthevarianceattributedtog. Factoranalysisisafamilyofmathematicaltechniquesthatcanbeusedtorepresentcorrelationsbetweenintelligencetestsintermsofasmallernumberofvariablesknownasfactors.Thepurposeistosimplifythecorrelationmatrixbyusinghypotheticalunderlyingfactorstoexplainthepatternsinit.Whenallcorrelationsinamatrixarepositive,astheyareinthecaseofIQ,factoranalysiswillyieldageneralfactorcommontoalltests.ThegeneralfactorofIQtestsisreferredtoasthegfactor,andittypicallyaccountsfor40to50percentofthevarianceinIQtestbatteries.[35] CharlesSpearmandevelopedfactoranalysisinordertostudycorrelationsbetweentests.Initially,hedevelopedamodelofintelligenceinwhichvariationsinallintelligencetestscoresareexplainedbyonlytwokindsofvariables:first,factorsthatarespecifictoeachtest(denoteds);andsecond,agfactorthataccountsforthepositivecorrelationsacrosstests.ThisisknownasSpearman'stwo-factortheory.LaterresearchbasedonmorediversetestbatteriesthanthoseusedbySpearmandemonstratedthatgalonecouldnotaccountforallcorrelationsbetweentests.Specifically,itwasfoundthatevenaftercontrollingforg,sometestswerestillcorrelatedwitheachother.Thisledtothepostulationofgroupfactorsthatrepresentvariancethatgroupsoftestswithsimilartaskdemands(e.g.,verbal,spatial,ornumerical)haveincommoninadditiontothesharedgvariance.[36] File:Carrollthreestratum.svg AnillustrationofJohnB.Carroll'sthreestratumtheory,aninfluentialcontemporarymodelofcognitiveabilities.Thebroadabilitiesrecognizedbythemodelarefluidintelligence(Gf),crystallizedintelligence(Gc),generalmemoryandlearning(Gy),broadvisualperception(Gv),broadauditoryperception(Gu),broadretrievalability(Gr),broadcognitivespeediness(Gs),andprocessingspeed(Gt).Carrollregardedthebroadabilitiesasdifferent"flavors"ofg. Throughfactorrotation,itis,inprinciple,possibletoproduceaninfinitenumberofdifferentfactorsolutionsthataremathematicallyequivalentintheirabilitytoaccountfortheintercorrelationsamongcognitivetests.Theseincludesolutionsthatdonotcontainagfactor.Thusfactoranalysisalonecannotestablishwhattheunderlyingstructureofintelligenceis.Inchoosingbetweendifferentfactorsolutions,researchershavetoexaminetheresultsoffactoranalysistogetherwithotherinformationaboutthestructureofcognitiveabilities.[37] Therearemanypsychologicallyrelevantreasonsforpreferringfactorsolutionsthatcontainagfactor.Theseincludetheexistenceofthepositivemanifold,thefactthatcertainkindsoftests(generallythemorecomplexones)haveconsistentlylargergloadings,thesubstantialinvarianceofgfactorsacrossdifferenttestbatteries,theimpossibilityofconstructingtestbatteriesthatdonotyieldagfactor,andthewidespreadpracticalvalidityofgasapredictorofindividualoutcomes.Thegfactor,togetherwithgroupfactors,bestrepresentstheempiricallyestablishedfactthat,onaverage,overallabilitydifferencesbetweenindividualsaregreaterthandifferencesamongabilitieswithinindividuals,whileafactorsolutionwithorthogonalfactorswithoutgobscuresthisfact.Moreover,gappearstobethemostheritablecomponentofintelligence.[38]Researchutilizingthetechniquesofconfirmatoryfactoranalysishasalsoprovidedsupportfortheexistenceofg.[37] Agfactorcanbecomputedfromacorrelationmatrixoftestresultsusingseveraldifferentmethods.Theseincludeexploratoryfactoranalysis,principalcomponentsanalysis(PCA),andconfirmatoryfactoranalysis.Differentfactor-extractionmethodsproducehighlyconsistentresults,althoughPCAhassometimesbeenfoundtoproduceinflatedestimatesoftheinfluenceofgontestscores.[39][17] Thereisabroadcontemporaryconsensusthatcognitivevariancebetweenpeoplecanbeconceptualizedatthreehierarchicallevels,distinguishedbytheirdegreeofgenerality.Atthelowest,leastgeneralleveltherearealargenumberofnarrowfirst-orderfactors;atahigherlevel,therearearelativelysmallnumber–somewherebetweenfiveandten–ofbroad(i.e.,moregeneral)second-orderfactors(orgroupfactors);andattheapex,thereisasinglethird-orderfactor,g,thegeneralfactorcommontoalltests.[40][41][42]ThegfactorusuallyaccountsforthemajorityofthetotalcommonfactorvarianceofIQtestbatteries.[43]ContemporaryhierarchicalmodelsofintelligenceincludethethreestratumtheoryandtheCattell–Horn–Carrolltheory.[44] "Indifferenceoftheindicator" Spearmanproposedtheprincipleoftheindifferenceoftheindicator,accordingtowhichtheprecisecontentofintelligencetestsisunimportantforthepurposesofidentifyingg,becausegentersintoperformanceonallkindsoftests.Anytestcanthereforebeusedasanindicatorofg.FollowingSpearman,ArthurJensenhasmorerecentlyarguedthatagfactorextractedfromonetestbatterywillalwaysbethesame,withinthelimitsofmeasurementerror,asthatextractedfromanotherbattery,providedthatthebatteriesarelargeanddiverse.[45]Accordingtothisview,everymentaltest,nomatterhowdistinctive,containssomeg.Thusacompositescoreofanumberofdifferenttestswillhaverelativelymoregthananyoftheindividualtestscores,becausethegcomponentscumulateintothecompositescore,whiletheuncorrelatednon-gcomponentswillcanceleachotherout.Theoretically,thecompositescoreofaninfinitelylarge,diversetestbatterywould,then,beaperfectmeasureofg.[46] Incontrast,L.L.Thurstonearguedthatagfactorextractedfromatestbatteryreflectstheaverageofalltheabilitiescalledforbytheparticularbattery,andthatgthereforevariesfromonebatterytoanotherand"hasnofundamentalpsychologicalsignificance."[47]Alongsimilarlines,JohnHornarguedthatgfactorsaremeaninglessbecausetheyarenotinvariantacrosstestbatteries,maintainingthatcorrelationsbetweendifferentabilitymeasuresarisebecauseitisdifficulttodefineahumanactionthatdependsonjustoneability.[48][49] Toshowthatdifferentbatteriesreflectthesameg,onemustadministerseveraltestbatteriestothesameindividuals,extractgfactorsfromeachbattery,andshowthatthefactorsarehighlycorrelated.[50]WendyJohnsonandcolleagueshavepublishedtwosuchstudies.[51][52]Thefirstfoundthatthecorrelationsbetweengfactorsextractedfromthreedifferentbatterieswere.99,.99,and1.00,supportingthehypothesisthatgfactorsfromdifferentbatteriesarethesameandthattheidentificationofgisnotdependentonthespecificabilitiesassessed.Thesecondstudyfoundthatgfactorsderivedfromfouroffivetestbatteriescorrelatedatbetween.95–1.00,whilethecorrelationsrangedfrom.79to.96forthefifthbattery,theCattellCultureFairIntelligenceTest(theCFIT).TheyattributedthesomewhatlowercorrelationswiththeCFITbatterytoitslackofcontentdiversityforitcontainsonlymatrix-typeitems,andinterpretedthefindingsassupportingthecontentionthatgfactorsderivedfromdifferenttestbatteriesarethesameprovidedthatthebatteriesarediverseenough.Theresultssuggestthatthesamegcanbeconsistentlyidentifiedfromdifferenttestbatteries.[53][40] Populationdistribution Theformofthepopulationdistributionofgisunknown,becausegcannotbemeasuredonaratioscale.(ThedistributionsofscoresontypicalIQtestsareroughlynormal,butthisisachievedbyconstruction,i.e.,byappropriateitemselectionbytestdevelopers.)Ithasbeenarguedthatthereareneverthelessgoodreasonsforsupposingthatgisnormallydistributedinthegeneralpopulation,atleastwithinarangeof±2standarddeviationsfromthemean.Inparticular,gcanbethoughtofasacompositevariablethatreflectstheadditiveeffectsofalargenumberofindependentgeneticandenvironmentalinfluences,andsuchavariableshould,accordingtothecentrallimittheorem,followanormaldistribution.[54] Spearman'slawofdiminishingreturns Anumberofresearchershavesuggestedthattheproportionofvariationaccountedforbygmaynotbeuniformacrossallsubgroupswithinapopulation.Spearman'slawofdiminishingreturns(SLDR),alsotermedtheabilitydifferentiationhypothesis,predictsthatthepositivecorrelationsamongdifferentcognitiveabilitiesareweakeramongmoreintelligentsubgroupsofindividuals.Morespecifically,SLDRpredictsthatthegfactorwillaccountforasmallerproportionofindividualdifferencesincognitivetestsscoresathigherscoresonthegfactor. SLDRwasoriginallyproposedbyCharlesSpearman,[55]whoreportedthattheaveragecorrelationbetween12cognitiveabilitytestswas.466in78normalchildren,and.782in22"defective"children.DettermanandDanielrediscoveredthisphenomenonin1989.[56]TheyreportedthatforsubtestsofboththeWAISandtheWISC,subtestintercorrelationsdecreasedmonotonicallywithabilitygroup,rangingfromapproximatelyanaverageintercorrelationof.7amongindividualswithIQslessthan78to.4amongindividualswithIQsgreaterthan122.[57] SLDRhasbeenreplicatedinavarietyofchildandadultsampleswhohavebeenmeasuredusingbroadarraysofcognitivetests.Themostcommonapproachhasbeentodivideindividualsintomultipleabilitygroupsusinganobservableproxyfortheirgeneralintellectualability,andthentoeithercomparetheaverageinterrelationamongthesubtestsacrossthedifferentgroups,ortocomparetheproportionofvariationaccountedforbyasinglecommonfactor,inthedifferentgroups.[58]However,asbothDearyetal.(1996).[58]andTucker-Drob(2009)[59]havepointedout,dividingthecontinuousdistributionofintelligenceintoanarbitrarynumberofdiscreteabilitygroupsislessthanidealforexaminingSLDR.Tucker-Drob(2009)[59]extensivelyreviewedtheliteratureonSLDRandthevariousmethodsbywhichithadbeenpreviouslytested,andproposedthatSLDRcouldbemostappropriatelycapturedbyfittingacommonfactormodelthatallowstherelationsbetweenthefactoranditsindicatorstobenonlinearinnature.HeappliedsuchafactormodeltoanationallyrepresentativedataofchildrenandadultsintheUnitedStatesandfoundconsistentevidenceforSLDR.Forexample,Tucker-Drob(2009)foundthatageneralfactoraccountedforapproximately75%ofthevariationinsevendifferentcognitiveabilitiesamongverylowIQadults,butonlyaccountedforapproximately30%ofthevariationintheabilitiesamongveryhighIQadults. Practicalvalidity Thepracticalvalidityofgasapredictorofeducational,economic,andsocialoutcomesismorefar-ranginganduniversalthanthatofanyotherknownpsychologicalvariable.Thevalidityofgisgreaterthegreaterthecomplexityofthetask.[60][61] Atest'spracticalvalidityismeasuredbyitscorrelationwithperformanceonsomecriterionexternaltothetest,suchascollegegrade-pointaverage,oraratingofjobperformance.Thecorrelationbetweentestscoresandameasureofsomecriterioniscalledthevaliditycoefficient.Onewaytointerpretavaliditycoefficientistosquareittoobtainthevarianceaccountedbythetest.Forexample,avaliditycoefficientof.30correspondsto9percentofvarianceexplained.Thisapproachhas,however,beencriticizedasmisleadinganduninformative,andseveralalternativeshavebeenproposed.Onearguablymoreinterpretableapproachistolookatthepercentageoftesttakersineachtestscorequintilewhomeetsomeagreed-uponstandardofsuccess.Forexample,ifthecorrelationbetweentestscoresandperformanceis.30,theexpectationisthat67percentofthoseinthetopquintilewillbeabove-averageperformers,comparedto33percentofthoseinthebottomquintile.[62][63] Academicachievement Thepredictivevalidityofgismostconspicuousinthedomainofscholasticperformance.Thisisapparentlybecausegiscloselylinkedtoabilitytolearnnovelmaterialandunderstandconceptsandmeanings.[64] Inelementaryschool,thecorrelationbetweenIQandgradesandachievementscoresisbetween.60and.70.Atmoreadvancededucationallevels,morestudentsfromthelowerendoftheIQdistributiondropout,whichrestrictstherangeofIQsandresultsinlowervaliditycoefficients.Inhighschool,college,andgraduateschoolthevaliditycoefficientsare.50–.60,.40–.50,and.30–.40,respectively.ThegloadingsofIQscoresarehigh,butitispossiblethatsomeofthevalidityofIQinpredictingscholasticachievementisattributabletofactorsmeasuredbyIQindependentofg.AccordingtoresearchbyRobertL.Thorndike,80to90percentofthepredictablevarianceinscholasticperformanceisduetog,withtherestattributedtonon-gfactorsmeasuredbyIQandothertests.[65] AchievementtestscoresaremorehighlycorrelatedwithIQthanschoolgrades.Thismaybebecausegradesaremoreinfluencedbytheteacher'sidiosyncraticperceptionsofthestudent.[66]InalongitudinalEnglishstudy,gscoresmeasuredatage11correlatedwithallthe25subjecttestsofthenationalGCSEexaminationtakenatage16.Thecorrelationsrangedfrom.77forthemathematicstestto.42forthearttest.ThecorrelationbetweengandageneraleducationalfactorcomputedfromtheGCSEtestswas.81.[67] ResearchsuggeststhattheSAT,widelyusedincollegeadmissions,isprimarilyameasureofg.Acorrelationof.82hasbeenfoundbetweengscorescomputedfromanIQtestbatteryandSATscores.Inastudyof165,000studentsat41U.S.colleges,SATscoreswerefoundtobecorrelatedat.47withfirst-yearcollegegrade-pointaverageaftercorrectingforrangerestrictioninSATscores(whencoursedifficultyisheldconstant,i.e.,ifallstudentsattendedthesamesetofclasses,thecorrelationrisesto.55).[62][68] Jobattainmentandperformance Thereisahighcorrelationof.90to.95betweentheprestigerankingsofoccupations,asratedbythegeneralpopulation,andtheaveragegeneralintelligencescoresofpeopleemployedineachoccupation.Atthelevelofindividualemployees,theassociationbetweenjobprestigeandgislower–onelargeU.S.studyreportedacorrelationof.65(.72correctedforattenuation).Meanlevelofgthusincreaseswithperceivedjobprestige.Ithasalsobeenfoundthatthedispersionofgeneralintelligencescoresissmallerinmoreprestigiousoccupationsthaninlowerleveloccupations,suggestingthathigherleveloccupationshaveminimumgrequirements.[69][70] Researchindicatesthattestsofgarethebestsinglepredictorsofjobperformance,withanaveragevaliditycoefficientof.55acrossseveralmeta-analysesofstudiesbasedonsupervisorratingsandjobsamples.Theaveragemeta-analyticvaliditycoefficientforperformanceinjobtrainingis.63.[71]Thevalidityofginthehighestcomplexityjobs(professional,scientific,anduppermanagementjobs)hasbeenfoundtobegreaterthaninthelowestcomplexityjobs,butghaspredictivevalidityevenforthesimplestjobs.Researchalsoshowsthatspecificaptitudeteststailoredforeachjobprovidelittleornoincreaseinpredictivevalidityovertestsofgeneralintelligence.Itisbelievedthatgaffectsjobperformancemainlybyfacilitatingtheacquisitionofjob-relatedknowledge.Thepredictivevalidityofgisgreaterthanthatofworkexperience,andincreasedexperienceonthejobdoesnotdecreasethevalidityofg.[69][72] Income Thecorrelationbetweenincomeandg,asmeasuredbyIQscores,averagesabout.40acrossstudies.Thecorrelationishigherathigherlevelsofeducationanditincreaseswithage,stabilizingwhenpeoplereachtheirhighestcareerpotentialinmiddleage.Evenwheneducation,occupationandsocioeconomicbackgroundareheldconstant,thecorrelationdoesnotvanish.[73] Othercorrelates Thegfactorisreflectedinmanysocialoutcomes.Manysocialbehaviorproblems,suchasdroppingoutofschool,chronicwelfaredependency,accidentproneness,andcrime,arenegativelycorrelatedwithgindependentofsocialclassoforigin.[74]Healthandmortalityoutcomesarealsolinkedtog,withhigherchildhoodtestscorespredictingbetterhealthandmortalityoutcomesinadulthood(seeCognitiveepidemiology).[75] Geneticandenvironmentaldeterminants Mainarticle:HeritabilityofIQ Heritabilityistheproportionofphenotypicvarianceinatraitinapopulationthatcanbeattributedtogeneticfactors.Theheritabilityofghasbeenestimatedtofallbetween40to80percentusingtwin,adoption,andotherfamilystudydesignsaswellasmoleculargeneticmethods.Ithasbeenfoundtoincreaselinearlywithage.Forexample,alargestudyinvolvingmorethan11,000pairsoftwinsfromfourcountriesreportedtheheritabilityofgtobe41percentatagenine,55percentatagetwelve,and66percentatageseventeen.Otherstudieshaveestimatedthattheheritabilityisashighas80percentinadulthood,althoughitmaydeclineinoldage.MostoftheresearchontheheritabilityofghasbeenconductedintheUSAandWesternEurope,butstudiesinRussia(Moscow),theformerEastGermany,Japan,andruralIndiahaveyieldedsimilarestimatesofheritabilityasWesternstudies.[76][77][78][40] Behavioralgeneticresearchhasalsoestablishedthattheshared(orbetween-family)environmentaleffectsongarestronginchildhood,butdeclinethereafterandarenegligibleinadulthood.Thisindicatesthattheenvironmentaleffectsthatareimportanttothedevelopmentofgareuniqueandnotsharedbetweenmembersofthesamefamily.[77] Thegeneticcorrelationisastatisticthatindicatestheextenttowhichthesamegeneticeffectsinfluencetwodifferenttraits.Ifthegeneticcorrelationbetweentwotraitsiszero,thegeneticeffectsonthemareindependent,whereasacorrelationof1.0meansthatthesamesetofgenesexplainstheheritabilityofbothtraits(regardlessofhowhighorlowtheheritabilityofeachis).Geneticcorrelationsbetweenspecificmentalabilities(suchasverbalabilityandspatialability)havebeenconsistentlyfoundtobeveryhigh,closeto1.0.Thisindicatesthatgeneticvariationincognitiveabilitiesisalmostentirelyduetogeneticvariationinwhatevergis.Italsosuggeststhatwhatiscommonamongcognitiveabilitiesislargelycausedbygenes,andthatindependenceamongabilitiesislargelyduetoenvironmentaleffects.Thusithasbeenarguedthatwhengenesforintelligenceareidentified,theywillbe"generalistgenes",eachaffectingmanydifferentcognitiveabilities.[77][79][80] Thegloadingsofmentaltestshavebeenfoundtocorrelatewiththeirheritabilities,withcorrelationsrangingfrommoderatetoperfectinvariousstudies.Thustheheritabilityofamentaltestisusuallyhigherthelargeritsgloadingis.[34] Muchresearchpointstogbeingahighlypolygenictraitinfluencedbyalargenumberofcommongeneticvariants,eachhavingonlysmalleffects.Anotherpossibilityisthatheritabledifferencesingareduetoindividualshavingdifferent"loads"ofrare,deleteriousmutations,withgeneticvariationamongindividualspersistingduetomutation–selectionbalance.[80][81] Anumberofcandidategeneshavebeenreportedtobeassociatedwithintelligencedifferences,buttheeffectsizeshavebeensmallandalmostnoneofthefindingshavebeenreplicated.Noindividualgeneticvariantshavebeenconclusivelylinkedtointelligenceinthenormalrangesofar.Manyresearchersbelievethatverylargesampleswillbeneededtoreliablydetectindividualgeneticpolymorphismsassociatedwithg.[40][81]However,whilegenesinfluencingvariationinginthenormalrangehaveprovendifficulttofind,alargenumberofsingle-genedisorderswithmentalretardationamongtheirsymptomshavebeendiscovered.[82] Severalstudiessuggestthattestswithlargergloadingsaremoreaffectedbyinbreedingdepressionloweringtestscores.Thereisalsoevidencethattestswithlargergloadingsareassociatedwithlargerpositiveheteroticeffectsontestscores.Inbreedingdepressionandheterosissuggestthepresenceofgeneticdominanceeffectsforg.[83] Neuroscientificfindings Mainarticle:Neuroscienceandintelligence ghasanumberofcorrelatesinthebrain.Studiesusingmagneticresonanceimaging(MRI)haveestablishedthatgandtotalbrainvolumearemoderatelycorrelated(r~.3–.4).Externalheadsizehasacorrelationof~.2withg.MRIresearchonbrainregionsindicatesthatthevolumesoffrontal,parietalandtemporalcortices,andthehippocampusarealsocorrelatedwithg,generallyat.25ormore,whilethecorrelations,averagedovermanystudies,withoverallgreymatterandoverallwhitematterhavebeenfoundtobe.31and.27,respectively.Somebutnotallstudieshavealsofoundpositivecorrelationsbetweengandcorticalthickness.However,theunderlyingreasonsfortheseassociationsbetweenthequantityofbraintissueanddifferencesincognitiveabilitiesremainlargelyunknown.[2] Mostresearchersbelievethatintelligencecannotbelocalizedtoasinglebrainregion,suchasthefrontallobe.Ithasbeensuggestedthatintelligencecouldbecharacterizedasasmall-worldnetwork.Forexample,highintelligencecouldbedependentonunobstructedtransferofinformationbetweentheinvolvedbrainregionsalongwhitematterfibers.Brainlesionstudieshavefoundsmallbutconsistentassociationsindicatingthatpeoplewithmorewhitematterlesionstendtohavelowercognitiveability.ResearchutilizingNMRspectroscopyhasdiscoveredsomewhatinconsistentbutgenerallypositivecorrelationsbetweenintelligenceandwhitematterintegrity,supportingthenotionthatwhitematterisimportantforintelligence.[2] Someresearchsuggeststhatasidefromtheintegrityofwhitematter,alsoitsorganizationalefficiencyisrelatedtointelligence.ThehypothesisthatbrainefficiencyhasaroleinintelligenceissupportedbyfunctionalMRIresearchshowingthatmoreintelligentpeoplegenerallyprocessinformationmoreefficiently,i.e.,theyusefewerbrainresourcesforthesametaskthanlessintelligentpeople.[2] Smallbutrelativelyconsistentassociationswithintelligencetestscoresincludealsobrainactivity,asmeasuredbyEEGrecordsorevent-relatedpotentials,andnerveconductionvelocity.[84][85] Otherbiologicalassociations Heightiscorrelatedwithintelligence(r~.2),butthiscorrelationhasnotgenerallybeenfoundwithinfamilies(i.e.,amongsiblings),suggestingthatitresultsfromcross-assortativematingforheightandintelligence.Myopiaisknowntobeassociatedwithintelligence,withacorrelationofaround.2to.25,andthisassociationhasbeenfoundwithinfamilies,too.[86] Thereissomeevidencethatagfactorunderliestheabilitiesofnonhumananimals,too.Severalstudiessuggestthatageneralfactoraccountsforasubstantialpercentageofvarianceincognitivetasksgiventosuchanimalsasrats,mice,andrhesusmonkeys.[87][85] Groupsimilaritiesanddifferences Seealso:Sexandpsychology,Raceandintelligence, andNationsandintelligence Cross-culturalstudiesindicatethatthegfactorcanbeobservedwheneverabatteryofdiverse,complexcognitivetestsisadministeredtoahumansample.ThefactorstructureofIQtestshasalsofoundtobeconsistentacrosssexesandethnicgroupsintheU.S.andelsewhere.[85]Thegfactorhasbeenfoundtobethemostinvariantofallfactorsincross-culturalcomparisons.Forexample,whenthegfactorscomputedfromanAmericanstandardizationsampleofWechsler'sIQbatteryandfromlargesampleswhocompletedtheJapanesetranslationofthesamebatterywerecompared,thecongruencecoefficientwas.99,indicatingvirtualidentity.Similarly,thecongruencecoefficientbetweenthegfactorsobtainedfromwhiteandblackstandardizationsamplesoftheWISCbatteryintheU.S.was.995,andthevarianceintestscoresaccountedforbygwashighlysimilarforbothgroups.[88] Moststudiessuggestthattherearenegligibledifferencesinthemeanlevelofgbetweenthesexes,andthatsexdifferencesincognitiveabilitiesaretobefoundinmorenarrowdomains.Forexample,malesgenerallyoutperformfemalesinspatialtasks,whilefemalesgenerallyoutperformmalesinverbaltasks.Anotherdifferencethathasbeenfoundinmanystudiesisthatmalesshowmorevariabilityinbothgeneralandspecificabilitiesthanfemales,withproportionatelymoremalesatboththelowendandthehighendofthetestscoredistribution.[89] Consistentdifferencesbetweenracialandethnicgroupsinghavebeenfound,particularlyintheU.S.A2001meta-analysisofmillionsofsubjectsindicatedthatthereisa1.1standarddeviationgapinthemeanlevelofgbetweenwhiteandblackAmericans,favoringtheformer.ThemeanscoreofHispanicAmericanswasfoundtobe.72standarddeviationsbelowthatofnon-Hispanicwhites.[90]Incontrast,AmericansofEastAsiandescentgenerallyslightlyoutscorewhiteAmericans.[91]Severalresearchershavesuggestedthatthemagnitudeoftheblack-whitegapincognitiveabilitytestsisdependentonthemagnitudeofthetest'sgloading,withtestsshowinghighergloadingsproducinglargergaps(seeSpearman'shypothesis).[92]IthasalsobeenclaimedthatracialandethnicdifferencessimilartothosefoundintheU.S.canbeobservedglobally.[93] Relationtootherpsychologicalconstructs Elementarycognitivetasks Mainarticle:Mentalchronometry File:Jensenbox.gif AnillustrationoftheJensenbox,anapparatusformeasuringchoicereactiontime. Elementarycognitivetasks(ECTs)alsocorrelatestronglywithg.ECTsare,asthenamesuggests,simpletasksthatapparentlyrequireverylittleintelligence,butstillcorrelatestronglywithmoreexhaustiveintelligencetests.DeterminingwhetheralightisredorblueanddeterminingwhethertherearefourorfivesquaresdrawnonacomputerscreenaretwoexamplesofECTs.Theanswerstosuchquestionsareusuallyprovidedbyquicklypressingbuttons.Often,inadditiontobuttonsforthetwooptionsprovided,athirdbuttonishelddownfromthestartofthetest.Whenthestimulusisgiventothesubject,heremoveshishandfromthestartingbuttontothebuttonofthecorrectanswer.Thisallowstheexaminertodeterminehowmuchtimewasspentthinkingabouttheanswertothequestion(reactiontime,usuallymeasuredinsmallfractionsofsecond),andhowmuchtimewasspentonphysicalhandmovementtothecorrectbutton(movementtime).Reactiontimecorrelatesstronglywithg,whilemovementtimecorrelateslessstrongly.[94] ECTtestinghasallowedquantitativeexaminationofhypothesesconcerningtestbias,subjectmotivation,andgroupdifferences.Byvirtueoftheirsimplicity,ECTsprovidealinkbetweenclassicalIQtestingandbiologicalinquiriessuchasfMRIstudies. Workingmemory Onetheoryholdsthatgisidenticalornearlyidenticaltoworkingmemorycapacity.Amongotherevidenceforthisview,somestudieshavefoundfactorsrepresentinggandworkingmemorytobeperfectlycorrelated.However,inameta-analysisthecorrelationwasfoundtobeconsiderablelower.[95]Onecriticismthathasbeenmadeofstudiesthatidentifygwithworkingmemoryisthat"wedonotadvanceunderstandingbyshowingthatonemysteriousconceptislinkedtoanother."[96] Piagetiantasks Psychometrictheoriesofintelligenceaimatquantifyingintellectualgrowthandidentifyingabilitydifferencesbetweenindividualsandgroups.Incontrast,JeanPiaget'stheoryofcognitivedevelopmentseekstounderstandqualitativechangesinchildren'sintellectualdevelopment.Piagetdesignedanumberoftaskstoverifyhypothesesarisingfromhistheory.Thetaskswerenotintendedtomeasureindividualdifferences,andtheyhavenoequivalentinpsychometricintelligencetests.[97][98]Forexample,inoneofthebest-knownPiagetianconservationtasksachildisaskediftheamountofwaterintwoidenticalglassesisthesame.Afterthechildagreesthattheamountisthesame,theinvestigatorpoursthewaterfromoneoftheglassesintoaglassofdifferentshapesothattheamountappearsdifferentalthoughitremainsthesame.Thechildisthenaskediftheamountofwaterinthetwoglassesisthesameordifferent. NotwithstandingthedifferentresearchtraditionsinwhichpsychometrictestsandPiagetiantasksweredeveloped,thecorrelationsbetweenthetwotypesofmeasureshavebeenfoundtobeconsistentlypositiveandgenerallymoderateinmagnitude.Acommongeneralfactorunderliesthem.IthasbeenshownthatitispossibletoconstructabatteryconsistingofPiagetiantasksthatisasgoodameasureofgasstandardIQtests.[99][100] Personality Thetraditionalviewinpsychologyisthatthereisnomeaningfulrelationshipbetweenpersonalityandintelligence,andthatthetwoshouldbestudiedseparately.Intelligencecanbeunderstoodintermsofwhatanindividualcando,orwhathisorhermaximalperformanceis,whilepersonalitycanbethoughtofintermsofwhatanindividualwilltypicallydo,orwhathisorhergeneraltendenciesofbehaviorare.Researchhasindicatedthatcorrelationsbetweenmeasuresofintelligenceandpersonalityaresmall,andithasthusbeenarguedthatgisapurelycognitivevariablethatisindependentofpersonalitytraits.Ina2007meta-analysisthecorrelationsbetweengandthe"BigFive"personalitytraitswerefoundtobeasfollows: conscientiousness-.04 agreeableness.00 extraversion.02 openness.22 emotionalstability.09 Thesamemeta-analysisfoundacorrelationof.20betweenself-efficacyandg.[101][102][103] Someresearchershavearguedthattheassociationsbetweenintelligenceandpersonality,albeitmodest,areconsistent.Theyhaveinterpretedcorrelationsbetweenintelligenceandpersonalitymeasuresintwomainways.Thefirstperspectiveisthatpersonalitytraitsinfluenceperformanceonintelligencetests.Forexample,apersonmayfailtoperformatamaximallevelonanIQtestduetohisorheranxietyandstress-proneness.Thesecondperspectiveconsidersintelligenceandpersonalitytobeconceptuallyrelated,withpersonalitytraitsdetermininghowpeopleapplyandinvesttheircognitiveabilities,leadingtoknowledgeexpansionandgreatercognitivedifferentiation.[101][104] Creativity Someresearchersbelievethatthereisathresholdlevelofgbelowwhichsociallysignificantcreativityisrare,butthatotherwisethereisnorelationshipbetweenthetwo.Ithasbeensuggestedthatthisthresholdisatleastonestandarddeviationabovethepopulationmean.Abovethethreshold,personalitydifferencesarebelievedtobeimportantdeterminantsofindividualvariationincreativity.[105][106] Othershavechallengedthethresholdtheory.Whilenotdisputingthatopportunityandpersonalattributesotherthanintelligence,suchasenergyandcommitment,areimportantforcreativity,theyarguethatgispositivelyassociatedwithcreativityevenatthehighendoftheabilitydistribution.ThelongitudinalStudyofMathematicallyPrecociousYouthhasprovidedevidenceforthiscontention.Ithasshowedthatindividualsidentifiedbystandardizedtestsasintellectuallygiftedinearlyadolescenceaccomplishcreativeachievements(forexample,securingpatentsorpublishingliteraryorscientificworks)atseveraltimestherateofthegeneralpopulation,andthatevenwithinthetop1percentofcognitiveability,thosewithhigherabilityaremorelikelytomakeoutstandingachievements.Thestudyhasalsosuggestedthatthelevelofgactsasapredictorofthelevelofachievement,whilespecificcognitiveabilitypatternspredicttherealmofachievement.[107][108] Challengestog Gf-Gctheory Mainarticle:Fluidandcrystallizedintelligence RaymondCattell,astudentofCharlesSpearman's,rejectedtheunitarygfactormodelanddividedgintotwobroad,relativelyindependentdomains:fluidintelligence(Gf)andcrystallizedintelligence(Gc).Gfisconceptualizedasacapacitytofigureoutnovelproblems,anditisbestassessedwithtestswithlittleculturalorscholasticcontent,suchasRaven'smatrices.Gccanbethoughtofasconsolidatedknowledge,reflectingtheskillsandinformationthatanindividualacquiresandretainsthroughouthisorherlife.Gcisdependentoneducationandotherformsofacculturation,anditisbestassessedwithteststhatemphasizescholasticandculturalknowledge.[109][44][2]Gfcanbethoughttoprimarilyconsistofcurrentreasoningandproblemsolvingcapabilities,whileGcreflectstheoutcomeofpreviouslyexecutedcognitiveprocesses.[110] TherationalefortheseparationofGfandGcwastoexplainindividuals'cognitivedevelopmentovertime.WhileGfandGchavebeenfoundtobehighlycorrelated,theydifferinthewaytheychangeoveralifetime.Gftendstopeakataroundage20,slowlydecliningthereafter.Incontrast,Gcisstableorincreasesacrossadulthood.Asinglegeneralfactorhasbeencriticizedasobscuringthisbifurcatedpatternofdevelopment.CattellarguedthatGfreflectedindividualdifferencesintheefficiencyofthecentralnervoussystem.Gcwas,inCattell'sthinking,theresultofaperson"investing"hisorherGfinlearningexperiencesthroughoutlife.[44][2][111][31] Cattell,togetherwithJohnHorn,laterexpandedtheGf-Gcmodeltoincludeanumberofotherbroadabilities,suchasGq(quantitativereasoning)andGv(visual-spatialreasoning).WhileallthebroadabilityfactorsintheextendedGf-Gcmodelarepositivelycorrelatedandthuswouldenabletheextractionofahigherordergfactor,CattellandHornmaintainedthatitwouldbeerroneoustopositthatageneralfactorunderliesthesebroadabilities.Theyarguedthatgfactorscomputedfromdifferenttestbatteriesarenotinvariantandwouldgivedifferentvaluesofg,andthatthecorrelationsamongtestsarisebecauseitisdifficulttotestjustoneabilityatatime.[112][113][2] However,severalresearchershavesuggestedthattheGf-Gcmodeliscompatiblewithag-centeredunderstandingofcognitiveabilities.Forexample,JohnB.Carroll'sthree-stratummodelofintelligenceincludesbothGfandGctogetherwithahigher-ordergfactor.Basedonfactoranalysesofmanydatasets,someresearchershavealsoarguedthatGfandgareoneandthesamefactorandthatgfactorsfromdifferenttestbatteriesaresubstantiallyinvariantprovidedthatthebatteriesarelargeanddiverse.[44][114][115] Theoriesofuncorrelatedabilities Severaltheoristshaveproposedthatthereareintellectualabilitiesthatareuncorrelatedwitheachother.AmongtheearliestwasL.L.Thurstonewhocreatedamodelofprimarymentalabilitiesrepresentingsupposedlyindependentdomainsofintelligence.However,Thurstone'stestsoftheseabilitieswerefoundtoproduceastronggeneralfactor.Hearguedthatthelackofindependenceamonghistestsreflectedthedifficultyofconstructing"factoriallypure"teststhatmeasuredjustoneability.Similarly,J.P.Guilfordproposedamodelofintelligencethatcomprisedupto180distinct,uncorrelatedabilities,andclaimedtobeabletotestallofthem.LateranalyseshaveshownthatthefactorialproceduresGuilfordpresentedasevidenceforhistheorydidnotprovidesupportforit,andthatthetestdatathatheclaimedprovidedevidenceagainstgdidinfactexhibittheusualpatternofintercorrelationsaftercorrectionforstatisticalartifacts.[116][117] Morerecently,HowardGardnerhasdevelopedthetheoryofmultipleintelligences.Hepositstheexistenceofeightdifferentandindependentdomainsofintelligence,suchaslinguistic,spatial,musical,andbodilykinestheticintelligences,andcontendsthatindividualswhofailinsomeofthemmayexcelinothers.AccordingtoGardner,testsandschoolstraditionallyemphasizeonlylinguisticandlogicalabilitieswhileneglectingotherformsofintelligence.Whilepopularamongeducationalists,Gardner'stheoryhasbeenmuchcriticizedbypsychologistsandpsychometricians.Onecriticismisthatthetheorydoesviolencetobothscientificandeverydayusagesoftheword"intelligence."SeveralresearchershavearguedthatnotallofGardner'sintelligencesfallwithinthecognitivesphere.Forexample,Gardnercontendsthatasuccessfulcareerinprofessionalsportsorpopularmusicreflectsbodily-kinestheticintelligenceandmusicalintelligence,respectively,eventhoughonemightusuallytalkofathleticandmusicalskills,talents,orabilitiesinstead.AnothercriticismofGardner'stheoryisthatmanyofhispurportedlyindependentdomainsofintelligenceareinfactcorrelatedwitheachother.Respondingtoempiricalanalysesshowingcorrelationsbetweenthedomains,Gardnerhasarguedthatthecorrelationsexistbecauseofthecommonformatoftestsandbecausealltestsrequirelinguisticandlogicalskills.HiscriticshaveinturnpointedoutthatnotallIQtestsareadministeredinthepaper-and-pencilformat,thatasidefromlinguisticandlogicalabilities,IQtestbatteriescontainalsomeasuresof,forexample,spatialabilities,andthatelementarycognitivetasks(forexample,inspectiontimeandreactiontime)thatdonotinvolvelinguisticorlogicalreasoningcorrelatewithconventionalIQbatteries,too.[118][119][67][120] RobertSternberg,workingwithvariouscolleagues,hasalsosuggestedthatintelligencehasdimensionsindependentofg.Hearguesthattherearethreeclassesofintelligence:analytic,practical,andcreative.AccordingtoSternberg,traditionalpsychometrictestsmeasureonlyanalyticintelligence,andshouldbeaugmentedtotestcreativeandpracticalintelligenceaswell.Hehasdevisedseveralteststothiseffect.Sternbergequatesanalyticintelligencewithacademicintelligence,andcontrastsitwithpracticalintelligence,definedasanabilitytodealwithill-definedreal-lifeproblems.Tacitintelligenceisanimportantcomponentofpracticalintelligence,consistingofknowledgethatisnotexplicitlytaughtbutisrequiredinmanyreal-lifesituations.Assessingcreativityindependentofintelligencetestshastraditionallyproveddifficult,butSternbergandcolleagueshaveclaimedtohavecreatedvalidtestsofcreativity,too.ThevalidationofSternberg'stheoryrequiresthatthethreeabilitiestestedaresubstantiallyuncorrelatedandhaveindependentpredictivevalidity.Sternberghasconductedmanyexperimentswhichheclaimsconfirmthevalidityofhistheory,butseveralresearchershavedisputedthisconclusion.Forexample,inhisreanalysisofavalidationstudyofSternberg'sSTATtest,NathanBrodyshowedthatthepredictivevalidityoftheSTAT,atestofthreeallegedlyindependentabilities,wassolelyduetoasinglegeneralfactorunderlyingthetests,whichBrodyequatedwiththegfactor.[121][122] Othercriticisms PerhapsthemostfamouscritiqueoftheconstructofgisthatofthepaleontologistandbiologistStephenJayGould's,presentedinhis1981bookTheMismeasureofMan.Hearguedthatpsychometricianshavefallaciouslyreifiedthegfactorasaphysicalthinginthebrain,eventhoughitissimplytheproductofstatisticalcalculations(i.e.,factoranalysis).Hefurthernotedthatitispossibletoproducefactorsolutionsofcognitivetestdatathatdonotcontainagfactoryetexplainthesameamountofinformationassolutionsthatyieldag.AccordingtoGould,thereisnorationaleforpreferringonefactorsolutiontoanother,andfactoranalysisthereforedoesnotlendsupporttotheexistenceofanentitylikeg.Moregenerally,Gouldcriticizedthegtheoryforabstractingintelligenceasasingleentityandforrankingpeople"inasingleseriesofworthiness",arguingthatsuchrankingsareusedtojustifytheoppressionofdisadvantagedgroups.[123][37] ManyresearchershavecriticizedGould'sarguments.Forexample,theyhaverejectedtheaccusationofreification,maintainingthattheuseofextractedfactorssuchasgaspotentialcausalvariableswhoserealitycanbesupportedorrejectedbyfurtherinvestigationsconstitutesanormalscientificpracticethatinnowaydistinguishespsychometricsfromothersciences.CriticshavealsosuggestedthatGoulddidnotunderstandthepurposeoffactoranalysis,andthathewasignorantofrelevantmethodologicaladvancesinthefield.Whiledifferentfactorsolutionsmaybemathematicallyequivalentintheirabilitytoaccountforintercorrelationsamongtests,solutionsthatyieldagfactorarepsychologicallypreferableforseveralreasonsextrinsictofactoranalysis,includingthephenomenonofthepositivemanifold,thefactthatthesamegcanemergefromquitedifferenttestbatteries,thewidespreadpracticalvalidityofg,andthelinkageofgtomanybiologicalvariables.[38][124][37] JohnHornandJohnMcArdlehavearguedthatthemoderngtheory,asespousedby,forexample,ArthurJensen,isunfalsifiable,becausetheexistenceofacommonfactorfollowstautologicallyfrompositivecorrelationsamongtests.TheycontrastedthemodernhierarchicaltheoryofgwithSpearman'soriginaltwo-factortheorywhichwasreadilyfalsifiable(andindeedwasfalsified).[31] Seealso CharlesSpearman Factoranalysisinpsychometrics Fluidandcrystallizedintelligence Flynneffect Intelligence Intelligencequotient Malleabilityofintelligence Spearman'shypothesis Notes ↑1.01.1Kamphausetal.2005 ↑2.02.12.22.32.42.52.62.7Dearyetal.2010 ↑Jensen1998,545 ↑Neisseretal.1996 ↑AdaptedfromJensen1998,24.ThecorrelationmatrixwasoriginallypublishedinSpearman1904,anditisbasedontheschoolperformanceofasampleofEnglishchildren.Whilethisanalysisishistoricallyimportantandhasbeenhighlyinfluential,itdoesnotmeetmoderntechnicalstandards.SeeMackintosh2011,44ff.andHorn&McArdle2007fordiscussionofSpearman'smethods. ↑Gottfredson1998 ↑Deary2001,12 ↑Spearman1904 ↑Deary2000,6 ↑10.010.110.2Jensen1992 ↑Jensen1998,28 ↑12.012.112.212.3vandeerMaasetal.2006 ↑AdaptedfromChabris2007,Table19.1. ↑Jensen1998,26,36-39 ↑Jensen1998,26,36-39,89-90 ↑Jensen2002 ↑17.017.1Floydetal.2009 ↑Jensen1980,213 ↑Jensen1992 ↑Jensen1980,213 ↑Jensen1998,94 ↑Hunt2011,94 ↑Jensen1998,18–19,35–36,38.Theideaofageneral,unitarymentalabilitywasintroducedtopsychologybyHerbertSpencerandFrancisGaltoninthelatterhalfofthe19thcentury,buttheirworkwaslargelyspeculative,withlittleempiricalbasis. ↑Jensen2002 ↑Jensen1998,91–92,95 ↑Jensen2005 ↑Mackintosh2011,157 ↑Jensen1998,117 ↑Bartholomewetal.2009 ↑Jensen1998,120 ↑31.031.131.2Horn&McArdle2007 ↑Jensen1998,120–121 ↑Mackintosh2011,157-158 ↑34.034.1Rushton&Jensen2010 ↑Mackintosh2011,44-45 ↑Jensen1998,18,31-32 ↑37.037.137.237.3Carroll1995 ↑38.038.1Jensen1982 ↑Jensen1998,73 ↑40.040.140.240.3Deary2012 ↑Mackintosh2011,57 ↑Jensen1998,46 ↑Carroll1997.Thetotalcommonfactorvarianceconsistsofthevarianceduetothegfactorandthegroupfactorsconsideredtogether.Thevariancenotaccountedforbythecommonfactors,referredtoasuniqueness,comprisessubtest-specificvarianceandmeasurementerror. ↑44.044.144.244.3Davidson&Kemp2011 ↑Mackintosh2011,151 ↑Jensen1998,31 ↑Mackintosh2011,151-153 ↑McGrew2005 ↑Kvist&Gustafsson2008 ↑Hunt2011,94 ↑Johnsonetal.2004 ↑Johnsonetal.2008 ↑Mackintosh2011,150–153 ↑Jensen1998,88,101–103 ↑Spearman1927 ↑Detterman&Daniel1989 ↑Deary&Pagliari1991 ↑58.058.1Dearyetal.1996 ↑59.059.1Tucker-Drob2009 ↑Jensen1998,270 ↑Gottfredson2002 ↑62.062.1Sackettetal.2008 ↑Jensen1998,272,301 ↑Jensen1998,270 ↑Jensen1998,279-280 ↑Jensen1998,279 ↑67.067.1Brody2006 ↑Frey&Detterman2003 ↑69.069.1Schmidt&Hunter2004 ↑Jensen1998,292-293 ↑Schmidt&Hunter2004.Thesevaliditycoefficientshavebeencorrectedformeasurementerrorinthedependentvariable(i.e.,jobortrainingperformance)andforrangerestrictionbutnotformeasurementerrorintheindependentvariable(i.e.,measuresofg). ↑Jensen1998,270 ↑Jensen1998,568 ↑Jensen1998,271 ↑Gottfredson2007 ↑Dearyetal.2006 ↑77.077.177.2Plomin&Spinath2004 ↑Haworthetal.2010 ↑Kovas&Plomin2006 ↑80.080.1Penkeetal.2007 ↑81.081.1Chabrisetal.(inpress) ↑Plomin2003 ↑Jensen1998,189–197 ↑Mackintosh2011,134–138 ↑85.085.185.2Chabris2007 ↑Jensen1998,146,149–150 ↑Jensen1998,164–165 ↑Jensen1998,87–88 ↑Mackintosh2011,360–373 ↑Rothetal.2001 ↑Hunt2011,421 ↑Jensen1998,369–399 ↑Lynn2003 ↑Jensen1998,213 ↑Ackermanetal.2005 ↑Mackintosh2011,158 ↑Weinberg1989 ↑Lautrey2002 ↑Humphreysetal.1985 ↑Weinberg1989 ↑101.0101.1vonStummetal.2011 ↑Jensen1998,573 ↑Judgeetal.2007 ↑vonStummetal.2009 ↑Jensen1998,577 ↑Eysenck1995 ↑Lubinski2009 ↑Robertsonetal.2010 ↑Jensen1998,122-123 ↑Sternbergetal.1981 ↑Jensen1998,123 ↑Jensen1998,124 ↑McGrew2005 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