fei75766_ch13_408-434.indd 411  02/06/20 01:05 PM
Chapter 13    McCrae and Costa’s Five-Factor Trait Theory411
Basics of Factor Analysis
Acomprehensive knowledge ofthemathematical operations involved infactor 
 analysis isnotessential toanunderstanding oftraitandfactor theories ofpersonality, 
butageneral description ofthistechnique should behelpful. 
Tousefactor analysis, onebegins bymaking specific observations ofmany individ -
uals.These observations arethenquantified insome manner; forexample, height ismea-
sured ininches; weight inpounds; aptitude intestscores; jobperformance byrating scales; 
andsoon.Assume thatwehave1,000 suchmeasures on5,000 people. Ournextstepis
todetermine which ofthese variables (scores) arerelated towhich other variables and
towhatextent. Todothis,wecalculate thecorrelation coefficient between eachvariable 
andeachoftheother 999scores. (Acorrelation coefficient isamathematical procedure 
forexpressing thedegree ofcorrespondence between twosetsofscores.) Tocorrelate 
1,000 variables withtheother 999scores would involve 499,500 individual correlations 
(1,000 multiplied by999divided by2).Results ofthese calculations would require a
tableofintercorrelations, oramatrix, with1,000 rowsand1,000 columns. Some ofthese 
correlations would behighandpositive, some nearzero,andsome would benegative. 
Forexample, wemight observe ahighpositive correlation between leglength andheight, 
because oneispartially ameasure oftheother. Wemayalsofindapositive correlation 
between ameasure ofleadership ability andratings onsocial poise. Thisrelationship 
might existbecause theyareeachpartofamore basic underlying trait—self-confidence.
With 1,000 separate variables, ourtableofintercorrelations would bequite cum-
bersome. Atthispoint, weturntofactor analysis, which canaccount foralargenumber of
variables withasmaller number ofmore basic dimensions. These more basic dimensions 
canbecalled traits, thatis,factors thatrepresent acluster ofclosely related variables. For
example, wemayfindhighpositive intercorrelations among testscores inalgebra, geom -
etry,trigonometry, andcalculus. Wehavenowidentified acluster ofscores thatwemight 
callFactor M,which represents mathematical ability. Insimilar fashion, wecanidentify 
anumber ofother factors, orunitsofpersonality derived through factor analysis. The
number offactors, ofcourse, willbesmaller thantheoriginal number ofobservations.
Ournextstepistodetermine theextent towhich eachindividual score con-
tributes tothevarious factors. Correlations ofscores withfactors arecalled factor 
loadings. Forexample, ifscores foralgebra, geometry, trigonometry, andcalculus 
contribute highly toFactor Mbutnottoother factors, theywillhavehighfactor load-
ingsonM.Factor loadings giveusanindication ofthepurity ofthevarious factors 
andenable ustointerpret theirmeanings.
Traits generated through factor analysis maybeeither unipolar orbipolar. 
Unipolar traits arescaled from zerotosome large amount. Height, weight, andintel-
lectual ability areexamples ofunipolar traits. Incontrast,  bipolar traits extend from 
onepoletoanopposite pole, withzerorepresenting amidpoint. Introversion versus 
extraversion, liberalism versus conservatism, andsocial ascendancy versus timidity 
areexamples ofbipolar traits.
Inorder formathematically derived factors tohavepsychological meaning, 
theaxesonwhich thescores areplotted areusually turned orrotated intoaspecific 
mathematical relationship witheachother. Thisrotation canbeeither orthogonal 
oroblique, butadvocates oftheFive-Factor Theory favor theorthogonal rotation. 
Figure 13.1shows thatorthogonally rotated axesareatrightangles toeachother. AsFinal PDF to printer