KR 20 Dan KR 21 Pada SPSS
Kuder-Richardson Reliability Coefficients KR20 and KR21
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Technote (troubleshooting) Problem(Abstract) Can SPSS calculate the Kuder-Richardson 20 (KR20) and KR21 coefficients of reliability for a scale? Resol ing the !roblem KR20: The KR20 is a s ecial case of Cronbach!s "l ha in #hich the ite$s are binary %ariables (usually scored as 0 or 1)& The R'()"*)()T+ rocedure can calculate "l ha and therefore can calculate KR20 for binary ite$ %ariables& "l ha is re,uested in the -./'( subco$$and0 as in: R'()"*)()T+ 12"R)"*('S3aite$1 aite$2 aite$4 aite$5 aite$6 aite$7 aite$8 aite$9 aite$: aite$10 1SC"('(scorea)3"(( 1-./'(3"(P;" 1ST"T)ST)CS3/'SCR)PT)2' SC"(' 1S<--"R+3T.T"( -'"=S 2"R)"=C' & )n the >ra hic user interface0 R'()"*)()T+ is a%ailable on the "naly?e-@Scale-@Reliability "nalysis $enu& "l ha is the default -odel choice in the -odel scrollbar in the Reliability "nalysis dialo>& ClicA the Statistics button to enter the scale and su$$ary statistics that are s ecified in the 1ST"T)ST)CS and 1S<--"R+ subco$$ands& KR21: There is no direct rocedure o tion for calculatin> the KR210 #hich is based on the (usually unrealistic) assu$ tion that all ite$s in the scale ha%e e,ual difficulty le%els (i&e& e,ual ro ortions of !successes! on the ite$s)& The KR21 could be calculated in SPSS by usin> the "BBR'B"T' rocedure to sa%e KR21 for$ula co$ onents to an acti%e file0 #here they could be in ut into a C.-P<T' co$$and to calculate KR21& "n eCa$ le of such a set of co$$ands is ro%ided belo#0 ;o#e%er0 KR20 is >enerally considered to be a better reliability esti$ate than KR21& (See Cha ter 5 of (ord D =o%icA0 1:79) or Traub (1::5)&) (ord0 E&-0 D =o%icA0 -&R& (1:79)& Statistical Theories of -ental Test Scores& Readin> -": "ddison -Fesley& Traub0 R&'& (1::5)0 Reliability for the Social Sciences: Theory and " C": Sa>e& lications& Thousand .aAs
The for$ula for KR21 for scale score G is K1(K-1) H (1 - <H(K-<)1(KH2)) 0 #here K is the nu$ber of ite$s0< is the $ean of G and 2 is the %ariance of G& Su ose that you ha%e ite$ scores (0 or 1) on siC binary ite$s ()T'-1 to )T'-7) and that you #ant the KR21 coefficient for the scale score that is co$ rised as the su$ of these siC ite$ scores (Score")& The follo#in> co$$ands run the Reliability rocedure to roduce the KR20 coefficient as Cronbach!s "l ha& Score" is co$ uted for cases #ith full data on the siC ite$s& The ">>re>ate rocedure is used to co$ ute the ieces of the KR21 for$ula and sa%e the$ in a ne# data set0 (Ar21Iinfo)& Fith that ne# data set acti%e0 a Co$ ute co$$and is then used to calculate the KR21 coefficient&& R'()"*)()T+ 12"R)"*('S3ite$1 ite$2 ite$4 ite$5 ite$6 ite$7 1SC"('(!"(( 2"R)"*('S!) "(( 1-./'(3"(P;" 1ST"T)ST)CS3/'SCR)PT)2' SC"(' 1S<--"R+3T.T"( -'"=S 2"R)"=C'& co$ ute =ite$s 3 n%alid(ite$1 to ite$7)& if (n$issin>(ite$1 to ite$7) 3 0) score" 3 su$(ite$1 to ite$7)& descri ti%es score" 1ST"T)ST)CS3-'"= ST//'2 2"R)"=C' -)= -"G& /"T"S'T /'C("R' KR21Iinfo& "BBR'B"T' 1.<TE)('3!KR21Iinfo! 1*R'"K3 1score"I$ean3-'"=(score") 1K !=u$ber of ite$s!3-"G(=ite$s) 1score"Isd3S/(score") 1=IScore"3=(score")& /"T"S'T "CT)2"T' KR21Iinfo& co$ ute Ar21IScore" 3 A1(A - 1) H (1 - (score"I$eanH (A - score"I$ean)1 (AHscore"IsdHH2H(=IScore" -1)1=IScore")))& list& ;ere are a fe# eC lanatory notes for the co$$ands& 1& Reliability uses only cases #ith co$ lete data on the ite$ %ariables& Score" is co$ uted here only for cases #ith such co$ lete data so that the KR21 is based on the sa$e cases as the Reliability out ut& 2& The KR21 for$ula uses the o ulation (JbiasedJ) esti$ate of the scale score %ariance0 #hereas ">>re>ate co$ utes the sa$ le (JunbiasedJ) esti$ate& "lso0 ">>re>ate #ill sa%e the standard de%iation of a %ariable to the ne# data set0 but does not ha%e a function to sa%e the %ariance& Therefore the standard de%iation is sa%ed by ">>re>ate as score"Isd and this %alue is s,uared and then $ulti lied by (=-1)1= in the Co$ ute co$$and to >et the o ulation %ariance esti$ate for Score" in the KR21 for$ula& 4& " *reaA %ariable does not need to be desi>nated in current %ersions of SPSS Statistics #hen the a>>re>ation is erfor$ed o%er the full data set& )f the reliability analysis #as erfor$ed #ithin
sub>rou s of the data as defined by a s lit file %ariable0 then that %ariable #ould be the *reaA %ariable in the ">>re>ate rocedure& +ou #ould not need to turn on the S lit Eile structure #hen #orAin> in the KR21Iinfo data set& 5& "ll of the ste s in the KR21 calculation can be erfor$ed in the $enu syste$0 or >ra hic user interface (B<))& The ">>re>ate rocedure is a%ailable under /ata-@">>re>ate& "fter runnin> ">>re>ate0 the KR21Iinfo data set #ill #ill be listed in the Findo#s $enu of SPSS Statistics and can be acti%ated by clicAin> that ite$& The Co$ ute co$$and o eration is a%ailable under Transfor$-@Co$ ute 2ariable& Ty e the resultin> %ariable (Score") into the Tar>et 2ariable *oC and the transfor$ation eC ression into the =u$eric 'C ression boC& The )E co$$and o eration is also a%ailable in the Transfor$-@ Co$ ute 2ariable dialo> by enterin> the Tar>et 2ariable and =u$eric 'C ression boC and then clicAin> the )E button& )n the J)f casesJ dialo>0 clicA the radio button beside J)nclude if case satisfies conditionJ and enter the conditional eC ression (J(n$issin>(ite$1 to ite$7) 3 0) J in this eCa$ le) into the boC belo# that radio button& ClicA Continue and .K&
