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bdkbZ—17% ek²dx iz.kkyh % vko';drk] leL;k,¡] ?kVd
vifjo£rr jgrh gSA¸ bl lEcU/ vuqekiu (scaling) vFkok ifjekik¡dksa osQ :ikUrj.k dks O;Dr djus osQ uksV
eq[;r;k% fuEu izdkj gSμ
1- flXek ;k tSM izkIrk¡d (Sigma or Z-scores)μifjekik¡d ekSfyd ifjekik¡dksa (original scores) dks flXek
vuqeki (σ-scale) dh bdkb;ksa esa ifjo£rr dj nus ij izkIr gksrs gSaA flXek LosQy dk vkSlr (Mean) lnSo 'kwU;
gksrk gS rFkk og LosQy osQ Bhd chp esa fLFkr jgrk gSA ;g 'kwU; (zero) gh LosQy dh bdkb;ksa dk vH;qís'; fcUnq
(point of reference) gksrk gSA blosQ Åij&uhps nksuksa vkSj σ bdkb;k¡ jgrh gSa tks uhps Í.kkRed (negative)
rFkk Åij /ukRed (positive) fpUgksa }kjk O;Dr dh tkrh gSaA lEiw.kZ LosQy dh yEckbZ ± 3 σ gksrh gS ftlls σ
lnSo lesd (unity) vFkkZr~ 1-0 jgrk gSA uhps osQ fp=k ls ;g Li"V gks tk;sxkμ
–3 –2 –1 0 + 1 +2 +3
(mean )
σ- ifjekik¡dksa (σ-scores) dks Z-ifjekik¡d (Z-scores) vFkok laf{kIr ifjekik¡d (reduced scores) Hkh dgrs
gSaA Z-ifjekik¡d forj.k osQ ekud fopyu (SD) osQ vk/kj ij eè;eku ls O;fDr osQ izkIrk¡dksa dh nwjh O;Dr djrs
gSaA nwljs 'kCnksa esa ;g bafxr djrs gSa fd izkIr fd;s ewy izkIrk¡d fdlh forj.k osQ eè;eku ls fdrus ekud fopyu
(SD) fopfyr gSaA Z izkIrk¡d Kkr djus osQ fy;s fuEu lw=k dk iz;ksx fd;k tkrk gSA
X − M
Z =
σ
tgk¡] X = ewy izkIrkad
M = ewy izkIrkadksa dk eè;eku
σ = ewy izkIrk¡dksa dk ekud fopyu
mnkgj.kkFkZ] eku yhft;s ehuw dks xf.kr dh 8oha d{kk dh ijh{kk esa 55 vad izkIr gksrs gSa vkSj fo|k£Fk;ksa osQ iwjs
lewg vFkok d{kk dk ekud fopyu (SD) 10 gS rFkk vkSlr 40 gS rks σ-LosQy osQ vuqlkj LosQy ij mldh fLFkfr
vkSlr ls = 1.5σ Åij gksxh vFkkZr~ σ-LosQy esa :ikUrj.k djus ij mldk izkIrkad
+ 1.5σ gksxkA blh izdkj] eksfguh dks xf.kr dh fdlh nwljs LowQy dh 8oha d{kk dh ijh{kk esa 65 vad izkIr gksrs
gSa tcfd ml LowQy dh iwjh d{kk osQ izkIrkadksa dk vkSlr 50 rFkk (SD) 15 gSA ns[kus ij yxrk gS fd eksfguh osQ
izkIrk¡d ehuw ls vf/d gSa ysfdu σ-ifjekik¡dksa esa :ikarj.k djus ij fLFkfr cny tk;sxhA nwljh fLFkfr esa eksfguh
dk σ-ifjekik¡d 65&50@15 = 1σ gksxk vr% ehuw dh xf.krh; ;ksX;rk eksfguh ls vf/d vPNh gSA
ifjHkk"kk osQ :i esa] flXek izkIrkad dks tsEl Mªsoj (james Drever) osQ 'kCnksa es bl izdkj O;Dr fd;k tk ldrk
gSA “Z izkIrkad σ osQ :i esa O;fDr dk og izkIrkad gS tgk¡ ewy izkIrk¡d esa ls eè;eku izkIrkadksa dks ?kVkdj O;fDr
dk fopyu izkIrkad Kkr dj fy;k tkrk gSA ,oa fiQj ekud fopyu (SD) ls ml fopyu izkIrkad dks Hkkx nsdj
Z- izkIrkad ;k σ-izkIrkad Kkr dj fy;k tkrk gSA (Sigma score in terms of sigma is that deviation from
the mean divided by σ with sign plus or minus according it is above or below the mean)
bu :ikUrfjr σ-ifjekik¡dksa osQ lkFk ,d vlqfo/k ;g gksrh gS fd os /ukRed rFkk Í.kkRed nksuksa vkrs gSa ftlosQ
iQyLo:i muosQ iz;ksx esa dfBukbZ mRiUu gksrh gS rFkk le>us esa Hkh vlqfo/k gksrh gSA lkFk gh] buosQ eku n'keyo
fHkUuksa esa vkrs gSa ftlls muosQ iz;ksx esa vkSj Hkh vlqfo/k gksrh gSA fiQj Hkh] bu izkIrkadksa dk viuk egRo gSA
gs.Mjlu (Henderson) us bl egRo dks Lohdkjrs gq, fy[kk gSA
LOVELY PROFESSIONAL UNIVERSITY 225
