Observer Bias and Reliability By Xunchi Pu
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1 Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir masurmnts bfor undrtaking furthr analyss. Obsrvr bias is systmatic rror producd in obsrvational data by an obsrvr's xpctations or wishs. Th rror is strongly associatd with obsrvations mad on variabls that rquir jctiv assssmnt. Th goal of all masurmnt is to achiv accurat rsults. Howvr, this is not compltly possibl bcaus masurmnt rror, to som xtnt, is introducd into all masuring procdurs. In many aras of mdical rsarch, rliability studis ar frquntly conductd in ordr to assss th lvl of obsrvr variability in th masurmnt procdur. According to th collctd data, thr ar diffrnt mthods to assss th rliability of masurmnts. Rliability masurs for Catgorical data Normally, whn studying th variability of obsrvr ratings, two componnts of possibl inaccuracis must b distinguishd, thy ar intr-obsrvr bias and Intra-obsrvr bias. Th intr-obsrvr bias is rflctd by diffrnc among th marginal distribution of th rspons variabl for ach of th obsrvrs. Fliss showd that th omnibus tst of th intr-obsrvr bias can b usd by th following Q-tst: r(r 1) (y.j y.. r) j1 Q n ry.. y i. j1 Whr: r n is th numbr of jcts; r is th numbr of obsrvrs;
2 y ij is 1 if th ith jct is judgd by th jth obsrvr to hav th symptom prsnt, 0 othrwis; y i. Is th total numbr of obsrvrs who judg th ith jct to hav th symptom; y.j is th total numbr of th jcts th j th obsrvr judgs as having th symptom psnt; y.. is th total numbr of prsnt judgmnts mad. If th hypothsis of no intr-obsrvr bias is tru, thn Q has an approximatly a chisquar distribution with r-1 dgrs of frdom. Exampl 1: In th tabl, 5 psychiatrists valuat whthr th patints hav a sysmptom. If th patint has th symptom, th valu is 1; othrwis, 0. Psychiatrist total Proportion total Proportion For th data prsntd in th tabl, th tst statistic Q is givn by 5 4 ( ) Q Rfrring this to chi-squar distribution with 4 dgrs of frdom, w s that thr is som vidnc of intr-obsrvation bias for th psychiatrists on this particular symptom. Howvr, th invstigator may fl it is important to compar th diffrnt sts of obsrvrs. In this cas, w can us th paramtr of kappa to assss th obsrvr agrmnt or rliability.
3 Kappa (κ ) cofficint is usd to valuat th agrmnt of th obsrvrs. Po Pc κ 1 P Whr: c P o is dfind as th proportion of th jcts classifid into th sam catgory by th two obsrvrs; P c is dfind as th agrmnt to b xpctd by chanc. Th calculation of P o, P c and κ ar shown in xampl. Exampl : Th tabl containd th rsults that two pathologist sparatly classifid biopsy slids into on of fiv catgoris, Pathologist Row Total Pathologist P o P c κ P P o 1 P c c Kappa s possibl valus ar constraind to th intrval [0, 1]; κ 0 mans that agrmnt is not diffrnt from chanc, and κ 1 mans prfct agrmnt. Howvr, just obtaining a significantly gratr than zro is not sufficint to assss th quality of th agrmnt. Various scals to assss Kappa s significanc hav bn proposd. Landis and Koch gav som arbitrany but potntially usful valu for valuating obsrvd valu:
4 Tabl Evaluation of obsrvd kappa valus κ Strngth of agrmnt 0 Poor Slight Fair Modrat Substabtial Almost prfct Th concpt of a chanc corrctd masur of agrmnt can b xtndd to th situations involving mor than two obsrvrs. For th dtails sn Fliss and Cuzick (1979) and Schoutn (1985). Masuring Rliability of Quantitativ Variabls For th quantitativ data, any individual obsrvation x can b dscribd as: x µ Whn w assum th thr variabls t, o and indpndnt of on anothr and th varianc of an obsrvation is consquntly givn by: obs Whr: is th varianc of jcts; obs is th varianc of th obsrvrs; rr is th varianc of rror. A singl quantitativ that rflcts th rlativ magnitud of th componnts of varianc is th intraclass corrclation cofficint R, givn by: R obs
5 R can b stimatd from th man squars found by prforming a simpl two-way analysis of varianc on th data. Th gnral form of such an analysis is shown xampl 3. Exampl 3: Sourc of varianc d.f. MS Patints 19,493,469.1 Obsrvrs 3 36,481. Error 57 7,70.3 Bcaus: PMS r t RMS n EMS o So: PMS EMS ) t r ) o RMS EMS n ) EMS , R )
6 Rfrnc: 1. Evritt, B.S. Statistical Mthods for Mdical Invstigations, Oxford Univrsity Prss, Nw York, ( Barbara Di Eugnio, On th usag of Kappa to valuat agrmnt on coding tasks, Elctrical Enginring and Computr Scinc. 3. Krippndorff, Klaus, Contnt Analysis: an Introduction to its Mthodology. Bvrly Hills: Sag Publications. 4. Carolyn Fhr Waltz, Ora L. Strickland, Elizabth R. Lnz, Masurmnt in nursing rsarch, Philadlphia : F.A. Davis Co., c1991, nd d.
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