- 73 - PHN PHI CHUNPhnphichun(Normaldistribution)cnurabimtngiAnhgc PhptnlAbrahamdeMoivre(1733).SauGauss,mtnhtonhcngi c,dnglutphnphichunnghincuccdliuvthinvnhc (1809)vdovycngcgilphnphiGauss.Theotinbchkhoav khoa hc thng k, c l ngi u tindng t normal l ng C.S Pierce (1780) vvothingitachorngmihintngtnhinccoinhcphn phichunnhngthtracncnhnglutphnphikhc.Tuyvyhuhtl thuyt thng k c xy dng trn nn tng ca phn phi chun. Nh vy t normal c dng theo thi quen nhng thc ra khng ng, v vytrongtingVittakhngthdchlphnphibnhthngmgilphn phi chun. Haithngsquantrngtrongmtphnphilgitrtrungtmhaygil trung bnh v phng sai o2 (hoc lch chun o) v thng biu th bng X ~ N (,o2) (N vit tt t normal). Nu phn phi chun c chun ha vi trung bnh=0 v lch chun o=1,cvitttl:Z~N(=0,o=1),cgilphnphichunchunha (standardized normal distribution) nghe cv khng c xui tai nh ting Anh v chnormalcdch lchunri,dovy dngtphnphichuntccvn hn !Ni chung cc c tnh sinh trc hc ca ngi khe mnh (cn nng, chiu cao, tr s mch, huyt p, ng mu, s lng hng cu), thng tun theo lut phn phi chun. V d: xt nghim ng mu 100 ngi ln khe mnh cc kt qu thu thp trong bng 10.1.Bng 10.1 Kt qu ng mu (mg%) 100 ngi ln khe mnh 971001101061031089792113112 881009510112495111998493 8211588857990100104109100 90841029893102102102110109 90114106115103899383100106 1001111018880891039191119 9711611811795921238110295 10610694103968994122110100 8010810111198971051059886 10597871111071159611079107 Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 74 - Bng 10.2Biu cung-l ca ng mu: 4 3 3 3 3 92 829 829 4828 47284 37173 937172 937161 49270619 48260618 38160617 28150606 170505054 9060505053 9050505052 7080809090100100110110120 Tn s279121520141173 Nhn vo biu cung-l ta thy c: 2 ngi c tr ng mu 120 mg%: 3% V biu tn sut (histogram) ca phn phi ng mu (Biu 10.1): Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 75 - Biu 10.1Phn phi ng mu ca 100 ngi ln khe mnhNh vy ta thy phn phi lng ng mu tun theo lut chun vi tr s trung bnh =100 v lch chun o=10 vi: 68% gi tr quan st nm trong khong o ca . 95% gi tr quan st nm trong khong 2o ca . 99,7% gi tr quan st nm trong khong 3o ca . (cn gi l lut 68-95-99,7) 10.1 Hm mt phn phi chun Hmmtphnphichun(Normaldensityprobabilityfunction)cdng tng qut nh sau: Trong : t = 3,14159... e = 2,71828... (c s logarit Neper) : tr s trung bnh o : lch chun Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 76 - Bin ngu nhin X c n v l mg% by gi ta mun chuyn n v o lng ca binsXtheonvo lngtngqutchomiphnphichunnghaltheo n v lch chun. Lc phn phi chun theo X s tr thnh phn phi chun tc (standadized normal distribution) vi bin s mi l Z. Mun i hm y=f(x) ra hm chun tc y=f(z) ta t:

o - xz = Th =100 v o=10 ta c: 10100 - xz =Nh vy khi: x=80 z=-2 x=90 z=-1 x=100 z=0 x=110 z=+1 x=120 z=+2 V ng cong chun y=f(z) s l: S10.1BiniphnphichunX(trtrungbnh,lchchuno)thnh phn phi chun tc Z (tr trung bnh=0, lch chun=1) Tmli:BinXtuntheolutchunvitrungbnhvphngsaio2

thngcvittt l:X~N(,o2 )vbinZtuntheo phnphichuntcc =0 v o2=1c vit l Z ~ N(0,1). Nh vy lc ny Z c n v l lch (v d: 1, 2 hoc 3 lch chunso vi tr trung bnh) v khng ty thuc vo n v o lng theo bin X (v d. mg% ng mu). Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 77 - Phng trnh ng cong chun tc theo Z s l: ( )2e21z f2z = Lc ny mun bit xc sut ng mu t 100-110mg% (theo X) ch cn tnh xc sut t 0 n 1 n v lch chun theo Z hoc tm din tch di ng cong t 0 n 1 (phn mu m-hnh 3). Tch phn ca hmf(z) t 0 1 chnh l din tchdingcongny.Trong thngk gif(Z) l hmxcsutchun tch ly (cummulative normal probability function) Biu 10.2 Din tch di ng cong chun t 0 +1o ( )dz2z 102e21z f}= Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 78 - Cng thc tnh tch phn hm F(z) kh rc ri thng ta dng bng Z-score (phn ph lc) tnh. Xem bng khi z=0 z=1: F(z)=0,34 ( )dz2z 102e211 z 0 P}= s s= 0,34 NhvyxcsutP(0Z1)l0,34hocxcsutnhngngictr ngmutX=100mg%(tngngvi Z=0) nX=110mg%(tngng vi Z=1) l 34% (biu ) Cc khong c bit c th tnh nhm xc sut: ( )dz2z0-2e210 z P}= s s = 0,5 ( )dz2z02e21z 0 P +}= + s s= 0,5 ( )dz2z-2e21z - P +}= + s s = 1 Mtvdkhc:Muntnhxcsutcazt-n1,2taly:xcsut khong t- n 0 l p=0,50 cng vi xc sut khong t 0 n 1,2 l 0,38 (xem bng z-score phn ph lc), tng cng 2 xc sut ny l0,88 (tng ng 88% ngi c ng mu 115mg%) (1 n v z bng 10mg%) 10.2Nhn bit mt phn phi chun trong SPSS C nhiu cch nh gi mt phn phi chun trong SPSS. (1) n gin nht l xem biu vi ng cong chun (Histograms with normal curve) vi dnh hnh chung i xng vi tn s cao nht nm ngay gia v cc tn s thp dn nm 2 bn. Tr trung bnh (mean) v trung v (mediane) gn bng nhau v xp (skewness) gn bng zero. (2) V biu xc sut chun (normal Q-Q plot). Phn phi chun khi biu xc sut ny c quan h tuyn tnh (ng thng) Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 79 - (3) Dng php kim nhKolmogorov-Smirnov khi c mu ln hn 50 hoc php kimShapiro-Wilk khi c mu nh hn 50. c coi l c phn phi chun khi mc ngha (Sig.) ln hn 0,05. V d 1. Kho st men ALT (U/L) trn 30 ngi bnh thng, kt qu c nhp vo SPSS nh sau: V thc n Analyze > Descriptive Statistics> Frequencies Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 80 - M mn hnh Frequencies. Nhp chuyn bin ALT t bn tri vo Variable(s). Nhp hp thoi Statistics Vo mn hnh Statistics, nh du nhy vo 4 : Mean, Median, Std. deviation v Skewness v nhp Continue Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 81 - Nhp tip hp thoi Charts.. nh du vo trn Histograms: v nh dy nhy vo With Normal curve, nhp Continue. Nhn OK s cho kt qu sau. Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 82 - Tr trung bnh (mean)= 23,97, trung v (mediane)=24,00 v xin(skewness)=0,533 Trong phn phi ny, tr s trung bnh v trung v gn bng nhau v xin dao ng t -1 n +1. Nh vy y c th l mt phn phi chun. Tht vy xem biu phn phi vi ng cong chun c dng hnh chung, c tr trung bnh l 23,97 v s liu phn phi kh u 2 bn. kim nh Kolmogorov-Smirnov hoc v biu xcsut chun Q-Q (Normal Q-Q plot) vo thc n:Analyze> Descriptive Statistics> Explore Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 83 - Khi xut hin mn hnh Explore, chuyn ALT t bn tri vo Dependent List:

Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 84 - Nhn vo hp thoi Plots. Sau khi mn hnh Explore:Plots xut hin, nhp du nhy vo Histogram v Normality plots with tests. Nhp Continue v nhp OK Kt qu kim nh phn phi chun nh sau: Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 85 - V c mu 30 (nh hn 50), dng kim nhShapiro-Wilk viSig.=0,571 (ln hn 0,05). Chng t phn phi ny l phn phi chun. Xem biu Normal Q-Q Plot bn di, cc tr s quan st v tr s mong i u nm gn trn ng thng Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 86 - V d 2. Kho st men ALT (U/L) trn 30 ngi mc vim gan siu vi B mn tnh Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 87 - Vo Analyze> Descriptive > Frequenciesnh phn trn Kt qu Phn phi ny c trung bnh (301,82) v trung v (190,00) kh khc bit. Hn na xp (2,17) ln hn +1, v vy c th khng phi l phn phi chun. Tht vy, xem biu vi ng cong chun cho thy s liu khng phn phi u, tp trung nhiu v pha ui tri v t v pha ui phi (xp phi) Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 88 - r hn vo Analyze>Descriptives> Explore xem kim nh Kolmogorov-Smirnov v biu Normal Q-Q plot Kim nh Shapiro-Wilk vi Sig=0,000 ( nh hn 0,05 bc b gi thuyt khng). Nh vy phn phi ny khng phi l phn phi chun. Trn biu Q-Q plot ta thy s lin h gia tr s quan st v tr s mong i khng nm trn ng thng. Ti liu tham kho: 1. Armitage P. and Berry G. The normal distribution, in Statistical methods in medical research, 3rd edition, Backwell Scientific publication 1994, pp;66-71. 2. Altman DG. The normal distribution. statistic notes.BMJ 1995; 310:298.3.Website:http://www.stat.wvu.edu/SRS/Modules/Normal/normal.htmltruycp ngy 12/02/09. Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.- 89 - Phu lc 1. Tnh xc sut (din tch) di ng cong chun: V d: Z=1 th AUC=0,3412 (34,1%) Z=1,5 th AUC=0,4332 (43,3%) Please purchase PDF Split-Merge on www.verypdf.com to remove this watermark.