Tài liệu Bài giảng thống kê y tế

C K .0 0 0 0 0 4 5 7 6 2 B A UXTNG CAN BO QUAN LY Y TE BO MON THONG KE - TIN HQC . I G I A N G A THONG KE Y TE (DUNG CHO BAC ST CHUYEN KHOA SAU DAI HQC CHUY£ n NGANH Y TE CONG C0NG) NHA XUAT BAN Y HOC ■ _ J T R l/d N G CAN BO QUAN LY Y TE Bo m on Thong ke - Tin hpc Bai giang THONG KE Y TE DUNG CHO BAC SY CHUYEN KHOA SAU DAI HOC CH UYEN NGANH Y T E CONG CONG NHA XUAT BAN Y HOC HA NOI - 1997 B a n bien soan: T hacsl : NGUYEN D l/C AN B dcsl : TRAN THI TUtJNG VY B dc si : TRAN THI LlTU Cit n h a n : PHAN VU D lfiM HANG Ldl NOI DAU Tap bai giang nay dugc bien soan voi muc tieu la trinh bay nhirng van de c a s a cua Thong ke y te, diroc ung dung trong Nganh. Doi tirgng cua tap bai giang chu yeu la cac hoc vien chuyen khoa cap mot cua Tnrong Can bo Quan ly Y te. Nhirng bai giang nay da ft nhidu dugc Bo mon Thong ke dua vao giang day nhi6u nam cho cac lop bac sy chuyen tu va chuyen khoa cap mot 6 trucmg nay. Vc noi dung khoa hoc, cac bai giang dugc xem xet. sira chua va b6 sung ciin than; c a c vi du va bai tap gSn ly luan vo'i thu'c ti6n cua Nganh Y te Viet Nam. Noi dung cua tap bai giang nay dugc chia thanh ba phan: • Phfin thir nhat: Thong ke mo ta. • Phan thu hai: Suy luan thong ke. • Ph^n thu' ba: Bo chi so thong ke y te co ban va phan loai thong ke Quoc te benh tat Ian tlur X. Tap bai giang gio'i thieu voi cac hgc vien cua Truong Can bo Quan ly Y te co su tham khao cua cac tai lieu: 1. Betty R. Kirkwood. Essentials Scientific Publications, 19S8 of Medical Statistics. Blackwell 2. Phirong phap nghien cuu khoa hoc y hoc, Hoc vien quan y, Nha xuat ban quan doi nhan dan, Ha Noi, 1995. 3. Dr. J.F . Osborn. Intensive Course in Medical Statistics. London School o f Hygiene and Tropical Medicine. Centre for Population Studies, Department o f Epidemiology and Population Sciences, 1991. 4. Phuong phap nghien cuu y te. To chii'c Y te The gioi, Khu vuc l ay Thai Binh Duong, Manila, 1992. Vien Vc sinh Dich td hgc. Ha Noi, 1993. 5. PGS, PTS. Pham Huy DCing. Chi so y te cho tuyen co so' xa, phuong. Khoa hgc y te cong cong Viet Nam, Truong dai hgc Y Ha Noi, 1990. va mot so tai lieu khac. Chung toi hy vgng rang voi noi dung nhu tren, tap bai giang nay co the: phu hop voi cac hgc vien chuyen khoa cap mot, chuyen nghanh y te cong cong cua Truong C B Q L Y T Ha Noi. Vi kien thiic va kinh nghiem con han che, chac chdn rang tap bai giang nay con nhi6u thieu sot. Chung toi rat mong nhan dugc nhung y kien phe binh va dong gop cua ban trong va ngoai nganh de tap bai giang ngay cang chat lugng hon v6 n6i dung, phong phu hon vt hinh thuc, da dang hon v6 cac loai bai tap . Xin chan thanh cam on. Ha Noi, ngay I thdng 7 nam 7 9 9 7 Tran Thi Liru THONG KE Y TE MUC TIEU MON HOC • • ♦ Trinh bay dudc cac so lieu nghien ctiu bAng bang thong ke, do thi, bieu do va cac chi so thong ke thich hdp. ♦ Kiem dinh dtfdc so trung binh, so' titdng doi bang test t , x ' tieu chuan hoa . ♦ Danh gia dudc mol lien he tUdng quan gitia cac hien tadng nghien cCtu . ♦ Trinh bay dudc viec phan loai thong ke quoc te" cac benh tat (sUa doi lan thuf mUdi) va cac qui tac hu6ng dan ma hoa tu vong . ♦ Phan tich dudc cac so lieu thong ke y te. ♦ Biet xay dung va to chiic cac nghien cCfu thong ke y te NOIDUNG Bai 1. Bai 2. Do thi, bieu do thong ke y te" Bai 3. Phep do vi tri va do bien thien Cac phan phoi tan so - Trung binh, trung vi, mode - Do bien thien, phudng sai, do lech tieu chuan, he so bien thien Bai 4. Xac suat, cac luat phan phoi xac suat cua dai ludng ngau nhien - Bien co* ngau nhien - khai niem xac suat - Dinh nghla co dien ve xac suat, dinh nghia thong ke ve xac suat - Phan loai sU kien ngau nhien - Phan phoi nhi thtic, phan phoi poisson, phan phoi chu^n - Lien he giuta ba luat phan phoi - Ung dung va tAm quan trong cua phan phoi chu&n. Bai 5. Cac phan phoi mau va cac khoang tin cay Bai Bai Bai Bai 6. Cac phep kiem dinh co y nghia 7. Kiem dinh gia thuyet thong ke 8. Lien he tUdng quan va hoi qui 9. Phudng phap tieu chuftn hoa - Phudng phap true tiep - Phudng phap gian tiep Bai 10. Thong ke tinh hinh mac benh cua nhan dan Bai 11. Bo chi so' thong ke y te cd ban Phu luc. Phan loai thong ke quoc te cac benh tat va cac qui t&c hu6ng d^n ma hoa tii vong. 1 GIClI THIEU Thong ke y te la mot mon khoa hoc ting dung, ngUdi ta da svt dung cac phudng phap thong ke y te vao cong tac nghien ctiu y te. No la mot trong nhQng mon khoa hoc cd sd c&n thiet cho viec dieu tra, danh gia cac van de trong y te : Tit sinh ly hoc te bao den nghien ciiu stic khoe cong dong...v.v. Mac du tvf lau sinh hoc da ufng dung cac phudng phap cua khoa hoc thong ke mot cach rong rai, nhung chi trong mot vai nam gan day, thong ke y te mdi thtfc sU la van de noi com . Su dung thong ke y te doi hoi phai dudc dao tao kien thtic ca ve toan hoc va y hoc. Tuy nhien de hieu va ap dung dudc cac phudng phap thong ke cd ban doi hoi phai biet mot it toan hoc dang ke . L6p hoc chuyen khoa mot cua TrUdng Can bo Quan ly Y te khong can biet trudc kien thtic toan hoc hoac thong ke, ma mot it kien thiic do neu ckn se dudc gi6i thieu trong qua trinh hoc tap. Cac phudng phap thorig ke cd ban dudc chia thanh hai ph^n chinh : Trong ph^n thti nhat chung ta co mot tap hdp so' lieu dudc quan sat va can tom tat chung, xay dilng chung thanh cac bang qua do co the hieu dudc de dang va mo ta dudc nhflng dac trUng cua chung. Cac phudng phap sik dung cho muc dich nay thUdng dudc goi la thong ke mo ta. NgUdc l a i , chung ta co the tong quat hoa cac thong tin tren m lu quan sat. Vi du: Co the chung ta muon ket luan rang , nhin chung dung thuoc A tot hdn dung thuoc B cho nhiing benh nhan co chan doan dac biet , vi vay chung ta phai sU dung cac phep thu co y nghia va cac khoang tin cay. Cac phudng phap sU dung cho muc dich nay dudc goi la phudng phap suy luan thong ke. Cac nha nghien cilu sinh y hoc, cac bac sy lam cong tac quan ly y te va y te cong cong , cac nha chilc trach c&n lam gi ? chdc r&ng ho c4n mot it thdi gian de hoc nhflng tu tUdng cd ban cua thong ke , muc dich la hieu day du y 2 nghia, cach trinh bay va cac ky hieu thong ke nhu: p, t, X’ , r ... v.v. va cac th u at ngiJ chuyen mon khac ma ho se tim thay trong cac bao cao cung nhvt trong cac tap chi chuyen nganh. 2 B a i l . CAC PHAN PHOI TAN SO MUC TIEU Hoan thanh bai 1 hoc vien co the: • Phan loai cac bien dinh tinh , dinh ltfdng, rdi rac, lien tuc • Chia khoang bien thien cua mot day so' lieu thanh cac khoang cach to, va chi ro cac gia tri nao nam d khoang cach to nao. • Cho mot tap hdp lieu ban d&u, xay dung phan phoi t&n so ,t&n suat va tan suat tich luy • Ve bieu do phan phoi tin so' co khoang cach to blng nhau va khong bang nhau • Ve bieu do tin suat tich luy, va xac dinh trung vi Trong mot cuoc dieu tra thong ke, so' lieu thu th&p thudng chua dudc sap xep, cho ta mot hinh anh hon don, kho nhin , kho rut ra qui luat cua hien tUdng nghien ciiu. De trinh bay cac ket qua nghien ciiu ngUdi ta thudng dung 3 hinh thtfc: bang, do thi hoac cac tham so' dac trung. De bieu di§n cac so lieu ro hdn c&n s£p xep chung theo thti tu, thudng tti nho den 16n. Nhu vay ta se thay dudc tinh chat phan phoi va tinh quy luat cua chung, dong thdi cung biet dudc do bien thien do la hieu so cua gia tri 16n nhat va gia tri nho nhat cua day. Neu bang so' lieu chila toan bo day so' se rat kho nhin. Thong thudng ngUdi ta tap hdp 2 hoac nhieu gia tri quan sat vao mot to. 1. Muc dich va y nghia cua phan to thong ke. - La can ci'i vao mot hoac mot so' dac tinh de phan chia cac ddn vi cua hien tUdng nghien ciiu thanh cac to co tinh chat khac nhau. - La sap xep co he thong cac so lieu ban d&u de thay ro thanh ph&n, cd cau nhutng net gio'ng nhau, khac nhau cua hien tUdng nghien ciiu. - Bu6c d&u chuan bi cho tinh toan phan tich sau nay 2. Mot vai y nghia. - To: La so lifdng cac gia tri quan sat nam trong mot gidi han nhat dinh. - Gi6i han to: Do tri so' 16n nhat va tri so be nhat cua to tao nen. - Tri so giuta: So' trung binh cong cua 2 gicfi han to. 3 - Khoang cach to (k) ( con ky hieu la h ,d ......) la tri so cua 2 tri so giCta lien tiep nhau. < . . „ r - To md: La to bao gom cac gia tri nam du6i hoac tren mot gia tri gidi han. Vi du: Tren 100 tuoi, du<3i 18 tuoi....... 3. Dac tinh phan to ( con goi la dac tinh nghien ciifu). Moi don vi nghien ciiu co nhving dac diem (dau hieu) noi len mat liidng hay mat chat cua ddn vi do. Nhiing dac diem lien quan den muc dich nghien ciiu goi la dac tinh nghien ciiu. Co 2 loai dac tinh nghien ciiu: a. Dac tinh dinh tinh: La nhiing dac tinh nhan thiic bang giac quan. chung dac trifng cho chat lUdng, co tinh ch a t mieu ta , dien dat bang ldi noi, chut viet (vi du: Gi6i tinh, loai benh, nghe nghiep.......) , b. Dac tinh dinh-luc/ng: La nhufng dac tinh bieu hien bang nhiing con so' nhu can nang , chieu cao, huyet ap........ ) la nhiing dfic tfnh co the dem dudc hoac do dudc. 4. So to va khoang cach to. Tuy tfnh chat cua dac tinh nghien ciiu va muc dich nghien ciiu. a. Dac tinh dinh tinh: Neu the hien bang 2 tinh huong (vi du gi6i tinh nam , mi) hai bieu hien doi lap (dac tinh luan phien) thi chi co hai to. Neu the hien bang nhieu tinh huong (vi du nhu ket qua dieu tri) thi co nhieu to. Moi loai hinh la mot to hoac ghep nhieu to nho giong nhau thanh mot to 16n. Tu: bang so lieu ban dau ta xay diing bang phan Xi n, phoi thuc nghiem hay con goi la bang phan phoi tan so' Xi ni gom 2 cot cd ban: X, n2 Xk nk Cong In , = n - Cot 1: Ghi cac dac tinh nghien ciiu ky hieu la Xj neu la dac tinh dinh lUdng v6i i= l,2 ,3 ........ ,k - Cot 2 : Ghi so' lan xuat hien dac tinh nghien ciiu, con goi la tan so, ky hieu la n, (i= l,2 ,3 ............,k) 4 Tong so cac t in so" quan sat bang tong so ddn vi nghien ciiu (ky hieu la n) Snj = n (E : ky hieu cua tong ) b. D ac tinh d in h lUQng: - Dac tinh dinh lufdng rdi rac : Bieu hien bang so" nguyen ( so" benh nhan, so cd sd dieu tri....... ). Ta ghi cac gia tri x; theo chieu tang hoac giam din vao bang phan phoi t in so, roi ghi tan so xuat hien cua moi gia tri x, (tiic la cac tin so n, . Khi sU bien thien ve mat lildng giuta cac ddn vi it, co vai tri so, thi moi tri so hinh thanh mot to (so con trong gia dinh) Khi cac tri so bien thien nhieu, so to se qua nhieu, can phai phan to co khoang cach to, bao gom mot pham vi cac gia tri : Co gi6i han du6i cua to la tri so" nho nhat va gidi han tren cua to la tri so' 16n nhat cua to do. Neu mot gia tri rdi vao gidi han tren va cung la gidi han dudi cua to sau thi quy udc xep vao to sau. - Dac tinh dinh ltfdng lien tuc : Bieu hien bang so' nguyen, so' thap phan. Thudng ta phan to co khoang cach to deu ( k = 1, 2, 3, 5, 10, 20......). De tien viec tinh toan, khoang cach to nen la mot so le, de tri so' giiia la so nguyen. Co the phan to v6i khoang cach to khong deu tuy muc dich nghien ciiu (vi du : Bien tuoi trong dieu tra dan so...) Phan to theo khoang cach to deu thi tri so khoang cach to dudc xac dinh theo cong thiic : X m —Xm xM : Tri so' 16n nhat trong day so lieu. xm : Tri so' nho nhat trong day so' lieu. T : So' to dii dinh chia Nen chon cach phan to do'i xiing : Tri so' co tan so 16n nha't d g in giuta phan phoi va khong co to trong (ns = 0 ) Phan nhoi tan so . Ddn gian la mot bang ghi cac gia tri co the la'y bdi mot bien va ghi tan so ling vdi moi gia tri da diidc quan sat. 5 B a n g 1: Phan phoi ket qua xet nghiem ddm , bien dinh tinh lay gia tri: - Soi lam am tinh - Cay am tinh - Soi lam am tinh, khong cay - Soi lam hoac cay dUdng tinh Streptomycin T in so Soi lam am , cay am tinh T in suat(%) Khong Streptomycin T in so T in suat(%) 141 45,0 117 41,8 Soi lam am tinh, khong cay 90 28,8 67 23,9 Soi lam hoac cay dUdng tinh 82 26,2 96 34,3 Tong cong 313 100,0 280 100,0 Cac ket qua khong biet 12 17 325 297 B a n g 2: Phan phoi so tre em nam trong cac gia dinh co 8 con So' tre nam 6 So gia dinh T in suat(%) 0 161 0,4 1 1152 3,0 2 3951 10,3 3 7603 19,7 4 10236 26,7 5 8948 22,1 6 4948 12,8 7 1655 4,3 8 264 0,7 38495 100,0 B a n g 3: Phan phoi cac ton thudng gay nen bdi virus d§u mua trong mang triing So ton thudng T in so (so mang) 0_ 1 10_ 6 20_ 14 30_ 14 40_ 17 50_ 8 60_ 9 70_ 3 80_ 6 90_ 1 100_ 0 110 119 1 Tong cong 80 B an g 4: Phan phoi tin so' co khoang cach tuoi cua 1375 benh nhan nam m ic ung thu phoi. T in so T in suat 25_ 17 1,2 1,2 35_ 116 8,5 9,7 45_ 493 36,3 46,6 55_ 545 40,2 86,2 65_74 186 13,7 99,9 Tong cong 1357 99,9 Tuoi T in suat tich luy Co vai phudng phap xay dung phan phoi tin so tti so' lieu ban diu : 7 1 CO 4 6 2 2 2 5 1 2 2 CO B a n g 5: Dem khac ciu trung trong mau d duoi cua cac con chuot 2 4 1 1 1 2 6 7 3 5 5 2 2 5 5 6 2 5 1 3 1 9 1 1 2 2 4 1 1 1 2 2 1 2 1 0 3 3 4 3 1 to CO 4 4 1 4 6 4 2 5 4 5 4 5 5 6 2 1 0 1 5 5 2 2 6 6 2 CO 4 CO 4 4 4 6 CO 5 3 2 6 4 3 3 7 4 2 6 1 3 1 5 3 3 6 8 2 0 1 0 1 5 2 2 1 9 1 1 1 5 3 1 3 6 2 3 5 Trong vi du nay chung ta se phan thanh 10 16p hoac ( 10 to), cac to danh so tu: 0,1,2 3...9 xem qua so' lieu mot lin ,phan phoi cac quan sat vao cac to va danh dau 0 //// 4 7 ^ 1 2 iW - 3 7 ^ tW 7 ^ 7 ^ 4 tW // 27 // 27 7 ^ 20 / 16 // 17 5 im - 7 ^ 6 tW tW 7 // 2 8 / 1 9 // 2 To ta i 8 Frequency Tally Count // 12 128 B an g 6 : Do day cua da (mm) do d diem giiia cd tam dau cho 121 nam gicii 11.4 15.3 9.1 18.4 10.9 4.7 9.6 20.6 10.4 20.5 22.4 14.3 11.7 11.4 12.7 18.2 15.1 14.6 25.3 11.5 13.2 7.9 12.6 13.9 1.8 11.4 27.3 16.3 13.9 13.2 11.9 20.0 13.2 9.4 18.9 10.7 14.8 17.8 10.8 16.0 15.7 17.7 13.5 11.5 11.1 9.6 15.1 13.6 13.6 8.6 6.9 19.1 18.7 10.1 16.0 20.4 7.9 16.6 18.5 16.2 17.4 18.8 12.6 22.0 9.6 11.1 15.7 23.7 13.3 4.9 8.3 20.1 15.5 23.1 10.2 10.7 15.8 17.6 21.3 16.2 14.9 9.9 9.1 9.9 9.8 8.6 11.8 9.3 14.8 17.3 9.5 13.6 12.4 9.5 14.3 25.7 12.9 22.7 12.1 10.7 16.8 11.3 11.3 11.4 5.9 10.7 14.6 19.8 25.5 7.7 18.4 7.9 7.6 23.3 9.6 8.4 9.0 30.1 10.4 8.1 12.5 B a n g 7: Bang phan phoi do day cua da Do day cua da 4681012141618202224262830-31,9 Tong cong Tan so 3 6 19 23 17 14 13 9 6 6 3 1 0 1 Tan suat(%) 2,5 5,0 15,7 19,0 14,0 11,6 10,7 7,4 5,0 5,0 2,5 0,8 T in su it tich luy 2,5 7,5 23,2 42,2 56,2 6,8 78,5 85,9 90,9 95,9 98,4 99,2 0,0 0,8 100,0 121 100,0 99,2 9 B an g 6 : Do day cua da (mm) do 0 diem giiia cd tam dau cho 121 nam gicii 11.4 15.3 9.1 18.4 10.9 4.7 9.6 20.6 10.4 20.5 22.4 14.3 11.7 11.4 12.7 18.2 15.1 14.6 25.3 11.5 13.2 7.9 12.6 13.9 1.8 11.4 27.3 16.3 13.9 13.2 11.9 20.0 13.2 9.4 18.9 10.7 14.8 17.8 10.8 16.0 15.7 17.7 13.5 11.5 11.1 9.6 15.1 13.6 13.6 8.6 6.9 19.1 18.7 10.1 16.0 20.4 7.9 16.6 18.5 16.2 17.4 18.8 12.6 22.0 9.6 11.1 15.7 23.7 13.3 4.9 8.3 20.1 15.5 23.1 10.2 10.7 15.8 17.6 21.3 16.2 14.9 9.9 9.1 9.9 9.8 8.6 11.8 9.3 14.8 17.3 9.5 13.6 12.4 9.5 14.3 25.7 12.9 22.7 12.1 10.7 16.8 11.3 11.3 11.4 5.9 10.7 14.6 19.8 25.5 7.7 18.4 7.9 7.6 23.3 9.6 8.4 9.0 30.1 10.4 8.1 12.5 B an g 7: Bang phan phoi do day cua da Do day cua da 4681012141618202224262830-31,9 Tong cong Tan so Tan suat(%) T^n suat tich luy 3 6 19 23 17 14 13 9 6 6 3 1 2,5 5,0 15,7 19,0 14,0 11,6 10,7 7,4 5,0 5,0 2,5 0 0,0 0,8 100,0 121 100,0 1 0,8 2,5 7,5 23,2 42,2 56,2 6,8 78,5 85,9 90,9 95,9 98,4 99,2 99,2 9 Bang 7: La bang phan phoi co khoang cach to bang nhau . Day la bien dinh lUdng lien tuc . Khoang cach 20_ la bao gom cac quan sat tit 20,0 den 21,9 va tri so' giiia cua khoang cach nay la 20,95. Do thi so' 1 la phan phoi tin suat tich luy. Do thi so' 2 la mot to chiic do bieu diln cac phan phoi tin so'. B an g 8: Phan phoi theo nhom tuoi cua nhiing ngtfdi khong co rang (chie'c rang cuoi cung cua ho da mat) Tuoi So ngUdi Khoang cach to (n i) n, 00 k, 11-15 1 5 0,02 16-19 7 4 1,75 20-24 21 5 4,20 25-29 35 5 7,00 30-34 40 5 8,00 35-44 58 10 5,80 45-54 28 10 2,80 55-74 10 10 0,50 Trong trUdng hdp phan to co khoang cach to khong bang nhau ta phai chu y tinh chieu cao cua kho'i hinh chut nhat khi ve do thi . Chieu cao cua kho'i do thi la ty so' giiia t&n so' v6i tri so' khoang cach to. Trung vi 13,0mm 10 18 % tong so trong m6i khoang cach So 2 Do thi tan so cac do day cua da 16 14 12 10 8 6 .. 4 .. 2 .. 0 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Cac do day cua da (mm) 8 7 .. So trung binh theo nSm cua do tuoi So 3 Do thi t in so cua do tuoi mat chiec r&ng cuoi cung 6 .. 5 -4 -3 -2 -1 -0 10 i 15 20 r~ 25 30 ------ 1 ■ 35 40 45 i------ 1— i------ 1------r 50 55 60 65 70 75 Do tuoi mat chiec rang cuoi cung 11 Bai tap 1. Xay dung bang phan phoi tin so theo tuoi cua 16p chuyen khoa mot sau: Nam sinh Nam sinh Nam sinh Nam sinh 1953 1963 1962 1958 1957 1965 1957 1954 1965 1957 1950 1958 1955 1960 1964 1950 1959 1955 1964 1949 2. Trong mot cuoc dieu tra 54 phu nii co thai tai benh vien X dudc phong van tien su ve tuoi va lan de cua ho ket qua du6i day : S tt Tuoi S o la n de Stt Tuoi So' lan de Stt Tuoi S o lan de 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 20 30 33 27 35 22 31 25 40 23 32 19 37 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 28 38 25 22 21 27 35 21 31 20 18 36 28 30 18 34 17 18 36 19 0 2 1 0 0 2 0 0 1 0 0 1 4 0 0 2 0 1 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 23 24 30 25 29 30 17 18 18 31 27 32 18 0 0 1 1 1 0 0 0 4 0 0 0 3 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 3 1 0 5 1 1 0 0 28 29 33 17 Hay xay dting bang phan phoi tan so theo tuoi va lln de, - Lan de: 0 lln , 1, va 2 lan trd len - T u o i: < 30 va tut 30 trd len 23 36 28 25 23 37 Bai 2. DO T H I. BIEU DO THONG KE Y TE 1. Y nghia , tac dung. - Do thi thong ke bao gom cac con so, hinh ve, dUdng net hinh hoc, mau sac de trinh bay khai quat, co ti'nh ch&'t quy u6c cac tai lieu thong ke nham so sanh, doi chieu , phan tich cac moi quan he, tim ra cac quy luat dac trUng so' liidng cua hien tUdng nghien ciiu. - Dung phudng phap do thi doi hoi it cong doc, nhan thiic de , nhanh, co tinh chat quin chung cao , hap dan, sinh dong, la phudng tien bieu dUdng tot. 2. Qui tac chung xay dvfng do thi thong ke. Yeu clu cua do thi phai chi'nh xac, de hieu, de xem, trinh bay my thuat. - Qui mo : To, nho tuy muc dich su dung. Ty le chieu cao , chieu dai la 1/1,5 hoac 3/3,5. . - Ky hieu hinh hoc : La cac cham , dUdng thang, dUdng cong, cot, hinh vuong, hinh chii nhat, hinh tron ..... - He toa do vuong goc : True hoanh bieu thi cac dac tfnh nghien ciiu. True tung ghi cac t i n so' (n ; ) hoac cac t in suat ( co,) - Thang , ty le xich: Thang dUdng th&ng, thang dUdng cong, thang co khoang cach deu dan hoac khong deu (thang logarit) - P h ln giai thich: Ten do thi, cac con so' ky hieu quy u6c. 3. Cac loai do thi thong ke. a. Do thi dieting day (ditdng g a p kh u c) : Bieu dien tinh hinh phat trien cua hien tUdng nghien ciiu. Tren trUdng cua he thong toa do vuong goc ta ghi cac gia tri cua x, hoac cac dac ti'nh nghien ciiu tiidng ling vdi true hoanh va cac tin so' hoac tin suat tUdng ling v6i true tung. Noi cac diem nay lai v6i nhau ta se dudc dUdng bieu dien. b. Do thi h in h cot: La nhiing hinh chii nhat xep lien tiep nhau (con goi la to chiic do ) . Day cac hinh chii nhat bang be rong cua cac to. Chieu cao bang tin so hoac tin suat tUdng ting. Day cua cac hinh chii nhat blng nhau khi khoang cach to blng nhau. 7 8G 13 Khi khoang cach to khong bang nhau thi chieu cao cua cac hinh chii nhat bang : h, : Chieu cao cua to i nj : Tan so' cua to i k, : Khoang cach cua to i Do thi hinh cot bieu hien cac chi tieu cUdng do noi len mtic do pho bien cua hien tUdng nghien ctiu, dung cho cac phan phoi co ghep to. c. Do thi h in h trd n : Bieu hien ket cau cua hien tUdng nghien ciiu (thudng dung de mieu ta cac dac tfnh dinh tinh bieu hien bang phan tram) ngUdi ta thudng doi phan tram thanh do, cii 1% = 3" 6 (chu vi hoac dien tich hinh tron la 360 0 ). Chu vi hinh tron dtfdc chia ty le vcii tinh hinh phan phoi cua hien tUdng nghien ciiu. 14