bài giảng thống kê y tế phần 1

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

C K 0 0 0 0 0 4 5 7 6 2 UXTNG CAN BO QUAN LY Y T E

BO MON THONG KE - TIN HQC

A THONG KE Y TE

(DUNG CHO BAC ST CHUYEN KHOA SAU DAI HQC

NHA X U A T BAN Y HOC■ _ J

T R l/d N G CAN BO QUAN LY Y TE

Bo m on T hong 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 h a c s l : NGUYEN D l/C AN

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 ca

sa 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 of Medical Statistics Blackwell Scientific Publications, 19S8

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.

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 Cac phan phoi tan so

Bai 2 Do thi, bieu do thong ke y te"

Bai 3 Phep do vi tri va do bien thien

- 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 6 Cac phep kiem dinh co y nghia

Bai 7 Kiem dinh gia thuyet thong ke

Bai 8 Lien he tUdng quan va hoi qui

Bai 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 thdigian 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 lientiep 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 n i

- 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, Xk nk

con goi la tan so, ky hieu la n, (i= l,2 ,3 ,k) Cong I n , = n

4

Tong so cac tin 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 tin 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 an 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 Khong Streptomycin

T in so T in suat(%) T in so T in suat(%)

Cac ket qua khong biet 12 17

B an g 2: Phan phoi so tre em nam trong cac gia dinh co 8 con

So' tre nam So gia dinh T in suat(%)

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)

8

93

6

101

B an g 5: Dem khac ciu trung trong mau d duoi cua cac con chuot

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 22.414.3 11.7 11.4 12.7 18.2 15.1 14.6 25.3 11.5 13.2 7.912.6 13.9 1.8 11.4 27.3 16.3 13.9 13.2 11.9 20.0 13.29.4 18.9 10.7 14.8 17.8 10.8 16.0 15.7 17.7 13.5 11.511.1 9.6 15.1 13.6 13.6 8.6 6.9 19.1 18.7 10.1 16.020.4 7.9 16.6 18.5 16.2 17.4 18.8 12.6 22.0 9.6 11.115.7 23.7 13.3 4.9 8.3 20.1 15.5 23.1 10.2 10.7 15.817.6 21.3 16.2 14.9 9.9 9.1 9.9 9.8 8.6 11.8 9.314.8 17.3 9.5 13.6 12.4 9.5 14.3 25.7 12.9 22.7 12.110.7 16.8 11.3 11.3 11.4 5.9 10.7 14.6 19.8 25.5 7.718.4 7.9 7.6 23.3 9.6 8.4 10.4 8.1 12.5 9.0 30.1

B a n g 7: Bang phan phoi do day cua da

Do day cua da Tan so Tan suat(%) T in su it tich luy

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 22.414.3 11.7 11.4 12.7 18.2 15.1 14.6 25.3 11.5 13.2 7.912.6 13.9 1.8 11.4 27.3 16.3 13.9 13.2 11.9 20.0 13.29.4 18.9 10.7 14.8 17.8 10.8 16.0 15.7 17.7 13.5 11.511.1 9.6 15.1 13.6 13.6 8.6 6.9 19.1 18.7 10.1 16.020.4 7.9 16.6 18.5 16.2 17.4 18.8 12.6 22.0 9.6 11.115.7 23.7 13.3 4.9 8.3 20.1 15.5 23.1 10.2 10.7 15.817.6 21.3 16.2 14.9 9.9 9.1 9.9 9.8 8.6 11.8 9.314.8 17.3 9.5 13.6 12.4 9.5 14.3 25.7 12.9 22.7 12.110.7 16.8 11.3 11.3 11.4 5.9 10.7 14.6 19.8 25.5 7.718.4 7.9 7.6 23.3 9.6 8.4 10.4 8.1 12.5 9.0 30.1

B an g 7: Bang phan phoi do day cua da

Do day cua da Tan so Tan suat(%) T^n suat tich luy

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)

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

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

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

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.

PHUONG PHAP TRINH BAY V A DIEN GIAI C>

LIEN Q U A N DEN SUC KHOE

BANG DO THI VA BIEU DO

Mac du khong co nhiing quy tac nghiem ngat va i cach xay dung bang, song cung co mot so nguyen tac chi nhan nhu chuEin

1 Bang phai cang don gian cang tot.

Lam hai hoac ba bang nho con tot hcin la mot bang l<3n <tiet hoac bien so Thudng ba bien so la so toi da (*o the doc du<

2 Bang phai de hieu.

a Cac ma so, chu viet tat hoac ky hieu phai co giai t] thich 0 cuoi trang

b Moi hang va moi cot phai ghi tieu de chinh xac va r

c Cac ddn vi do lUdng dac biet dung cho so lieu phai c

d Tieu de phai ro rang, chinh xac va dung vao van de Cai gi" Khi nao? d dau?

3 Thong thifcfng dau de phai cach phan than ban mot

Hoac khoang trong Trong nhiing bang nho, co the

dUdng ke doc de phan cach cac cotv

4 Neu cac so lieu khong phai la goc thi phai cho bi chu thich.

5 Vi du dac trifng.

Hoc van cua cha So trUdng hdp de songTot nghiep cao hoc

Dudi 12 nam hoc

50.68431.774

Nguon: "Thong ke sinh tit cua my" 1968 Tap ltr81

b Bang 1 co the md rong ra de bao gom phan loai dudi nGa, nhu ndi de va ngUdi dd de, trong bang 2

B an g 2

Phan loai cac trtfdng hop de song theo I19C van cua ngvfofi cha, nOi d e

va ngtfdi dof de, bat ky bang nao, 1968.

Trong benh vien

Ngoai benh vienTot nghiep cao hoc 46.606 3014 910

Dudi 12 nam hoc 14.334 3094 13.930

Nguon: "Thong ke sinh tit cua My", 1968 Tap l,tr81.

c Viec tom tat tong ket so lieu se difdc xuc tien va ddn gian hoa bang cach chuan bi trudc mot bang chu yeu Trong bang nay, tat ca cac so lieu san co phai dudc xep loai dly du Khi viec xep loai dly du da xong, cac so lieu lien quan den

mot bien so duy nhat hoac den bat cti phoi hdp nao cua bien so' cung co the co dudc

ma khong phai clu vien den cac so lieu goc

Tuf khuon kho bang chu yeu nhu bang 3, chung ta co the xac dinh dudc bao nhieu ngUdi thanh thi (A), bao nhieu ngUdi nam gidi (B) va bao nhieu nam gidi

thanh pho d nhom tuoi qui dinh (C) da dudc nhap vien, v.v

B an g 3

So ngtfdi vao bat cii benh vien nao trong hai nam 1968, xep loai theo

tuoi, ndi d va gidi tinh

16

Tuoi ti'nh T h anh thi Nong thon Cong

theo nam Nam m Cong Nam m Cong Nam Nut Cong

Co nhieu kieu do thi khac nhau, trong do co vai kieu la toa do vuong goc, toa

do cUc, cac kieu v6i muc dich dac biet (3 chieu) v.v Chung ta chi han che trong do

do thi co toa do vuong goc

A KHAI NIEM CHUNG

Do thi co toa do vuong goc la do thi gom hai true dudng vuong goc vdi nhau Tren moi true dudng co mot thang bac chia do de nhan dang Hinh 1 gidi thieu cau true chung cua do thi toa do vuong goc Thong thudng, bien so an dinh cua true x

dudc coi la bien so doc lap (phudng phap phan loai), trong khi bien so an dinh cho true y la bien so phu thuoc (tan so) Vi the khi ve do thi, chung ta danh dau su

thay doi cua v theo x

H inh I:

Do Thi D ai CtfcJng

17

PHUONG PHAP PHAN LOAI

B NGUYEN TAC CHUNG

Khi do thi dudc ve mot cach dung dan, chung cho phep ngUdi doc nhanh chong nAm dudc toan bo so lieu Mot vai net quan trong nhat cua do thi la:

1 Do thi quan trong nhat la do thi co hieu qua nhat Khong dung them dtfdng ve hoac ky hieu trong mot do thi ma mat co the de dang theo doi dudc

2 Do thi phai de hieu, khong giai thich them

3 Tieu de co dat tren dudi do thi

A. Khi co hdn mot bien so dudc trinh bay tren do thi, moi bien so phai dudc phan biet ro rang bang cac ghi chu hoac cac ky hieu

5: Khong ve them dudng toa do ngoai cai can thiet de de nhin thay

6 Cac dudng cua ban than do thi phai dam hdn cac dudng toa do khac

7 Thudng thudng, tin so' dudc bieu thi tren thang do cua true tung va phudng phap phan loai tren thang do cua true hoanh

8 Tren thang do so' hoc, cac ltfdng gia bang nhau tren thang de phai dai dien cho cac ddn vi bang nhau

9 Khoang chia tren thang do phai dudc vach ra ro rang cung nhu cac ddn vi trong do thang do dudc phan chia ra

C NHUNG VI DU DAC TRUNG

1 Do thi hinh day theo thang so hoc.

La do thi trong do mot quang bang nhau bieu thi mot so ltfdng bang nhau bat cii d cho nao tren true, nhung khong nhat thiet phai blng nhau giiia cac true C ln phai chu y trong viec lua chon hoac dung nhung khoang each bang nhau tren ea 2 true hoac nhiing khoang each rong tren true x lien quan vdi true y hoac ngUdc lai Cac thang do phai dudc xac dinh the nao de san pham cuoi eung phai dep mat Mot thang do dirt quang co the dUdc dung vdi mot do thi day, nhung neu dung, phai cln

than de khong giai thich sai llm do thi Hinh 2 la mot wi du do thi hinh day theo thang so hoc.

18

Ty le rubeon difote bao cao trong 13 ky 4 tuan d My nam 1968

H inh 2

Thai ky ket thuc

Nguon: Dctn vi g iam sat Rubeon.

2 Do thi hinh day theo thang ban logarit.

Do thi hinh day theo thang ban logarit cua ddn vi, trong do true kia dudc do ltfdng theo don vi so' hoc Do thi nay co l'ch 6 cho khi xem xet chuoi so' lieu theo mot giai doan thdi gian, chung ta thudng chu y den su thay doi tUdng doi (hoac ty le thay doi) hdn la cai tuyet doi (hoac so' luong hien tai) Ldi diem cua do thi ban logarit la:

a Duong thang chi mot ty le bien doi hang dinh,

b Do doc chi ty le tang len hoac giam xuo'ng,

c Hai dudng (hoac nhieu hdn) theo cac dtfdng song song cho thay cac ty le gia tang (hoac thuyen giam) nhu nhau

Minh hoa cho do thi nay dtfdc trinh bay d hinh 3

19

H inh 3

Bao cao hang nam ve ty le m ac mdi, ty le chet va ty so chet

tren mac benh bach hau, My 1920-1968

N am Nguon: Dcfn vi g iam sat bach hau

3 Gian do •

Gian do la do thi chi dung de trinh bay sU phan bo” tan so cua cac so' lieu dinh liidng Khong co khoang cach giiia cac vach (thtfdng lien quan den cac vach ng&n) tren gian do Khong dudc nhlm lan do thi nay vdi bieu do hinh cot co khoang cach giiia cac

o Khong dudc sU dung thang do diit quang trong gian do vi gian do mieu ta toan bo dien tich dtfdng cong Do dac diem nay, loai gian do ddn gian nhat de xay dung se la mot do thi cd cac khoang cach bo' tri deu nhau nhu trinh bay trong hinh 4

20

Cac triicfng hofp benh phat ban, trifotag cap hai thanh pho Sample, tit 22 thang 2 den thang 3, 1970

Mot gian do vdi cac khoang cach khong bang nhau doi hoi phai suy nghi

nhieu hdn khi xay dung vi khai niem dien tich toan bo Hinh 5 da dudc chon de

minh hoa trUdng hdp nay.

Noi chung, tren mot gian do, chi dudc trinh bay mot loai so lieu; tuy nhien, trong llnh vUc y te cong cong, h lu nhu thudng dung gian do de trinh bay so lieu tru'dng hdp benh - tu vong, n am - nU, v.v

21

So trtfcfng hofp uon van da diftfc bao cao theo cac nhom 5 tuoi, My, 1968

so-Neu muon trinh b ly hai loai so' lieu trd len theo mot phan phoi tan so' thi cac

so lieu nen dtfdc trinh bay dtfdi dang mot da giac tan so' Da giac tan so' dtfdc xay dung ttf gian do nghia la nhiing diem giiia cac khoang cach phan loai dtfdc noi vdi nhau bang mot dtfdng thing Dieu nay dtfdc minh hoa trong hinh 6

Vi da giac tin so dtfdc xay dtfng tti gian do, nen cac quy tac lien quan den dien tich dudi dtfdng cong, cd cac khoang cach deu hoac khong deu nhau, se dtfdc giu' vUng Vi vay, can thiet phai minh hoa cach lam dd trong khai niem nay dtfdc gitf lai Da giac tin so phai dtfdc khep lai de mieu ta dien tich Cach khep lai dudc thUc hien bang cach noi diem dlu tien va diem cuo'i vdi nen cua do thi Dien tich trong da giac tin so phai gin bln g dien tich cd trong gian do Hinh 7 cho thay phudng phap khep dung mot da giac tin so Hinh 8 cho thay phudng phap khep sai

Trong hinh 7 dien tich A phai la bo phan cua gian dd neu cac so lieu dtfdc len so' do bang phtfdng phap nay D§ bu cho dien tich nay nlm ngoai da giac, diem ('

22

dtfdc noi vdi dtfdng day bang cach de dien tich B dtfdc gdn bang dien tich A Hinh 8 minh hoa phtfdng phap khep da giac tan so khong dung, vi toan bo dien tich D bi

bo sot va khong co cho bu vao dien tich do

Trong hinh 9 la da giac tan so' co nhiing khoang cach phan loai deu nhau Them vao do, hinh 10 minh hoc mot da giac tan so co cac khoang cach phan loai khong deu nhau

Hinh 11 cho thay mot da giac ta n so minh hoa cho 3 so lieu

So trvfdng hdp nghi cum hang tuan, thanh pho Sample, 1970

H inh 11

So trvtfdng hcfp viem nao dufcfc bao cao hang thang,

theo can nguyen benh, My, 1965

Tha ng

5 Do thi phan tan.

Do thi phan tan la do thi dac biet, no co ich vi vach ra nhiing moi lien quan hoac ket hdp giiia 2 bien so Trong loai do thi nay nhieu day so lieu cap doi diidc ve len tren cung mot do thi Mo hinh ve len bang nhiing diem cM'm, bieu thi mot moi lien he neu co Neu cac diem cham co chieu htfcing theo mot dtfdng th in g, thi moi lien he co ban chat tuyen tinh Neu mo hinh dung la mot stf phan tan cac diem cham, thi chieu htfdng nay gdi cho thay kha nang khong co moi lien he nao Hinh

12 cho thay mot do thi phan tan

25

Thuf nghiem ngoai da bang histoplasmin so sanh cac quan sat cua

2 ngvfofi doc theo 51 doi tifofng Green Wood, nam Carolina, 1963

A BIEU DO DUA TREN CHIEU DAI

Hai trong so'bieu do quan trong trong loai nay la bieu do hinh cot va hoat do

1 Bieu do hinh cot.

Bieu do hinh cot co nhiing o, co cung chieu rong (khong gio'ng nhuf gian do), co khoang cach giQa cac cot (cung khong giong nhu gian do) Loai bieu do nay thich hdp mot cach ly ttfdng de trinh bay cac so lieu so sanh Cac cot co the xep theo hang

26

ngang cung nhu hang doc (nhu minh hoa d hinh 13 va 14) Tot nhat la xep cac cot theo thU tu hoac tang len, hoac giam di de de doc Khong bao gid dudc dung thang

do dUt quang v6i bieu do hinh cot vi dieu do se dan den dieu giai sai l&m Cac cotphai co nhan d phla du6i chU khong phai cf giUa bieu do, vi nhu vay se lam cho bieu

do them roi m&t, ma diic tinh chu yeu cua bieu do la sU ddn gian Khi so sanh , khoang giUa cac cot trong cung nhom rong tuy y, nhung khoang cach gitia cac nhom thi phai theo qui dinh

H inh 13

Ty le phan tram phan bo theo tuoi cua quan the mau so sanh

vdi ty le phan tram phan bo theo tuoi cua quan the dufofc dieu tra tiem chung, thanh pho Sample

1 1 Quan the mau

□ Quan the dudc kiem tra

t< 1 1-4 5-14 15-44 45+

Nhom tuoi

27

(1) 1954, Bo Y te, (2) chi co (3) Dan ban xti (4) 1951 so' lUu khai sinh, da loai

bo tre de song bi chet trUcJc khi khai sinh (5) So’ lUu khai sinh, da loai bo so lieucua vung Bihar Madhva Fradesh va Orissa (6) Da loai bo cac trUdng hdp abirugube thu^n giong; (7) Loai bo quan the Bedouin d Negev

Nguon: Sw aroop S Gidi thieu ve Thong ke y te L on don 1960.

28

2 Hoa do.

Hoa do la mot dang cua bieu do hinh cot stf dung nhiing ky hieu nho d§ trinh bay so' lieu Thong thtfdng cac hinh anh dtfdc sap dat theo chieu ngang, nhtfng cung co the theo chieu doc Moi ky hieu co the the hien mot ngtfdi hoac mot ddn vi dac biet Nhin chung, moi ky hieu the hien mot so ltfdng ngtfdi hay ddn vi nhat dinh So ltfdng cac muc dich xac dinh bdi bien so' dtfdc dtfa len hoa do, va chung se xac dinh do dai cua cot Hinh 15 minh hoa mot hoa do trong do moi ky hieu the hien mot ngtfdi

H inh 15

Tinh hinh tiem chung cua cac trtfcfng hop benh dau miia

VtfOng quoc Anh - 1962 va Thuy Dien- 1963

B BIEU D O DUA TREN TY LE

Hai trong so' bieu do quan trong nhat cua loai nay la bieu do hinh cot hdp ph&n va bieu de hinh banh