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Chuong 9. Thi)ng k~ trong kiem dinh Jy thuyet khoa hoc 317 C/IU'(Tng 9 Thong ke dung trong kiem dinh It thuyet khoa hoc Chuong nay gi6'i thi~u cac nQi dung: 7. T6m fdf t/r(~hgk~cho mflll 2. Kyv{mg 3. Bia" cilllli'll trung bill!' vii clllIan hoa 4. Qllan flf gifrn tham sf! /lin" vii dam dong 5. Uac [/((I1lg thO'Tlgke 6. Kif;1I dinh IIIoIIg ke 7. MiJi qllall IIf gil;a hai bie,l IIgnu nhien 8. 51( d!wg 51'55 de'lilllrirf SQ'tUlJllgquail 318 Phuong phap nghlen ciru khoa hoc trong kinh doanh Chuong njy c6 m~ICarch on lai nhfrng kien tlurc ve thong ke can ban can thiet rrong danh gia thang do va kiern dinh cac ly thuyet khoa hoc. De d~ theo doi, trong dam dong, cac bien duoc ky hi~u bAng chii' in hoa (vd, X, Y, vv) va h.rc:mgirng cua chUng trong m~u, duoc ky hi~u bAng chii' tbuong (vd, x, y, vv). 1. Tom tAt thong ke cho m~u Tom tiit tI,(j;,g ki! (statistical summarization) thong qua cac do luong mlrc dQ t~p trung (measure of centrality) nhir trung binh (mean), trung vi (median), mode, va mire di} phan tan (measure of dispersion) nhtr phuong sai (variance), do l~ch chum (standard deviation), khoang bien thien (range) cua cac dir li~u. Chu Y III cac cOng thrrc sau day str dung cho m5u (t6m tilt Iii t6m tit cac thong tin ella m5u). 1.1. Do luong m(re eli} t~p trung Ba dai lu·qng thuong Sll' dung trong do luong muc dQ t~p trung cua cac bien 111(1) trung blnh, (2) trung vi, va (3) mode. 1.1.1.Trung binh Trung blnh cua day so xi(i = 1, 2, ..., n) cua mau co kich thu6c (sample size) n duoc tinh bAng cong thirc sau: 1.1.2.Trung vi Trung vi la so n3m giii'a (neu soluqng cac chii' so trong day la le) hay trung binh cua c~p so n3m gifra (neu soluqng cac chfr so trong day Iii Clurong 9. Thong kc rrong kiem djnh eh3n) cua mot day nguc;Tcl<)i. so do 19lhuyet khoa hoc 319 duoc xep theo thir tv nr nho den lon ho~c l.l.3.Mode Mod« Iii giii tr] co tan so xuilt hi~n 16n nhat ala mot t~p hop cae so do. 1.2. Do luang mti'c do phan tan Hai d~i luong thtrOng nghien cuu kie'm dinh khoang bien Ihien. su dung Iy de do luang rmrc do philn tan trong thuyet khoa hoc la (1) phuong sai va (2) 1.2.1.Phu'O'ngsai va dQ J~dl chuan Phuong sai do luong mLI'Cdo phan tiln cua mot ~~lP so do xung quanh trung blnh cua no. Can so b~c hai ella phuong sai d uoc goi lil ric) I~c"c/m'n S, Phuong sai Sl va dQ I~chchuan S cua mall duoc tlnh theo dc cong tlurc sau: . -::)s= I II _ " -I(xi-x)II-I ,.1 1.2.2.Khoang bie'n thH!n Khoang bien thien la khoiing each giiia gia tri l<.'m nhat va gia trj nh6 nhat cua mot t~p so do. l'hU'Clngphap nghien 320 Cll'U khoa hoc trong kinh doanh 2. Ky vong 2.1. Trung blnh dam dong Ky vQng (Expectation) cia bien X, ky hi~u Iii E(X), Iii trung blnh cia dam dong, thuUng duoc ky hi~u IiiJ.ix· Neu X Iii bien lien tuc (continuous variable), ky vQng E(X) cua no diroc tinh nlur sau: E(X) = Jlr = Ix Xf(X)dX Trong do, f(X) la ham phan b5 (probability density function) cua X: r:Xf(X)dX =1 Nell x III bien gian doan (discrete variable; chu y Iii trong tlurc ti@nnghien cuu, cac bien nghien cuu thU'Ong 113bien gian doan), ky V~l11g E(X) ella 116 du'qc tfnh nhusau: E(X) = !Ix __ 1 "N X - N L./., / = L,rXP(X) Trong d6, N Iii kich thuoc dam dong vii P(X) Iii ham phan b5 (probability function) cua X: L,P(X)=l Chucng 9. Thong kii trong kit\l'mdjnh I)' thuy"t khoa hoc 32'1 2.2. Phuong sai dam dong Phuong sai ella dam dong eo klch thuoc N, thuong ky hieu la (J'x' va dlrqe tinh nhir sau: Var(X) = (J'~ =_!_N ,," LJ,.,( x i - J.lx )' = £l(X - J.lxfl = CCX') - JI~ 2.3. MQI so qui I~c ve tinh toan ky vong £(X + Y + Z) = £(X)+ GQi c III ml;lt h~ng E(Y) + E(Z) so chung ta co: li(e) =c E(X+c)=E(X)+c = cE(X) + Y)'I = E(X~ + y2 + 2XY) = E(X') + E(Y')+ 2£(XY) E(cX) £[(X 3. Bien chuin Irung blnh va chuan h6a 3.1. Bien chuan trong binh Bien c1lUalt lrung blnh (mean-deviated variable) la bien co trung binh b~ng 0 nhung phuong sai khac vo; 1. De chuyen mQt bien ng~u nhien thanh bien chuan trung binh, chUng ta lay bien do trtf cho Phtrong phrip nghien ciru khoa hoc trong kinh doanh 322 trung blnh cua n6. Gia trung blnh X nhu sau: SLY chung ta chuyen bien Y thanh bien chua'n x = y - u, ::;. E(X) = E(Y - II,) =E(y}-E(Pr) = Pr -}I, =0 Nhir v~y bien chuii'n trung binh X c6 trung blnh E(X) = O. Tuy nhien din chu y la phuong sai Var(X) eua n6 van khac 1: Var(X) = £[(X - P.I')'] = E(X') '" J Tll' d6 chung ta co: Cov(X, y)., f[(X - f.lx)(Y - ,Lly») Cor(X,Y) = Cov(X,Y) (J'.• a, = £(XY) _ E(XY) (J'x(J' y 3.2, lJien chuan h6a Bien chua'n h6a (standardized variable) la bien co trung binh b5ng 0 va phuong sai b~ng 1. Nell muon chuyen m{it bien Y thanh bien chufin hoa Z, chung ta lay bien do tTlr cho tTung brnh va chia cho d(> I~ch chlliln (standard deviation) ella no. Chung ta se co bien ehua'n hoa c6 trung binh b~ng khong va phuong sai bAng 1: Clurong 9. ThQ'''g kc trong kilim din" I.>'thuyct khoa hoc 323 z = Y -Py CT) =:> E(2) = E( Y- JI) ) CT, = Va/'(Z) = E(Z = _I [E(Y) - Pr 1= 0 CT) - Pz)'] = £(l 1 ) = E[( Y-p, ) t] CT) = Var(Z) = E( Y CT,-II )1) 1 t CT' = ~= 1 CT, Tu do, chlmg ta c6: COI'(X, I') = E[(X -11,,)(Y - ,lit)] = e(XY) Co/'(X, I') = Cov(X. Y) = E(XY) = Cov(XY) a a, i 4. Quan h~ giii'a tham 55 m~u va dam dong Trong nghicn cuu khoa h9C,nhu' ali trlnh bay trong phan chon milu (Chuong 6), chung ta khong the' thu th~p dCt·lieu ella dam dong do ton kern thOi gian va chi phi. Vi v~y, chung ta phai thu th~p drr li~u cua m5u va dung drr li~u cua m~ll de' uoc IUQ'Ilghoac kiem dinh cac tham so dln thiC't trong dam dong. Chung ta lam OLfqC dieu nay vi co moi quan h~ gifra tham so m~u va tharn so dam dong. Chung ta gioi thi~u mi)t so m8'i quan co ban gilta tham so milu va tharn so dam he dong. 4.1. Trung binh m5u x va trung binh dam dong p, GQi x 111trung binh cua mi;>tmilu c6 kich thiroc n, diroc chon ngiiu nhien ru mi;>tdam dong c6 trung binh 111P.r va phuong sai I11CT~. Phuong phap nghien ciru khoa hoc trong kinh doanh 324 Trung blnh E(x) va sai I~ch chuan (standard error) O"rcua phan bo m~u (sampling distribution) duoc tinh nhir sau (vd, Newbold 1991): Neu dam dong c6 phan bo chuan N(Jlx'O"~) hay neu klch thuoc m~u n nrong doi IOn (n

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