l. Phin tich phuong sai
Ph6n tich phuong sai ld cdng cq chri y6u d6 phdn tich c6c si5 liqu kii theo doi anh
hu6ng cia crlc nhdn t6 (factor) va Anh hudng tuong tiic cia chUng.
. D6 thu thlp s6 lipu, thi nghifm cin tluop thiiit f6 phl hgp vdi mgc dlch nghi€n cuu
vri tli€u ki€n cu th€ noi ti6n hinh thinghi€m.
Dd phen tich mQt nh6n ti5, thi nghiQm thudng tluo. c thiiit kii theo kiEu hoin toin ng6u
nhi€n, ki€u kh6i hoin toin ng6u nhidn, hay 0 vudng La tinh.
D,! phan tich hai nhin tii, thi nghifm dugc b5 tri theo ki6u kh6i ngdu nhi€n. ki6u truc
giao, kiiiu chia 6 l6n, O viia, 6 nhd, ho{c k6t hqp vla chia bing vtra chia 6.
Tt ba nhin td trd len thi can b6 tri thi nghiem sao cho m5i nhen tii c6 hai mrlc hay
mor nnan to co ba muc.
1.1. Ph6n tich phuong sai mQt nhin ti
PhAn tich phuong sai mQt nhAn t6 rluo;c dirng dd phin tich s6 lieu kl',i theo ddi inh
hudng cta ciic mfc cUa nh6n t6 tdi k6t qui, nhu 6nh hudng cria c6c c6ng thrlc cho 6n tt6n
ning su6t thlt lgn, anh hudng cta c6c c6ng thrlc phun thu5c siu ct6n t! lQ s6u bQnh...S6 mric>2EC phen tich phuong sai mot nhen tO cen thiet kO thi nghipm kidu hoin toan ngeu EC phen tich phuong sai mot nhen tO cen thiet kO thi nghipm kidu hoin toan ngeu
nhidn, m6i mric lgp l4i m6r s6 IAn, s6 lAn l|p c0a ciic mfc cia nh6n tti khdng cin phriLi bin.gnhau. S5 licu tluoc tlGn theo cQt hofc theo hang (n6u theo hing thi m6i hang rlng vdi mQt nhau. S5 licu tluoc tlGn theo cQt hofc theo hang (n6u theo hing thi m6i hang rlng vdi mQt mric cria nhdn t6), 6 rliu ti€n ghi ten mfc, c6c 6 ti6p theo ghi s5 lieu.
a. C6c bufc thuc hietr
Chgn Data > Data Analysis > Anota: Single Faclor vd khai bdo:
- [nput range: Khai b6o midn dt li€u vdo (m0t chii nhat bao trtrm todn bO ciic 0 chta
t0n mtc va toan bO c6c s6 liQu). .
- Grouped by: Column (s6 lieu theo cot) hoic rolv Gi5 lieu theo hang).
' - Label in First column :nhin ddng diu.
- alpha: 0.05 mfc j nghia o. - Output range: midn ra.
b. Phin ticl k6t qun
- K€t qui in ra gdm cac th6ng k€ co bAn cho tilng mrlc (trung binh, phuong sai...) vd
bing phdn tich phuong sai.
- N6u giii tri xdc su6t P-value < alpha (ho{c F thuc nghiem > F ly thuy6t) thi cdc c6ng
thftc c6 riicd6ng khac nhau tdi k€t qud, ngugc lqi cric cOng thrlc kh6ng c6 kh6c bift d6ng k0.
. - N6u ki5t ludn c6c cong thriJ c6 trii <lQng kh6c nhau_tdi k6t qud thi phdi tiiin hinh bu6c tiilp theo ld so sdnh cric c6ng thic d6 rit ra c6ng thLic nAo tiit nh5t.
- rtoilt ,t1/ta ,hr.)' tlt/ t/ lr4 lra $L 18& 4t'+- 1cl \ t.q \ /Ll* 4Kc 481 llb (\q ,1, t 143 ,tq Y 4,r t t6U 1a'/ ii" .1i+ cic 4q e? .,{ c( ^-J) (3 qtl zt 9t ?.( r-r i 46' 4"F 418 .t6 & .1 b( 477 I [ ;:t1[ ri) ,tt1t ltry ,{3s
thu duoc nhu bAns sau. Hav cho t1 D E A B D E 2 091 0.43 0.70 1.00 0.90 0.8i 0.45 0.90 0.95 1.0c 0.8i 0.40 0.? 5 090 0.9t 5 0.9( 0.42 0.70 0.9c 0.9i
Vi d9 l; Theo d6i tdng trgng cria c5 (kg), thi nghiQm vdi 5 cdng thlic nu6i (A, B, C, D, E). .
Sii lieu thu duoc nhu bins sau. Hay cho biilt c6ns thric ndo r6t nhAt
* Cric bra6c thyc hiQn trong Excel
Chgn Dota > Data Analysis > Anova: Singie Factor vi khai b6o theo hQp thoqi sau::
K6t lu$n: P- value < 0.05 ( m&c j nghia cia kirim tlinh ) n6n k6t ludn cric c6ng thfc c6 tric ddng khric nhau tdi k6t qud.
Ti6p theo cin ti6n hdnh so siinh trung binh ciic cdng thtc ild tim rac6ng thuc t6t nh6t.
1.2. So sirh cdc trurg binh dtng chi sd LSD (Least sitrilicance diffrence)
Phin m€m Excel kh6ng cho phip so senh. ciic trung bi;h cia c6c nh6m tng vdi cdc
mfc cia nhan t6 (c6c c6ng thfc). Tuy nhi€n, n6u cin so s6nh trung binh m; (vdi 1 lAn hp) vdi
trung binh m; (1 lin lap) ngudi ding c6 th6 tg tinh th€m LSD (Leist Significance Diflerence)
theo c6ng thtc LSD = t",s x SQRTG2(l/rj + I/rr), trong d6 s2 li phuonE sai chung dugc udclugng bdi trung binh sai s6 binh phuong trong nQi bQ nh6m (MS within groups), c = l-p, vi lugng bdi trung binh sai s6 binh phuong trong nQi bQ nh6m (MS within groups), c = l-p, vi
t", r li gi6 tri t cria bing Student tmg v6i mtc f nghia o vi fb{c tg?g. L, r c6 th6 tim dugcbEng c6ch tra bing sO hay tnng hdm TINV trong Excel. bEng c6ch tra bing sO hay tnng hdm TINV trong Excel.
* Tinh tri tuyet d6i cia hi€u c{c trung binh m,, m; : I m;- m;l
+ So sdnh n6u lm,- mll > LSD thi hai trung binh li kh6c nhau, nguoc lai 2 hung binhduoc coi ld. kh6ng khdc nhau. Th6ngthudng ngubi_ta ldp biLng hi€u c6c trung binh, sau d6 lap duoc coi ld. kh6ng khdc nhau. Th6ngthudng ngubi_ta ldp biLng hi€u c6c trung binh, sau d6 lap bing ghi k€t qui so sdnh. ISI)ii: .u. Th6ng thudng ngubi ta ldp biLne hi€u c6c trung binh, sau f sni,:iit iL41t.(.\)./(1" t (.a.'i<'"-sci,, \7;'z LW-:1Ld,44'll. ;t[."2 d6 lip" / I
ilh .L-*^ 4j
* So sinh cdc vidul&
thu tr€n c6c 6 thi nehi€m nhu sau:
25A 21 B 27C 27E 32D 26A
208 25A 234 208 29D ?1 E
22C 20B 26E 23C 24C 24E
30D 238 zJv 32D 29D
22E 28D 238 25E 24E 23A
Hiy ph6n tich phuong sai m6t nhen t6 kdt luin xem
l.J. Phin tich phuong sai hai nh6n
Vi du 2: Thi nghi€m b6 tri hoan toan ng6u nhi€n tr6n 5 gi5ng IUa ( A, B,C, D, E )
thu <luoc nins sudt tr€n cric 6 thi nshi€m nhu sau:
t{';
),,
lia ndo cho ket qua tOt nhat.
hial iitla 6,ra
f ugit F h'"nE 1. nE 1.
Khi phin rich phuong sai hai nhiin 16 A vi B thi co rhE xay ra cac hai truong hqp:
truong hgp A va B kiong tuong tric (bi6n dQng g6i nen bdi tlic ddng dong thoi cua A vd B gin
sdt 0) ve truong hop A va B ruong tdc (n6u trii lqi). a. Phen tich phudag sai hai nhen t6 khArg tudng tdc
Phdn tich phuong sai mQt nhdn t6 bii tri kidu kh6i hoan todn ngiu nhidn duo. c coi li
truong hgp ri€ng cia phdn tich phuoxg sai hai nhrin t5 kh6ng tuong tec (nhdn 16 kh6i Ie nhan td rht hai kh6ng trrong tiic vdi nhdn t6 rhf nhSr).
Khi ph6n tich phuong sai hai nhdn t6 kh6ng tuong r6c, s6 lieu cAn duoc sdp xiip theo
ciich sau: hdng ld c6c mirc cia nhAn t5 th* nh5t, c6t Ii ciic mfc crla nh6n t6 tht:hai (trongtruirng hqp cin phdn rich phuong sqi mQr nhin t6 b6 tri kidu kh5i ngiu nhi€n ihi hang ia cai truirng hqp cin phdn rich phuong sqi mQr nhin t6 b6 tri kidu kh5i ngiu nhi€n ihi hang ia cai
mLic cia nh6n t6, cQt li cdc kh6i nglu nhi€n).
* Cric btrrlc thyc hifn
Chgn Data >Data Andlysis >Anoya: Two Factor Without Replication sau do khai brio tiilp
ciic th6ng tin trong high I.l0 vd kich OK.
Vi d!t 3-'-Bd trithi nghiem phiin rich nhan 16 I (c6 b6n mric) theo kh6i hodn todn ngiu nhi€n
(nhdn tO 2 cd b6n khdi). ra thu duo-c cric so lidu nhu trong bang I.5.
B6ng L5. 56
Choo Dqte >Dqtq Analysis >Anoyz:
ciic th6ng tin trong hinh sau:
tich rn6t nhAn tii theo kh6i nsiu nhiGn.
Kh6i I Kl6i 2 _Knor J Kh6i 4
Mtic I 47 52 62 5l
Mrlc 2 50 54 67
Mrlc 3 5'7 53 69 57
Mric 4 54 65 74 59
Two Factor Without Replication sau d6 khai b6o ti6p
Kdt qud thu du-oc khi phdn tich phuong sai cho o bdng 1.6.
* Phin tich kdt oui
- eaC m*c cria nfran t6 I (ddng) c6 dnh hudng kh6c nhau di5n kdt qui vi F thgc nghipm > F If
thuyet.
- C6c mirc cria nh6nt5 2 (cO0 cd anh hudng kh6c nhau d6n k6t qua vt F thyc nghiem > F l!
thuydt.
Chrt !: F l! thuy6t c6 the tim bing hdm FINV(0.05, 3, g) =3.86254, va giA tri t cong c6 th6
tim duo.c bans hemTINV(O.05,9) =2.262.
Niiu k6t luin cdc m*c cia m.Qt nhdn t5 dnh huong khec nhau.thl ta so senh trung binh cria cac mfc trong cing,nhdn t6 vdi nhau dd tim mric t6t nhet ( lem tuong ty nhu mqc 1.2 d tren),
trong vi du niy,c6 th6 so siinh trung blnh c6c mrlc crla nhan t6 ddng, so s6nh trung binh c{c
mfc cria nhdn t6 c6t.
b. Phdn tich phuong sai hai nhAn t6 trong tic
Trongirudng-hqp ney khi ph6n tich phuong sai ta phii tinh d6n sqr t6c dQng d6ng thdi
ctia A vd B.
Si5 liQu s6p x6p nhu sau:
- Nhnn t6 I d6nh theo hdng v6i ciic mrfc khiic nhau, nhan t6 2 danh theo cot vfi c6c
nrrr khlic nhau.