chuong_3.pdf

23 Chng 5

B MN TON GVGD: Nguyn nh Huy

Chng 3

P DNG MS-EXCEL

TRONG QUY HOCH THC NGHIM V PHN TCH PHNG SAI

Phn tch phng sai mt yu t

Phn tch phng sai hai yu t

Khng lp

C lp

Phn tch phng sai ba yu t

24 Chng 5


A- PHN TCH PHNG SAI

MT YU T

5.1 Khi nim thng k

Php phn tch phng sai c dng trong cc trc nghim so snh cc gi tr trung

bnh ca hai hay nhiu mu c ly t cc phn s. y c th c xem nh phn m rng

ca trc nghim t hay z (so snh hai gi tr trung bnh).

Mc ch ca s phn tch phng sai mt yu t l nh gi s nh hng ca mt yu t

(nhn to hay t nhin) no trn cc gi tr quan st, Yi, (i = 1, 2, , k).

M hnh

Yu t th nghim

1 2 k

Y11

Y12

Y1N

Y21

Y22

Y2N

Yk1

Yk2

YkN

Tng cng

Trung bnh

T1

1Y

T2

2Y

Tk

kY

T

Y

Bng ANOVA

Ngun sai s Bc t

do Tng s bnh phng

Bnh phng

trung bnh

Gi tr thng

k

Yu t

Sai s

k-1

N-k

N

T

N

TSSF

2k

1i

2

i

SSFSSTSSE

1k

SSFMSF

kN

SSEMSE

MSE

MSFF

Tng cng N-1

k

1i

N

1j

2

2

nN

TYSST

Trc nghim

* Gi thuyt:

H0: k21 ... Cc gi tr trung bnh bng nhau

H1: ji t nht c hai gi tr trung bnh khc nhau

25 Chng 5


* Gi tr thng k: MSE

MSFF

* Bin lun:

Nu )kN;1k(FF Chp nhn gi thuyt H0.

5.2 p dng MS-EXCEL

Th d 12: Hm lng alcaloid (mg) trong mt loi dc liu c thu hi t ba vng khc

nhau c trnh by trong bng sau:

Vng I Vng II Vng III

7,5 6,8 7,1 7,5 6,8 6,6 7,8

5,8 5,6 6,1 6,0 5,7

6,1 6,3 6,5 6,4 6,5 6,3

Hm lng alcaloid c khc nhau theo vng?

Nhp d liu vo bng tnh

A B C

1 Vng I Vng II Vng III

2 7.5 5.8 6.1

3 6.8 5.6 6.3

4 7.1 6.1 6.5

5 7.5 6.0 6.4

6 6.8 5.7 6.5

7 6.6 6.3

8 7.8

p dng Anova: Single Factor

a. Nhp ln lt n lnh Tools v lnh Data Analysis.

b. Chn chng trnh Anova: Single Factor trong hp thoi Data Analysis ri nhp nt OK.

c. Trong hp thoi Anova: Single Factor. ln lt n nh:

- Phm vi u vo (Input Range)

- Cch sp xp theo hng hay ct (Group By)

- Nhn d liu (Labels in Fisrt Row/Column)

26 Chng 5


Anova: Single Factor

SUMMARY

Groups Count Sum Average Variance

Vng I 7 50.1 7.157143 0.202857

Vng II 5 29.2 5.84 0.043

Vng III 6 38.1 6.35 0.023

ANOVA

Source of Variation SS df MS F P-value F crit

Between Groups 5.326968 2 2.663484 26.56148

1.18E-

05 3.68232

Within Groups 1.504143 15 0.100276

Total 6.831111 17

Hnh 5.1 Hp thoi Anova: Single Factor

Kt qu v bin lun

F = 26.561 > F0.05 = 3.682

Bc b gi thuyt H0.

Vy hm lng alcaloid khc nhau theo vng.

27 Chng 5


B- PHN TCH PHNG SAI

HAI YU T (KHNG LP)

5.3 Khi nim thng k

S phn tch ny nhm nh gi s nh hng ca hai yu t trn cc gi tr quan st Yij (i

= 1. 2. r: yu t A; j = 1. 2. . c: yu t B).

M hnh

Yu t A Yu t B Tng

cng

Trung

bnh 1 2 c

1

2

r

Y11

Y21

Yr1

Y12

Y22

Yr2

Y1c

Y2c

Yrc

Y1.

Y2.

Yr

1Y

2Y

rY

Tng cng

Trung bnh

T.1

1.Y

T.2

2.Y

Tc

c.Y

T..

..Y

Bng ANOVA

Ngun

sai s

Bc t

do

Tng s bnh

phng

Bnh phng

trung bnh

Gi tr

thng k

Yu t A

(Hng)

(r-1)

r

1i

2

..

2

iT

c

TSSB

)1r(

SSBMSB

MSE

MSBFR

Yu t B

(Ct)

Sai s

(c-1)

(r-1)(c-1)

c

1j

2

..

2

j

rc

T

r

T

SSB

SSE = SST (SSF +

SSB)

)1c(

SSFMSF

)1r(

SSBMSB

MSE

MSFFC

Tng

cng

(rc-1)

r

1i

c

1j

2

..2

ijr

TYSST

Trc nghim

* Gi thuyt:

H0: k21 ... Cc gi tr trung bnh bng nhau

H1: ji t nht c hai gi tr trung bnh khc nhau

* Gi tr thng k: MSE

MSBFR v

MSE

MSFFC

28 Chng 5


* Bin lun:

Nu })1b)(1k(,1b[FFaR

Chp nhn H0 (yu t A)

Nu })1b)(1k(,1k[FFaC

Chp nhn H0 (yu t B).

5.4 p dng MS-EXCEL

Th d 13: Hm lng flavonoid (mg) trong cng mt mu dc liu c chit xut bi 5

phng php vi 5 loi dung mi khc nhau:

Phng

php

Dung mi

I II III IV V

A

B

C

D

E

12.9

13.4

15.6

12.7

13.5

17.1

18.1

16.9

17.8

19.3

11.6

19.6

16.8

21.3

18.7

23.4

22.1

21.5

20.9

23.2

17.6

16.8

18.1

17.9

17.3

Phng php hay dung mi c nh hng n kt qu ca s chit xut dc liu nu trn?


A B C D E F

1 I II III IV V

2 A 12.9 17.1 11.6 23.4 17.6

3 B 13.4 18.1 19.6 22.1 16.8

4 C 15.6 16.9 16.8 21.5 18.1

5 D 12.7 17.8 21.3 20.9 17.9

6 E 13.5 19.3 18.7 23.2 17.3

p dng Anova: Two-Factor Without Replication

a. Nhp ln lt n lnh Tools v lnh Data Analysis.

b. Chn chng trnh Anova: Two- trong hp thoi Data Analysis ri nhp nt OK.

c. Trong hp thoi Anova: Two-Factor Without Replication. ln lt n nh cc chi tit:

- Phm vi u vo (Input Range).

- Nhn d liu (Labels in Fisrt Row/Column)

- Ngng tin cy (Alpha).

- Phm vi u ra (Output Range).

29 Chng 5


Hnh 5.2: Hp thoi Anova: Two-Factor Without Replicatio

Anova: Two-Factor Without Replication

SUMMARY Count Sum Average Variance

A 5 82.6 16.52 21.537

B 5 90 18 10.495

C 5 88.9 17.78 5.107

D 5 90.6 18.12 11.842

E 5 92 18.4 12.29

I 5 68.1 13.62 1.337

II 5 89.2 17.84 0.908

III 5 88 17.6 13.885

IV 5 111.1 22.22 1.157

V 5 87.7 17.54 0.263

ANOVA

Source of Variation SS df MS F P-value F crit

Rows 10.6736 4 2.6684 0.717234706 0.59240848 3.00691728

Columns 185.5576 4 46.3894 12.46892807 8.5462E-05 3.00691728

Error 59.5264 16 3.7204

Total 255.7576 24

Kt qu v bin lun

FR = 0.717 < F0.05 = 3.007 Chp nhn gi thuyt H0 (Phng php)

FC = 12.469 > F0.05 = 3.007 Bc b gi thuyt H0 (Dung mi)

Vy ch c dung mi nh hng n kt qu chit xut.

30 Chng 5


C- PHN TCH PHNG SAI HAI YU T (C LP)

5.5 Khi nim thng k

Tng t nh m hnh phn tch phng sai hai yu t (xem tr.67). ch l mi mc mc

(A1. B1) c s lp li k ln th nghim mi hng s biu th mt bn sao ca d liu v trong u

ra s thm mt i lng tng tc (interaction term) F1 gia hai yu t A v B.

Th d 14: hm lng saponin (mg) ca cng mt loi dc liu c thu hi ma (kh v

ma: trong mi ma ly mu ba ln - u. gia v cui) v t ba min (nam. trung v bc) c

tm tt nh sau:

Ma

Thi im

Min

Nam Trung Bc

Ma kh

u ma 2.4 2.1 3.2

Gia ma 2.4 2.2 3.2

Cui ma 2.5 2.2 3.4

Ma ma

u ma 2.5 2.2 3.4

Gia ma 2.5 2.3 3.5

Cui ma 2.6 2.3 3.5

Hy cho bit hm lng saponin c khc nhau theo ma hay min? Nu c th hai yu t

ma v min c s tng tc vi nhau hay khng?

5.6 p dng MS-EXCEL


A B C D

1 Nam Trung Bc 2 Ma kh 2.4 2.1 3.2 3 2.4 2.2 3.2 4 2.5 2.2 3.4 5 Ma ma 2.5 2.2 3.4 6 2.5 2.3 3.5 7 2.6 2.3 3.5

p dng Anova: Two-Factor With Replication

Hnh 5.3: Hp thoi Anova: Two-Factor With Relication

31 Chng 5


Anova: Two-Factor With Replication

SUMMARY Nam Trung Bc Total

Ma kh

Count 3 3 3 9

Sum 7.3 6.5 9.8 23.6

Average 2.433333 2.166667 3.266667 2.622222

Variance 0.003333 0.003333 0.013333 0.251944

Ma ma

Count 3 3 3 9

Sum 7.6 6.8 10.4 24.8

Average 2.533333 2.266667 3.466667 2.755556

Variance 0.003333 0.003333 0.003333 0.300278

Total

Count 6 6 6

Sum 14.9 13.3 20.2

Average 2.483333 2.216667 3.366667

Variance 0.005667 0.005667 0.018667

ANOVA

Source of

Variation SS df MS F P-value F crit

Sample 0.08 1 0.08 16 0.001762 4.747225

Columns 4.347778 2 2.173889 434.7778 6.36E-12 3.885294

Interaction 0.01 2 0.005 1 0.396569 3.885294

Within 0.06 12 0.005

Total 4.497778 17

Kt qu v bin lun

FR = 16 > F0.05 = 4.747 Bc b gi thuyt H0 (Ma).

FC = 434.778 > F0.05 = 3.385 Bc b gi thuyt H0 (Min)

F1 = 1 < F0.05 = 3.385 Chp nhn gi thuyt H0 (Ma x min).

Vy hm lng Saponin trong dc liu c kho st khc nhau khng nhng theo ma

m cn theo min. Tuy nhin. khng c s tng tc gia hai yu t ma v min trn hm

lng y.

32 Chng 5


D- PHN TCH PHNG SAI BA YU T

5.7 Khi nim thng k

S phn tch ny c dng nh gi v s nh hng ca ba yu t trn cc gi tr

quan st (i = 1. 2.... r: yu t A; j = 1. 2..... r: yu t B; k = 1. 2..... r: yu t C)

M hnh

Khi nghin cu nh hng ca hai yu

t. mi yu t c n mc. th ngi ta dng

m hnh vung la tinh n x n. th d nh m

hnh vung la tinh 4 x 4:

B C D A

C D A B

D A B C

A B C D

M hnh vung la tinh ba yu t c trnh by nh sau:

Yu t C (T..k. th d: T1 = Y111 + Y421 + Y331 + Y241)

Yu

t A

Yu t B

B1 B2 B3 B4 Ti

A1 C1 Y111 C2 Y122 C3 Y133 C4 Y144 T1

A2 C2 Y212 C3 Y223 C4 Y234 C1 Y241 T2

A3 C3 Y313 C4 Y324 C1 Y334 C2 Y342 T3

A4 C4 Y414 C1 Y421 C2 Y412 C3 Y443 T4

T.i. T.1. T.2. T.3. T.4.

Bng ANOVA

Ngun

sai s

Bc t

do Tng s bnh phng

Bnh phng trung

bnh

Gi tr thng

k

Yu t A

(Hng) (r-1)

2

2

...

r

1i

2

..i

r

T

r

TSSR

)1r(

SSRMSR

MSE

MSRFR

Yu t B

(Ct) (r-1)

2

2

...

r

1j

2

..j

r

T

r

T

SSC

)1r(

SSCMSC

MSE

MSCFC

Yu t C (r-1) 2

2

...

r

1k

2

..k

r

T

r

TSSF

)1r(

SSFMSF

MSE

MSFF

Sai s (r-1)(r-2) )SSCSSRSSF(

SSTSSE

)2r)(1r(

SSEMSE

Tng

cng (r

2-1)

i j k

2

2

...2

ijk

r

TYSST

Trc nghim

* Gi thit:

33 Chng 5


k210

:H Cc gi tr trung bnh bng nhau

ji1

:H C t nht hai gi tr trung bnh khc nhau

* Gi tr thng k: v

* Bin lun:

- Nu ( Chp nhn H0 (Yu t A)

- Nu ( Chp nhn H0 (Yu t B)

- Nu ( Chp nhn H0 (Yu t C).

5.8 p dng MS-EXCEL

Th d 15: Hiu sut phn trm (%) ca mt phn ng ha hc c nghin cu theo ba

yu t: pH (A). nhit (B) v cht xc tc (C) c trnh by trong bng sau:

Yu

t A

Yu t B

B1 B2 B3 B4

A1 C1 9 C2 14 C3 16 C4 12

A2 C2 12 C3 15 C4 12 C1 10

A3 C3 13 C4 14 C1 11 C2 14

A4 C4 10 C1 11 C2 13 C3 13

Hy nh gi v nh hng ca cc yu t trn hiu sut phn ng?


1 A B C D E F G H I J K L M

2 B1 B2 B3 B4

3 A1 9 14 16 12

4 A2 12 15 12 10

5 A3 13 14 11 14

6 A4 10 11 13 13

7

8 Ti.. 51 49 52 47 SUMSQTi.. 9915 SSR 3.69 MSR 1.2292 FR 3.106

9 T.j. 44 54 52 49 SUMSQT.j. 9957 SSC 14.2 MSC 4.7292 FC 11.95

10 T..k 41 53 57 48 SUMSQT..k 10043 SSF 35.7 MSF 11.896 F 30.06

11 T... 199 SQT... 39601 SSE 2.38 MSE 0.3958

12 SUMSQ

Yijk

2531 STT 55.9

Thit lp cc biu thc v tnh cc gi tr thng k

* Tnh cc gi tr Ti.... T.j.. T..k v T...

- Cc gi tr Ti..

Chn B7 v nhp biu thc =SUM(B2:E2)

34 Chng 5


Chn C7 v nhp biu thc =SUM(B3:E3)

Chn D7 v nhp biu thc =SUM(B4:E4)

Chn E7 v nhp biu thc =SUM(B5:E5)

Cc gi tr T.j.

Chn B8 v nhp biu thc =SUM(B2:B5)

Dng con tr ko k1i hiu t in t B8 n E8

- Cc gi tr T..k

Chn B9 v nhp biu thc =SUM(B2.C5.D4.E3)

Chn C9 v nhp biu thc =SUM(B3.C2.D5.E4)

Chn D9 v nhp biu thc =SUM(B4.C3.D2.E5)

Chn E9 v nhp biu thc =SUM(B5.C4.D3.E2)

Gi tr T...

Chn B10 v nhp biu thc =SUM(B2:E5)

* Tnh cc gi tr v

- Cc gi tr v

Chn G7 v nhp biu thc =SUMSQ(B7:B7)

Dng con tr ko k hiu t in t G7 n G9

- Gi tr

Chn G10 v nhp biu thc =POWER(B10.2)

- Gi tr

Chn G11 v nhp biu thc =SUMSQ(B2:E5)

* Tnh cc gi tr SSR. SSC. SSF. SST v SSE

- Cc gi tr SSR. SSC v SSF

Chn I7 v nhp biu thc =G7/4-39601/POWER(4.2)

Dng con tr ko k hiu t in t I7 n I9

- Gi tr SST

Chn I11 v nhp biu thc =G11-G10/POWER(4.2)

- Gi tr SSE

Chn I10 v nhp biu thc =I11-SUM(I7:I9)

* Tnh cc gi tr MSR. MSC. MSF v MSE

- Cc gi tr MSR. MSC v MSF

35 Chng 5


- Gi tr SST

Chn K7 v nhp biu thc =I7/(4-1)

Dng con tr ko k hiu t in t K7 n K9.

- Gi tr MSE

Chn K10 v nhp biu thc =I10/((4-1)*(4-2)).

* Tnh cc gi tr v F

Chn M7 v nhp biu thc = K7/0.3958

Dng con tr ko k hiu t in t M7 n M9.

Kt qu v bin lun

76,4)6,3(F10,3F05,0R

chp nhn H0 (pH).

76,4)6,3(F95,11F05,0C

Bc b H0 (nhit )

76,4)6,3(F05,30F05,0

bc b H0 (cht xc tc)

Vy ch c nhit v cht xc tc gy nh hng n hiu sut.

chuong_3.pdf

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