Chuong 1 Tin hoc CN

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Chng I X L D LIU TRONG CHN NUI TH Y

1. NG DNG MINITAB TRONG X L S LIU Minitab 14 for Windows XP c s dng minh ho cho cc bi tp trong phn

gio trnh ny. Nu bn c s dng cc phin bn khc ca Minitab c th s khng c h tr mt s cc cng c v giao din s khc so vi gio trnh ny.

1.1. Khi ng Minitab Nu ci t Minitab 14 for Windows XP theo mc nh ta c th khi ng phn mm

bng cch

1) Chn biu tng Minitab trn Desktop ca mn hnh hoc 2) Theo ng dn Stat > Progam > MINITAB 14 > MINITAB 14

3) C:\Progam Files\MINITAB 14\Mtb14.exe Giao din phn mm Minitab 14 for Windows XP gm mt s thnh phn chnh: 1)

Menu Bar, 2) Standard toolbar, 3) Project Manager Toolbar, 4) Worksheet Toolbar, 5) Title, 6) Session Window, 7) Data Window 8) Project Manager Window v 8) Status bar. Menu Bar Standard Toolbar Project Manager Toolbar

Title

Session Window

Data Window (Worksheet Windows)

Status Bar

Worksheet Toolbar Project Manager Windows

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1.2. Nht v thng k

a. Tm tt d liu i vi bin nh lng V d 1.1: Khi lng (gam) ca 16 chut ci ti thi im cai sa nh sau:

54,1 49,8 24,0 46,0 44,1 34,0 52,6 54,4 56,1 52,0 51,9 54,0 58,0 39,0 32,7 58,5

tnh cc tham s thng k m t S liu c nhp vo vo ct trong Windows Worksheet

Thay th du phy (,) bng du chm (.) trong phn thp phn. s liu khuyt c thay th bng du sao (*), khng c trng. Ct s liu phi di dng s. i vi mt ch tiu nghin cu, s liu c nhp di dng ct. Tn ct s liu lun nm trn hng th 1. t tn ct ngn gn, khng nn dng cc k t c bit (:, /) hoc cc k t ting Vit (, ). Trong cng mt worksheet khng t tn ct trng nhau. Phn mm Minitab khng phn bit c cc k t vit hoa v vit thng (v d: MINITAB = Minitab = minitab).

Chn Stat Basic Statistics Display Descriptive Statistics

Phn bn tri hp thoi hin th ct (C1) v tn ca ct s liu (P) Chn P v nhn Select hin th ct cn tnh cc tham s thng k m t vo Variables. Chn OK hin th kt qu. Kt qu thu c t Minitab nh sau

Descriptive Statistics: P Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum P 16 0 47.58 2.54 10.16 24.00 40.28 51.95 54.33 58.50

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Minitab cho kt qu theo mc nh. C th s dng mt trong cc ty chn (option) sau y cho ra kt qu ph hp

Chn Statisticsc th la chn cc tham s sau y

Mt s thut ng trong options Minitab ca thng k m t Minitab Ting Vit Minitab Ting Vit

Mean Trung bnh Trimmed mean Trung bnh hiu chnh SE of mean Sai s tiu chun Sum Tng s Standard deviation lch chun Minimum Gi tr b nht Variance Phng sai Maximum Gi tr ln nht Coefficient of variation H s bin ng Range Khong bin ng First quartile T v th nht Sum of squares Tng bnh phng Median Trung v Skewness lch Third quartile T v th 3 Kurtosis nhn Interquartile T v th 2 MSSD

N nonmissing N khng khuyt Cumulative N N cng gp N missing N khuyt Percent Phn trm N total N tng s Cumulative percent Phn trm cng gp

Chn Graphs hin cc loi th th sau y: Histogam of data t chc Histogam of data, with normal curve t chc vi ng cong chun Individual value plot v tng gi tr Boxplot of data th hp

Chn OK c c th V d chn Boxplot of data c c th hp di y

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Khai bo vo By variables (Optional) tnh cc tham s thng k theo phn loi nhm.

Xt V d 1.1, gi s rng 8 chut ci u tin sinh ra la th nht v 8 chut tip theo sinh ra la th 2. Ta c th b tr cu trc s liu thnh 2 ct, ct C1 (P) v ct C2 (LUA)

Kt qu t Minitab

Descriptive Statistics: P Variable LUA N N* Mean SE Mean StDev Minimum Q1 Median Q3 P 1 8 0 44.88 3.82 10.79 24.00 36.53 47.90 53.73 2 8 0 50.28 3.32 9.39 32.70 42.23 53.00 57.53

b. Tm tt d liu i vi bin nh tnh i vi bin nh tnh s liu th thu thp c t th nghim c th c trnh by

theo mt trong 2 cch sau y:

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V d 1.2: S b sa ba tri A, B, C ln lt l 106, 132 v 122 con. Chn ngu nhin v kim tra bnh vim ni mc t cung 3 tri, kt qu nh sau:

Cch 1: Tri A A A A A A A A A A A A A A A A A B s

1 2 3 4 5 6 7 8 9 10 1 12 13 14 15 16 17

Kt qu + - - - + + + - - - + - - - - - +

Tri B B B B B B B B B B B B B B B B B B B B B B B s

1 2 3 4 5 6 7 8 9 10 1 12 13 14 15 16 17 18 19 20 21 22

Kt qu - - + - - - - - + + - - - - - + - + - + - -

Tri C C C C C C C C C C C C C C C C C C C C B s

1 2 3 4 5 6 7 8 9 10 1 12 13 14 15 16 17 18 19 20

Kt qu + + - - - - + - - - + - + - - - - + + +

Cch 2: Tri Vim ni mc t cung Tng s

C Khng A 6 11 17

B 6 16 22

C 8 12 20

S liu c nhp vo ct trong Windows Worksheet (vi cch 1)

Nhp d liu vo 2 ct, Tri vo ct C1 (TRAI) v ct Kt qu xt nghim vo ct C2 (KETQUA). Lu : Sau khi nhp thng tin vo ct C1 v C2 k hiu thay i tng ng C1-T v C2-T. Minitab thng bo cc thng tin trong ct khng phi di dng s m di dng k t (Text) Vi s liu dng th (cch 1) c th to thnh bng tm tt nh cch 2 bng cc lnh sau Stat Tables Cross Tabulation and Chi-Square... Khai bo vo For rows v For columns

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Options Display hin th: Count tn s i vi tng trng hp Row percents t l (phn trm) theo hng Column percents t l (phn trm) theo ct Total percents t l (phn trm) theo hng/ct tng s

Chn OK c kt qu Tabulated statistics: TRAI; KETQUA Rows: TRAI Columns: KETQUA - + All A 11 6 17 B 16 6 22 C 12 8 20 All 39 20 59 Cell Contents: Count

i vi bin nh tnh c th m t bng biu thanh (Bar Chart), biu bnh (Pie Chart). Graph Bar ChartCounts of unique values Chn OK Chn Multiple Graphs

Chn OK c biu thanh

Thc hin tng t c biu bnh

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S liu c nhp vo ct trong Windows Worksheet (vi cch 2)

Nhp d liu vo 3 ct, Tri vo ct C1 (TRAI), ct Kt qu xt nghim vo ct C2 (KETQUA) v Tn sut vo ct C3 (TANSUAT). dng k t (Text) Vi s liu dng th (cch 1) c th to thnh bng tm tt nh cch 2 bng cc lnh sau Stat Tables Cross Tabulation and Chi-Square... Khai bo vo For rows, For columns v Frequencies are in.

Chn Counts v Row percents trong Display c kt qu

Tabulated statistics: TRAI; KETQUA Using frequencies in TANSUAT Rows: TRAI Columns: KETQUA - + All A 11 6 17 64.71 35.29 100.00 B 16 6 22 72.73 27.27 100.00 C 12 8 20 60.00 40.00 100.00 All 39 20 59 66.10 33.90 100.00 Cell Contents: Count

% of Row

Biu trong cch nhp s liu th 2 hon ton ging nh cch nhp s liu, tuy nhin cch khai bo trong hp thoi c mt s im khc Graph Bar ChartValues from table Khai bo vo Graph variables v Categorical variables

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1.3. c lng v kim nh gi tr trung bnh

a. Kim nh phn phi chun i vi tt c cc php th di y bin nh lng u c gi thit l s liu thu

thp c (s liu th) tun theo phn phi chun. Nu s liu khng tun theo phn phi chun th cc php th s khng c hiu lc. Trong trng hp ny cn bin i s liu v phn phi chun hoc s dng kim nh phi tham s.

Gi thit ca php th: H0: S liu c phn b chun v H1: S liu khng c phn b chun

V d 1.3: Tng trng trung bnh (gam/ngy) ca 36 ln nui v bo ging Landrace c rt ngu nhin t mt tri chn nui. S liu thu c nh sau: 577 596 594 612 600 584 618 627 588 601 606 559 615 607 608 591 565 586

621 623 598 602 581 631 570 595 603 605 616 574 578 600 596 619 636 589

Cn b k thut tri cho rng tng trng trung bnh ca ton n ln trong tri l 607gam/ngy. Theo anh ch kt lun ng hay sai, v sao? Bit rng lch chun ca tnh trng ny l 21,75 gam.

Nhp s liu vo Worksheet

Stat Basic Statistics Normality Test...

Chn OK c kt qu

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Gi tr P-Value = 0,997 trong th trn ln hn 0,05 (), nh vy H0 c chp nhn. Kt lun s liu tun theo phn phi chun.

b. Php th Z S dng php th Z kim nh mt gi tr trung bnh khi bit lch chun ca

qun th (). Minitab s tnh khong tin cy (CI 95%) v thc hin php kim nh. i vi kim nh 2 pha ta c gi thit: H0: = 0 vi i thit 0; trong l gi tr trung bnh ca qun th v 0 l gi tr kim nh. Stat Basic Statistics 1-sample Z...

Trong Samples in columns khai bo ct s liu (P). Trong Standard deviation in gi tr 21,75 ( lch chun ca qun th ). Trong Test mean in gi tr 607 (gi tr qun th kim nh 0). Chn OK c kt qu

One-Sample Z: P Test of mu = 607 vs not = 607 The assumed standard deviation = 21.75 Variable N Mean StDev SE Mean 95% CI Z P P 36 599.194 18.656 3.625 (592.090; 606.299) -2.15 0.031

Vi xc sut ca php th P = 0,031 < 0,05 (), bc b H0 v chp nhn i thit H1. Kt lun: Tng trng ca ln Landrace tri nu trn khng bng 607 gam/ ngy (P < 0,05). Khong tin cy 95% l 592,090 606,299 gam/ ngy.

Lu : Trong mt s trng hp, s liu c tm tt (s liu tinh) di dng cc tham s thng k m t. Nh

v d 1.3 ta c n = 36; _

x = 599,194 gam. V vy cc gi tr ny c th s dng khai bo vo la chn Summarized data, cc gi tr khc ( v ) c khai bo tng t c kt qu sau

One-Sample Z Test of mu = 607 vs not = 607 The assumed standard deviation = 21.75 N Mean SE Mean 95% CI Z P 36 599.194 3.625 (592.089; 606.299) -2.15 0.031

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c. Php th T Trong trng hp khng bit lch chun ca qun th (), php th T c s dng

kim nh gi tr trung bnh v lch chun ca mu (s) c s dng thay lch chun qun th. Gi thit ca php th, cu trc s liu tng t nh php th Z. Stat Basic Statistics 1-sample T... Khai bo i vi s liu th

.. v i vi s liu tinh

Chn OK c kt qu One-Sample T: P Test of mu = 607 vs not = 607 Variable N Mean StDev SE Mean 95% CI T P P 36 599.194 18.656 3.109 (592.882; 605.507) -2.51 0.017

Vi P = 0,017 ta cng c kt lun tng t nh i vi khi s php th Z.

1.4. Kim nh 2 gi tr trung bnh Khi tin hnh th nghim so snh s khc nhau gia 2 cng thc th nghim, c 2

trng hp chn mu c th xy ra: 1) Chn mu c lp v 2) chn mu theo cp (xem 2.4, tr.23, Gio trnh Thit k th nghim 2007). Tu thuc vo cch chn mu b tr th nghim m ta c th s dng php th T hay T cp cho ph hp.

a. Kim nh s ng nht ca phng sai khi ly mu c lp i vi kim nh 2 gi tr trung bnh, ngoi gi thit l s liu tun theo phn phi

chun, cn vn th 2 l Hai phng sai c ng nht hay khng? i vi kim nh hai pha ta c gi thit H0: Hai phng sai ng nht (1 = 2) v

H1: Hai phng sai khng ng nht (1 2) . Khi chp nhn gi thit H0, phng sai chung (2)s c s dng tin hnh kim nh trong php th T; ngc li (bc b H0) th php th T gn ng s c thc hin.

V d 1.4: so snh khi lng ca 2 ging b, tin hnh chn ngu nhin v cn 12 con i vi ging th nht v 15 con i vi ging th 2. Khi lng (kg) thu c nh sau:

Ging b th nht 187,6 180,3 198,6 190,7 196,3 203,8 190,2 201,0 194,7 221,1 186,7 203,1

Ging b th hai 148,1 146,2 152,8 135,3 151,2 146,3 163,5 146,6 162,4 140,2 159,4 181,8 165,1 165,0 141,6

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Theo anh (ch), khi lng ca 2 ging b c s sai khc khng? Cu trc s liu ca bi ton kim nh 2 gi tr trung bnh c th c trnh by bng

mt trong 2 cch sau y:

Cch 1: S liu ca 2 cng thc th nghim c nhp vo mt ct v ct th 2 xc nh gi tr ca tng cng thc ....

Cch 2: S liu c nhp vo 2 ct ring bit theo tng cng thc th nghim. Tn ct th hin gi tr trong mi cng thc

Lu : Cu trc s liu c th nhp trong cng mt Worksheet hoc 2 Worksheet ring bit. Stat Basic Statistics 2 Variances...

Cu trc s liu cch 1

... cch 2

C th s dng Summarized data khi s liu c tinh ho. i vi trng hp ny cn khai bo dung lng mu (Sample size) v phng sai (Variance) i vi tng cng thc th nghim tng ng (First hoc Second).

Chn OK c kt qu

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Test for Equal Variances: KL versus GIONG 95% Bonferroni confidence intervals for standard deviations GIONG N Lower StDev Upper

1 12 7.17875 10.6160 19.6238 2 15 8.63359 12.3014 20.8502 F-Test (normal distribution) Test statistic = 0.74; p-value = 0.631 Levene's Test (any continuous distribution) Test statistic = 0.46; p-value = 0.503

Xc sut p-value = 0,631 > 0,05 () v vy H0 c chp nhn. Kt lun hai phng sai ng nht (P > 0,05).

b. Php th T S dng php th T kim nh 2 gi tr trung bnh khi khng bit lch chun ca

qun th (). Minitab s tnh khong tin cy (CI 95%) s chnh lch gia 2 gi tr trung bnh qun th v thc hin php kim nh. i vi kim nh 2 pha ta c gi thit: H0: 1 = 2 vi i thit H1: 1 2; trong 1 v 2 l gi tr trung bnh ca qun th th nht v th 2.

Stat Basic Statistics 2-Sample T... C th s dng Summarized data khi s liu c tinh ho. i vi trng hp

ny cn khai bo dung lng mu (Sample size), gi tr trung bnh (Mean) v lch chun (Standard deviation) i vi tng cng thc th nghim tng ng (First hoc Second).

Chn Assume equal variances nu 2 phng sai ng nht v ngc li nu 2 phng sai khng ng nht (xem 4.1).

Chn hin th th trong Graphs... v mc tin cy trong Options..., theo mc nh Minitab tnh khong tin cy 95%.

Vi cu trc s liu cch 1

... cch 2

Chn OK c kt qu

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Two-Sample T-Test and CI: KL; GIONG Two-sample T for KL GIONG N Mean StDev SE Mean

1 12 196.2 10.6 3.1 2 15 153.7 12.3 3.2 Difference = mu (1) - mu (2) Estimate for difference: 42.4750 95% CI for difference: (33.2301; 51.7199) T-Test of difference = 0 (vs not =): T-Value = 9.46 P-Value = 0.000 DF = 25 Both use Pooled StDev = 11.5901

Xc sut p-value = 0,000 < 0,05 () v vy H0 b bc b v H1 c chp nhn. Kt lun rng Khi lng ca hai ging b c s sai khc (P-value < 0,05).

c. Php th T cp i i vi cc th nghim chn mu theo cp, iu kin duy nht ca bi ton l kim tra

phn b chun ca phn chnh lch (d) s liu gia 2 cng thc th nghim. Vi kim nh 2 pha ta c gi thit H0: d = 0 i thit H1: d 0 (d l trung bnh ca

s chnh lch gia 2 trung bnh 1 v 2). V d 1.5: Tng trng (pound) ca 10 cp b sinh i ging ht nhau vi hai ch

chm sc khc nhau (A v B). B trong tng cp c bt thm ngu nhin v mt trong hai cch chm sc.

Hy kim nh gi thit H0: Tng trng trung bnh hai cch chm sc nh nhau, i thit H1: Tng trng trung bnh hai cch chm sc khc nhau vi mc ngha = 0,05. S liu thu c nh sau: Cp sinh i 1 2 3 4 5 6 7 8 9 10

Tng trng cch A 43 39 39 42 46 43 38 44 51 43

Tng trng cch B 37 35 34 41 39 37 35 40 48 36

Chnh lch (d) 6 4 5 1 7 6 3 4 3 7

Nhp s liu vo Worksheet

Lu : S liu c nhp vo Worksheet theo mt cch duy nht vo 2 ct theo tng cp s liu tng ng. Th t cc cp s liu khng ng vai tr quan trng. S thay i v tr trong 1 cp c th a ta n cc kt lun thiu chnh xc.

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CalcCalculator...

chn OK c c phn chnh lch

Tin hnh kim nh phn b chun ca phn chnh lch D (xem 4.1) Stat Basic Statistics Paired T..

C th s dng Summarized data (differences) khi s dng cc thng tin ca ct chnh lch D kim nh. i vi trng hp ny cn khai bo dung lng mu (Sample size), gi tr trung bnh (Mean) v lch chun (Standard deviation) ca ct D. Chn hin th th trong Graphs... v mc tin cy trong Options..., theo mc nh Minitab tnh khong tin cy 95%. Chn OK c kt qu

Paired T-Test and CI: A; B Paired T for A - B N Mean StDev SE Mean A 10 42.8000 3.8239 1.2092 B 10 38.2000 4.1312 1.3064 Difference 10 4.60000 1.95505 0.61824 95% CI for mean difference: (3.20144; 5.99856) T-Test of mean difference = 0 (vs not = 0): T-Value = 7.44 P-Value = 0.000

Xc sut p-value = 0,000 < 0,05 () v vy H0 b bc b v H1 c chp nhn. Kt lun rng Tng trng trung bnh hai cch chm sc c s sai khc (P-value < 0,05). 1.5. Phn tch phng sai

Phn tch phng sai (Analysis of Variance - ANOVA) l cng c hu ch so snh nhiu gi tr trung bnh. iu kin ca bi ton phn tch phng sai l 1) s liu tun theo phn b chun v 2) phng sai ng nht. Trong khun kh gio trnh ny chng ti ch cp n vic kim tra iu kin ca bi ton i vi cc m hnh thit k th nghim n gin (Th nghim mt yu t hon ton ngu nhin).

kim nh 2 pha ta c gi thit H0: 1 = 2 = ... = a i thit H1: 1 2 ... a ( l trung bnh ca qun th cng thc th nghim th 1, 2, ...a).

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a. Th nghim mt yu t hon ton ngu nhin Xt trng hp n gin nht i vi bi ton phn tch phng sai. Ch c mt yu t

duy nht trong th nghim, cc yu t phi th nghim cn li c coi l c tc ng nh nhau n i tng th nghim.

V d 1.6: Theo di tng trng ca c (kg) trong th nghim vi 5 cng thc nui (A, B, C, D v E). Hy cho bit tng trng ca c cc cng thc nui. Nu c s khc nhau th tin hnh so snh s sai khc ca tng cp gi tr trung bnh.

A B C D E

0,95 0,43 0,70 1,00 0,90 0,85 0,45 0,90 0,95 1,00 0,85 0,40 0,75 0,90 0,95 0,90 0,42 0,70 0,90 0,95

Cu trc s liu ca bi ton kim nh nhiu gi tr trung bnh c th c trnh by bng mt trong 2 cch sau:

Cch 1: S liu ca cc cng thc th nghim c nhp vo mt ct v ct th 2 xc nh gi tr ca tng cng thc

Cch 2: S liu c nhp vo cc ct ring bit theo cng thc th nghim. Tn ct th hin gi tr trong mi cng thc

Kim tra iu kin ca bi ton (s ng nht ca phng sai v phn phi chun ca s liu) s c trnh by sau. Tin hnh so snh cc gi tr trung bnh bng php phn tch phng sai (ANOVA) i vi cu trc s liu cch 1 v cch 2.

Vi cc bi ton s dng php phn tch phng sai so snh, cu trc s liu cch 1 s ph hp v thun li hn trong qu trnh x l s liu. Trong cc v d tip theo chng ti ch cp n vic x l s liu c cu trc cch 1. Stat ANOVA One-Way...

Stat ANOVA One-Way (Unstacked)...

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Chn OK c kt qu One-way ANOVA: KL versus TA Source DF SS MS F P TA 4 0.76325 0.19081 60.99 0.000 Error 15 0.04693 0.00313 Total 19 0.81018 S = 0.05593 R-Sq = 94.21% R-Sq(adj) = 92.66% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev --+---------+---------+---------+------- A 4 0.8875 0.0479 (--*--) B 4 0.4250 0.0208 (--*--) C 4 0.7625 0.0946 (--*--) D 4 0.9375 0.0479 (--*--) E 4 0.9500 0.0408 (-*--) --+---------+---------+---------+-------

0.40 0.60 0.80 1.00 Pooled StDev = 0.0559

Xc sut p-value = 0,000 < 0,05 () v vy H0 b bc b v H1 c chp nhn. Kt lun rng Tng trng trung bnh ca c cc cng thc thc n c s sai khc (P-value < 0,05).

So snh cp khi bc b gi thit H0 chp nhn gi thit H1 Chn Comparisons... trong hp thoi One-Way Analysis of Variances

Cc la chn: Tukeys, family error rate: vi sai s ca ton b cc cp so snh l 5% Fishers, individual error rate: vi sai s ca tng cp so snh l 5% Dunnetts, family error rate: so snh vi nhm i chng, sai s ca ton b cc cp so snh l 5% Hsus MCB, family error rate: vi sai s ca ton b cc cp so snh l 5% Chn OK c kt qu

Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of TA Individual confidence level = 99.25% TA = A subtracted from: TA Lower Center Upper --------+---------+---------+---------+- B -0.58471 -0.46250 -0.34029 (---*--) C -0.24721 -0.12500 -0.00279 (--*---) D -0.07221 0.05000 0.17221 (--*---) E -0.05971 0.06250 0.18471 (---*--) --------+---------+---------+---------+-

-0.35 0.00 0.35 0.70

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TA = B subtracted from: TA Lower Center Upper --------+---------+---------+---------+- C 0.21529 0.33750 0.45971 (---*--) D 0.39029 0.51250 0.63471 (---*--) E 0.40279 0.52500 0.64721 (--*--) --------+---------+---------+---------+-

-0.35 0.00 0.35 0.70 TA = C subtracted from: TA Lower Center Upper --------+---------+---------+---------+- D 0.05279 0.17500 0.29721 (--*--) E 0.06529 0.18750 0.30971 (--*---) --------+---------+---------+---------+-

-0.35 0.00 0.35 0.70 TA = D subtracted from: TA Lower Center Upper --------+---------+---------+---------+- E -0.10971 0.01250 0.13471 (--*---) --------+---------+---------+---------+-

-0.35 0.00 0.35 0.70

Ngoi kt qu phn tch phng sai nh phn trn, Minitab cung cp kt qu so snh tng cp. S sai khc c ngha (P-value < 0,05) gia cc nghim thc da trn khong tin cy ca tng cp. Khng c s sai khc gia cc nghim thc nu khong tin cy c cha s 0 v ngc li c s sai khc nu khng cha s 0. V d trong kt qu nu trn nu so snh gia A-B ta c khong tin cy (-0,58471; -0,34029) khng cha s khng nn kt lun c s sai khc gia A v B (P-value < 0,05). Nu so snh A v D ta c khong tin cy (-0,07221; +17221) c cha s 0 nn kt lun khng c s sai khc gia A v D (P-value > 0,05). c th trnh by kt qu so snh cp i bn c c th tham kho trang 57 chng 4 Gio trnh Thit k th nghim (2007).

Kim tra s ng nht ca phng sai vi cu trc s liu cch 1

Stat ANOVA Test for Equal Variances...

Chn OK hin th th v

..kt qu Test for Equal Variances: KL versus TA 95% Bonferroni confidence intervals for standard deviations TA N Lower StDev Upper A 4 0.0231412 0.0478714 0.309607 B 4 0.0100628 0.0208167 0.134631 C 4 0.0457534 0.0946485 0.612137

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D 4 0.0231412 0.0478714 0.309607 E 4 0.0197348 0.0408248 0.264034 Bartlett's Test (normal distribution) Test statistic = 5.76; p-value = 0.218 Levene's Test (any continuous distribution) Test statistic = 0.81; p-value = 0.539

Xc sut p-value = 0,218 > 0,05 () v vy H0 c chp nhn. Kt lun rng Cc Phng sai ng nht (P-value > 0,05).

Kim tra phn b chun vi cu trc s liu cch 1 Khng tin hnh kim tra phn b chun ca ct s th (KL) m tin hnh kim tra

phn sai s ngu nhin ij theo m hnh: yi j = + ai + i j (i = 1, a; j = 1, ri)

trong yij = quan st th j cng thc i, = trung bnh chung, ai = chnh lch do nh hng ca cng thc i v ij = sai s ngu nhin; cc ij c lp, phn phi chun N(0,2). Nu phn sai s ngu nhin tun theo phn phi chun th s liu bi ton cng c phn phi chun. Stat ANOVA One-Way... Chn Store residuals v OK c RESI1 (ij)

Tin hnh kim tra phn b chun ca ct s liu RESI1 (xem 3.1 Kim nh phn phi chun). Php kim nh s cho ta P-Value = 0,159 > 0,05 () nn c th kt lun S liu tun theo phn phi chun (P > 0,05).

Lu : Vi cu trc s liu cch 2, c th kim nh phn phi chun ca s liu vi tng nghim thc ring bit. Kt qu kim nh, xc sut s liu cc nghim thc A, B, C, D v E c phn phi chun ln lt l 0,255; 0,845; 0,092; 0,255 v 0,410. Ta cng c kt lun tng t.

b. Th nghim mt yu t khi ngu nhin y Xem xt mt th nghim m i tng th nghim chu tc ng ng thi ca mt yu

t chnh (yu t th nghm) v yu t ph (khi). V d 1.7: Nghin cu s lng t bo lymph chut (1000 t bo mm-3 mu)

c s dng 4 loi thuc khc nhau (A, B, C v D; thuc D l placebo) qua 5 la; s liu thu c trnh by bng di. Cho bit nh hng ca thuc n t bo lymph?

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La 1 La 2 La 3 La 4 La 5

Thuc A 7,1 6,1 6,9 5,6 6,4

Thuc B 6,7 5,1 5,9 5,1 5,8

Thuc C 7,1 5,8 6,2 5,0 6,2 Thuc D 6,7 5,4 5,7 5,2 5,3

Cu trc s liu

S liu ca bi ton ny ch c mt cu trc duy nht trong Minitab; bao gm 3 ct:

1) ct S lng t bo C1 (TEBAO), 2) ct Thuc C2 (THUOC) v 3) ct La C3 (LUA) Trong th nghim ny i tng th nghim b tc ng bi yu t chnh (yu t th nghim) v yu t ph (khi)

So snh s sai khc gia cc nghim thc bng Phn tch phng sai (ANOVA) Stat ANOVA Two-Way...

Chn Store residuals c RESI1

Chn OK c kt qu Two-way ANOVA: TEBAO versus THUOC; LUA Source DF SS MS F P THUOC 3 1.8455 0.61517 11.59 0.001 LUA 4 6.4030 1.60075 30.16 0.000 Error 12 0.6370 0.05308 Total 19 8.8855 S = 0.2304 R-Sq = 92.83% R-Sq(adj) = 88.65%

Xc sut ca php th i vi yu t Thuc P = 0,001 < 0,05 (), bc b gi thit H0 v chp nhn i thit H1. Kt lun thuc c nh khc nhau ln t bo lymph ca chut (P < 0,05).

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V d 1.8: Mt th nghim c tin hnh xc nh nh hng ca 3 cng thc thc n (A1, A2 v A3) n tng trng trung bnh trn ngy (gam / ngy) ca b c. B c c cn v chia thnh 4 khi da theo khi lng bt u th nghim. Trong mi khi c 6 ng vt th nghim c chn ra v c phn ngu nhin v vi cc nghim thc. S liu thu thp sau khi kt thc th nghim nh sau:

Khi

I II III IV

A1 826 806 864 834

795 810

850 845

A2 827 800 871 881

729 709

860 840

A3 753 773 801 821

736 740

820 835

Cu trc s liu m hnh th nghim trong v d 1.8 tng t nh v d 1.7. Trong v d 1.8 c 2 n v th nghim mt nghim thc v khi v vy ngoi tc ng ca khi v cng thc th nghim cn tn ti s tng tc gia khi v cng thc th nghim.

Stat ANOVA General Linear Model...

Chn Comparisons so snh cp i

Chn OK c kt qu General Linear Model: KL versus CT, KHOI Factor Type Levels Values CT fixed 3 A1, A2, A3 KHOI fixed 4 I, II, III, IV Analysis of Variance for KL, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P CT 2 8025.6 8025.6 4012.8 7.08 0.005 KHOI 3 33816.8 33816.8 11272.3 19.90 0.000 Error 18 10197.4 10197.4 566.5 Total 23 52039.8 S = 23.8017 R-Sq = 80.40% R-Sq(adj) = 74.96%

Xc sut ca php th i vi yu t Thc n P = 0,005 nn bc b gi thit H0 v chp nhn i thit H1. Kt lun cng thc n c nh n tng trng ca b. Xc sut ca php th i vi yu t KHOI P = 0,000 nn bc b gi thit H0 v chp nhn i thit H1. Kt lun KHOI c nh n tng trng ca b.

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1.6. Tng quan v hi quy tnh h s tng quan v xy dng phng trnh hi quy, s liu lun phi to

thnh tng b v c nhp vo tng ct i tng ch tiu. V d 1.9: Tin hnh cn khi lng (P), o ng knh ln (D) v ng knh b (d)

ca 22 qu trng g. S liu thu c trnh by bng di y. P (gam) 66,80 60,10 71,20 61,60 61,20 59,00 67,90 59,00 51,50 62,60 64,20 D (mm) 58,37 54,95 60,58 56,73 57,36 53,26 57,07 58,17 52,28 55,62 56,82 d (mm) 45,12 44,35 45,56 44,34 43,57 44,86 46,27 42,82 41,91 44,95 44,79 P (gam) 71,20 54,20 54,50 69,10 55,90 66,00 68,00 62,00 56,70 67,00 53,80 D (mm) 61,15 54,24 54,99 60,99 54,41 58,19 59,93 56,80 55,66 58,49 52,44 d (mm) 46,00 42,58 42,32 44,85 42,62 45,69 45,50 44,20 42,41 45,56 43,38

Cu trc s liu trong Worksheet

Lu : tnh h s tng quan v xy dng phng trnh hi quy, s liu lun phi to thnh tng cp v c nhp vo tng ct i tng ch tiu. 1) Ct Khi lng C1 (KL) 2) Ct ng knh ln C2 (DL) 3) Ct ng knh b C3 (DB)

a. H s tng quan Gi thit i vi kim nh hai pha H0: = 0 v i thit H1: 0, trong l

tng quan gia 2 bin nghin cu. Stat Basic Statistics Correlation...

Chn OK c kt qu Correlations: KL; DL; DN KL DL DL 0.897 0.000 DN 0.905 0.648 0.000 0.001 Cell Contents: Pearson correlation P-Value

Chn Display p-values hin th xc sut i vi tng h s tng quan. Chn Store matrix (display nothing) nh ma trn h s tng quan vo b nh m v khng hin th kt qu ra mn hnh.

H s tng quan gia khi lng v ng knh ln l 0,897; khi lng v ng knh b l 0,905; ng knh ln v ng knh b l 0,648. Xc sut i vi tng h s

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tng quan (p-values) u b hn 0,05 () v vy kt lun mi quan h gia cc ch tiu ny khc 0.

b. Phng trnh hi quy tuyn tnh C th xy dng hi quy n bin y = a + bx hoc a bin y = a + b1x1 + b2x2

+...+bnxn. C th xy dng phng trnh hi tuyn tnh n bin quy c tnh khi lng trng thng qua ng knh ln/ng knh b hoc a bin thng qua ng knh ln v ng knh b. Stat Regression Regression...

Response: Khai bo ct C1 (KL) bin ph thuc. Predictors: Khai bo ct C2 (DL) bin c lp. Chn OK c kt qu

Regression Analysis: KL versus DL The regression equation is KL = - 53.7 + 2.04 DL Predictor Coef SE Coef T P Constant -53.67 12.78 -4.20 0.000 DL 2.0379 0.2250 9.06 0.000 S = 2.69651 R-Sq = 80.4% R-Sq(adj) = 79.4% Analysis of Variance Source DF SS MS F P Regression 1 596.60 596.60 82.05 0.000 Residual Error 20 145.42 7.27 Total 21 742.02 Unusual Observations Obs DL KL Fit SE Fit Residual St Resid 7 57.1 67.900 62.629 0.579 5.271 2.00R 8 58.2 59.000 64.871 0.658 -5.871 -2.25R R denotes an observation with a large standardized residual.

Phng trnh hi quy c tnh khi lng (y) thng qua ng knh ln (x) y = -53,7 + 2,04x. Bng th nht trong phn kt qu kim nh cc h s ca phng trnh hi quy. Vi xc

sut P = 0,000 ta c th kt lun cc h s trong phng trnh hi quy khc 0 (P < 0,05). H s xc nh ca phng trnh R = 80,4%, hiu chnh R = 79,4%. Cc quan st ngoi lai (Unusual Observations) trong m hnh v v d nu trn. Cc

gi tr hng th 7 v 8 trong v d trn c coi l ngoi lai. Stat Regression Regression...

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Predictors: Khai bo ct C2 (DL) v C3 (DN) bin c lp. xy dng phng trnh hi quy a bin, bin c lp bao gm t 2 bin tr ln. Chn OK c kt qu.

Regression Analysis: KL versus DL; DN The regression equation is KL = - 117 + 1.21 DL + 2.48 DN Predictor Coef SE Coef T P Constant -116.555 5.472 -21.30 0.000 DL 1.21473 0.08323 14.60 0.000 DN 2.4764 0.1623 15.26 0.000 S = 0.759757 R-Sq = 98.5% R-Sq(adj) = 98.4% Analysis of Variance Source DF SS MS F P Regression 2 731.05 365.53 633.24 0.000 Residual Error 19 10.97 0.58 Total 21 742.02 Source DF Seq SS DL 1 596.60

Ta c kt qu hon ton tng t nh vic xy dng phng trnh hi quy n gin.

2. NG DNG EXCEL TRONG X L S LIU Phn mm Excel cho php phn tch d liu ni chung, d liu d liu trong chn

nui, th y ni ring, mt cch kh hiu qu thng qua vic s dng menu Tools> Data Analysis (nu khng c mc ny th chn Tools> Add-in > Analysis ToolPak ci t thm). Sau y l mt s cng c x l s liu thng k m Excel cung cp. 2.1. Thng k m t v t chc

2.1.1. Thng k m t Thng k m t cho php tnh cc s c trng mu/ cc gi tr thng k mu nh

trung bnh, lch chun, sai s chun, trung v, mode... S liu tnh ton c b tr theo ct hoc theo dng.

a. Cc bc thc hin trong Excel Chn Tools>Data Analysis>Descriptive Statistics, khai bo cc mc sau trong hp thoi: - Input range: min d liu k c nhn. - Grouped by: Column (s liu theo ct, Row s liu theo hng). - Labels in first row: nh du vo ny nu c nhn dng u.

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- Confidence level for mean: 95% ( tin cy 95%).

- K-th largest: 1 (1 S ln nht, 2 s ln nh ). - K-th smallest: 1 (1 S nh nht, 2 s nh nh ). - Output range: min ra. - Summary Statistics: nh du nu mun hin cc thng k c bn. - OK. V d 1.1: Khi lng (gam) ca 16 chut ci ti thi im cai sa:

54.1 49.8 24 46 44.1 34 52.6 54.4 56.1 52 51.9 54 58 39 32.7 58.5

Chn Tools>Data Analysis>Descriptive Statistics, sau khai bo hp thoi (xem hnh sau)

Kt qu thu c cho trong hnh sau:

b. Phn tch cc kt qu thu c Mt s nhn xt trn cc thng k thu c nh sau: - Mean cho ta gi tr trung bnh ca dy s. - Median cho trung v (gi tr im gia ca dy s). Nu 2 gi tr Mean v Median xp x nhau ta th s liu l cn i. - Phng sai mu hay lch chun mu cho ta bit phn tn ca s liu quanh gi

tr trung bnh, nu cc gi tr ny cng nh chng t s liu cng tp trung.

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- Kurtosis nh gi ng mt phn phi ca dy s liu c nhn hn hay t hn ng mt chun tc. Nu trong khong t -2 n 2 th c th coi nhn xp x nhn chun.

- Skewness nh gi ng phn phi nghing tri hay nghing phi. Nu trong khong t -2 n 2 th c th coi s liu cn i xp x phn phi chun .

- Confidence Level c hiu l na di khong tin cy. Gi s Confidence Level l m th khong tin cy ca trung bnh tng th l: (Mean- m , Mean+m). Trong v d 1.1 ta c khong tin cy 95% ca di bng l:

(47.575 - 5.415 , 47.575 - 5.415), tc l (42.160, 52.990). 2.1.2. T chc Tn s xut hin ca s liu trong cc khong cch u nhau cho php phc ho biu

tn s, cn gi l t chc . v t chc cn phi tin hnh phn t s liu.

a. To min phn t tin hnh phn t s liu (to Bin), cn thc hin cc bc sau: - Dng cc hm Min, Max xc nh gi tr nh nht v gi tr ln nht.Tnh bin

= Max - Min. Da vo ta c th nh s t cn chia. S t c th theo cng thc k=6*log(n), n l s s liu. T ta nh ra khong cch t l h = bin /k.

nh ra gi tr cn di v gi tr cn trn ca min phn t, thng th ly gi tr cn di nh hn Min, gi tr cn trn ln hn Max.

- Ghi gi tr cn di vo u ca min phn t. Con tr ti ny. - Chn Edit > Fill > Series khai bo cc mc: + Trong mc Series in chn Columns (d liu theo ct). + Trong mc Type chn Linear (d liu tng theo cp s cng). + Trong Step value: nhp gi tr bc tng (h). + Trong Stop value: nhp gi tr cui (gi tr cn trn). + OK. V d 1.2: Da trn 30 s liu v chiu di c ta to min phn t (Bin) nh trn hnh

sau, vi min phn t t D2 ti D12 (k c nhn), gi tr cn di l 10, cn trn l 55, gi tr bc tng 5.

Hnh 1.1. To min Bin cho cc s liu v chiu di c

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b. V t chc Chn Tools> Data Analysis> Histogam khai bo cc mc: - Input range: min d liu. - Input Bin: min phn t. - Labels: nhn dng u nu c. - Output range: Min kt qu. - Pareto: tn s sp xp gim dn. - Cumulative Percentage: Tn sut cng dn %. - Chart output: Biu . - OK. Trong v d 1.2 chn Tools> Data Analysis> Histogam v khai bo nh trong hnh sau:

Hnh 1.2.

Cc khai bo v t chc

c. Kt qu v t chc

Hnh 1.3.

T chc

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d. Phn tch kt qu - Tn s s liu ri vo tng khong c ghi cn trn ca khong (Chng hn, c 2

s liu thuc vo khong (10,15], v vy s 2 c ghi tng ng vi s 15 l cn trn). - Nhn vo tn s ta c th thy trong khong no s liu xut hin nhiu nht. - Nhn vo hnh dng ca t chc cn cho bit: dy s liu kho st c v chiu

di ca c c th coi l tun theo lut chun.

2.2. So snh v kim nh Bi ton t ra l cn so snh phng sai ca 2 bin hoc so snh trung bnh ca 2

bin vi nhau. gii quyt vn ny ngi ta a v bi ton kim nh gi thit hai phng sai bng nhau hoc bi ton kim nh gi thit hai trung bnh bng nhau.

2.2.1. Kim nh s bng nhau ca 2 phng sai Bi ton y l thng qua hai mu kim nh gi thuyt H0: 12 =22 (phng sai

ca bin 1 bng phng sai ca bin 2) vi i thuyt H1: 1222 mc ngha . a. Cc bc thc hin Chn Tools >Data Analysis > F-Test Two Sample for Variance, sau ln lt tr li: - Variable 1 Range: min d liu ca bin 1, k c dng u cha nhn. - Variable 2 Range: Min d liu ca bin th hai, k c dng u cha nhn. - Labels: Chn mc ny nu min d liu chn c dng nhn. - Alpha: Mc ngha (thng l 0.05 hoc 0.01). - Output Range: Chn min trng a ra kt qu. - OK: Kt thc. V d 1.3: C 2 ging b, tin hnh chn ngu nhin v cn 12 con i vi ging th

nht v 15 con i vi ging th 2. Khi lng (kg) thu c nh sau: Hy kim nh gi thit: phng sai ca 2 dy s trn l nh nhau. Chn Tools >Data Analysis > F-Test Two Sample for Variance v khai bo nh sau:

So snh khi lng ca 2 ging b Ging 1 188 180 199 191 196 204 190 201 195 221 187 203 Ging 2 148 146 153 135 151 146 164 147 162 140 159 182 165 165 142

32

Kt qu thu c nh sau: F-Test Two-Sample for Variances

Ging 1 Ging 2 Mean 196.1750 153.7000 Variance 112.7002 151.3243 Observations 12 15 df 11 14 F 0.7448 P(F z-Test: Two Sample for Means, sau ln lt tr li: - Variable 1 Range: min d liu ca bin 1, k c dng u cha nhn. - Variable 2 Range: Min d liu ca bin th hai, k c dng u cha nhn. - Labels: Chn mc ny nu min d liu chn c dng nhn.

33

- Hypothesized means difference: Gi thuyt v hiu hai trung bnh ca hai tng th. Nu ly gi thuyt H0: m1=m2 th ghi 0. Nu ly gi thuyt H1: m1=m2+d th ghi d (d l 1 s) .

- Variable 1 variance: Phng sai ca bin 1 (nhp 21). - Variable 2 variance: Phng sai ca bin 2 (nhp 22). - Output Range: Chn min trng a ra kt qu. - Chn OK. V d 1.4: Thc hin th nghim o chiu di ca 2 ging c x v y. Vi ging c x ly

mu o 10 con c, Vi ging c y ly mu o 12 con c, ta c bng s liu sau, bit phng sai ca ging c x l 11.6, ca ging c y l 10.9.

Hy so snh chiu di ca 2 ging c x v y. Chn Tools >Data Analysis > z-Test: Two Sample for Means, sau khai bo theo

hp thoi sau:

Kt qu so snh hai mu cho bng sau: z-Test: Two Sample for Means

x y Mean 20.300 20.833 Known Variance 11.6 10.9 Observations 10 12 Hypothesized Mean Difference 0 z -0.37084 P(Z

34

- Observations: S quan st n1 v n2. - Hypothesized means difference: Gi thuyt v hiu hai trung bnh ca hai tng th. Nu

ly gi thuyt H0: m1=m2 th ghi 0. Nu ly gi thuyt H1: m1=m2+d th ghi d (d l 1 s) . - z: Gi tr z thc nghim tnh theo cng thc sau:

z=(a1-a2)/Sqrt(21/n1 + 22/n2 ) - P(ZData Analysis > t-Test: Paired Two Sample for Means, sau ln lt

tr li: - Variable 1 Range: min d liu ca bin 1, k c dng u cha nhn. - Variable 2 Range: Min d liu ca bin th hai, k c dng u cha nhn. - Labels: Chn mc ny nu min d liu chn c dng nhn

35

- Hypothesized means difference: Gi thit v hiu hai trung bnh ca hai tng th. Nu ly gi thuyt H0: m1=m2 th ghi 0. Nu ly gi thuyt H0: m1=m2+d th ghi d (d l mt s no )

- Output Range: Chn min trng t ra kt qu. V d 1.5: Tng trng (pound) ca 10 cp b sinh i ging ht nhau di hai ch

chm sc A v B khc nhau. B trong tng cp c bt thm ngu nhin v mt trong hai cch chm sc.

Hy kim nh gi thit H0: Tng trng trung bnh hai cch chm sc nh nhau, i thit H1: Tng trng trung bnh khc nhau hai cch chm sc vi mc ngha = 0,05. S liu thu c nh sau: Tng trng cch A 43 39 39 42 46 43 38 44 51 43 Tng trng cch B 37 35 34 41 39 37 35 40 48 36

Chn Tools >Data Analysis > t-Test: Paired Two Sample for Means, khai bo hp thoi nh sau:

Kt qu thu c nh sau:

t-Test: Paired Two Sample for Means

Tng trng cch A Tng trng cch B Mean 42.8 38.2 Variance 14.6222 17.0667 Observations 10 10 Pearson Correlation 0.8820 Hypothesized Mean Difference 0 df 9 t Stat 7.44046 P(T

36

b. Phn tch kt qu Bng kt qu c hai ct cho hai mu quan st. Bng ny c cc hng: - Mean: Trung bnh mu a1, a2. - Variance: Phng sai mu s12, s22. - Observations: S quan st n1 v n2 (bng nhau v bng s cp s liu n). - Pearson Correlation: H s tng quan r ca 2 mu. - Hypothesized means difference: Gi thuyt v hiu hai trung bnh ca hai tng th. Nu

ly gi thuyt H0: m1=m2 th ghi 0. Nu ly gi thuyt H1: m1=m2+d th ghi d (d l 1 s) . - df: Bc t do bng s cp tr 1 (n-1). - t Stat: Gi tr t thc nghim - P(T m2, c ngha l tng trng cch A ln hn tng trng ca cch B.

2.2.4. So snh trung bnh khi ly mu c lp vi gi thuyt hai phng sai bng nhau Trng hp mu ln: Khi vic rt hai mu quan st t hai tng th c tin hnh mt

cch c lp th chng ta c hai mu c lp. Nu dung lng ca c hai mu u ln (thng quy c l n1 30, n2 30) ta c th tin hnh z-test nhng thay hai phng sai ca tng th 21v 22 bng phng sai mu s12 v s22.

Trng hp mu b (n1,n2 nh hn 30) th ta gp bi ton kh, gi tn l bi ton Berens Fisher. Trong trng hp ny, nu coi hai phng sai ca hai tng th bng nhau (cn kim nh gi thuyt ph v s bng nhau ca hai phng sai) th c th tip tc tnh ton nh sau:

a. Cc bc thc hin: Chn Tools >Data Analysis > t-Test: Two-Sample Assuming Equal Variances, sau

ln lt tr li: - Variable 1 Range: min d liu ca bin 1, k c dng u cha nhn. - Variable 2 Range: Min d liu ca bin th hai, k c dng u cha nhn. - Labels: Chn mc ny nu min d liu chn c dng nhn - Hypothesized means difference: Gi thit v hiu hai trung bnh ca hai tng th.

Nu ly gi thuyt H0: m1=m2 th ghi 0. Nu ly gi thuyt H0: m1=m2+d th ghi d (d l mt s no ) .

- Output Range: Chn min trng t ra kt qu.

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V d 1.6: C 2 ging b, tin hnh chn ngu nhin v cn 12 con i vi ging th nht v 15 con i vi ging th 2. Khi lng (kg) thu c nh sau:

So snh khi lng ca 2 ging b Ging 1 188 180 199 191 196 204 190 201 195 221 187 203

Ging 2 148 146 153 135 151 146 164 147 162 140 159 182 165 165 142

Kim nh gi thit H0: khi lng trung bnh ca 2 ging b nh nhau. - Trc tin ta phi kim nh s bng nhau ca hai phng sai, trong mc 1.2.1 v

v d 1.3 ta c kt lun hai phng sai bng nhau. - Bc tip theo ta i so snh trung bnh vi gi thit phng sai bng nhau: Chn Tools >Data Analysis > t-Test: Two-Sample Assuming Equal Variances, khai

bo hp thoi nh sau:

Kt qu nh sau: t-Test: Two-Sample Assuming Equal Variances

Ging 1 Ging 2 Mean 196.175 153.7 Variance 112.7002 151.3243 Observations 12 15 Pooled Variance 134.3297 Hypothesized Mean Difference 0 df 25 t Stat 9.46241 P(T

38

b. Phn tch kt qu Bng kt qu thu c c hai ct cho hai mu quan st, v ln lt c cc hng sau: - Mean: Trung bnh mu a1, a2. - Variance: Phng sai mu s12, s22. - Observations: S quan st n1 v n2. - Pooled Variance: Phng sai chung tnh theo cng thc

s2=((n1-1)s12+( n2-1)s22)/(n1+n2-2) - Hypothesized means difference: Gi thit v hiu hai trung bnh ca hai tng th.

Nu ly gi thuyt H0: m1=m2 th ghi 0. Nu ly gi thuyt H0: m1=m2+d th ghi d (d l mt s no ) .

- df: Bc t do (n1+ n2-2) - t Stat: Gi tr t thc nghim tnh theo cng thc:

t = (a1-a2)/Sqrt(s2(1/n1+1/n2)) - P(T m2, c ngha l khi lng trung bnh ca ging b 1 ln hn khi lng trung bnh ca ging b 2.

2.2.5. So snh trung bnh khi ly mu c lp vi gi thuyt hai phng sai khc nhau Trong trng hp mu b v phng sai khc nhau th c th thc hin theo cc bc sau:

a. Cc bc thc hin Chn Tools >Data Analysis > t-Test: Two-Sample Assuming Unequal Variances, sau

ln lt tr li: - Variable 1 Range: min d liu ca bin 1, k c dng u cha nhn. - Variable 2 Range: Min d liu ca bin th hai, k c dng u cha nhn. - Labels: Chn mc ny nu min d liu chn c dng nhn - Hypothesized means difference: Gi thit v hiu hai trung bnh ca hai tng th.

Nu ly gi thuyt H0: m1=m2 th ghi 0. Nu ly gi thuyt H0: m1=m2+d th ghi d (d l mt s no )

- Output Range: Chn min trng t ra kt qu. V d 1.7: Thc hin th nghim o chiu di ca 2 ging c x v y. Vi ging c x ly

mu o 10 con c, Vi ging c y ly mu o 12 con c, ta c bng s liu sau. Hy so snh chiu di ca 2 ging c x v y.

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x 15 17 20 23 25 17 18 22 24 22 y 14 12 13 28 12 17 25 24 30 21 23 30

* Bc 1: Kim nh s bng nhau ca hai phng sai, thc hin theo mc 1.2.1, ta c kt qu sau:

F-Test Two-Sample for Variances

x y Mean 20.3 20.75 Variance 11.5667 48.2045 Observations 10 12 df 9 11 F 0.23995 P(FData Analysis > t-Test: Two-Sample Assuming Unequal Variances, khai

bo hp thoi nh sau:

Kt qu thu c nh sau: t-Test: Two-Sample Assuming Unequal Variances x y Mean 20.3 20.75 Variance 11.5667 48.2045 Observations 10 12 Hypothesized Mean Difference 0 df 17 t Stat -0.19784 P(T

40

b. Phn tch kt qu nh gi kt qu nh trng mc 1.2.4 trn. Kt lun: Theo kt qu trn gi thuyt H0 vn c chp nhn mc ngh 0.05 do P

hai pha ln hn mc ngha = 0.05, tc l chiu di ca 2 ging c khng khc nhau.

2.3. Phn tch phng sai Phn tch phng sai l cng c ch yu phn tch cc s liu khi theo di nh

hng ca cc nhn t (factor) v nh hng tng tc ca chng. thu thp s liu, th nghim cn c thit k ph hp vi mc ch nghin cu v iu kin c th ni tin hnh th nghim. phn tch mt nhn t, th nghim thng c thit k theo kiu hon ton ngu nhin, kiu khi hon ton ngu nhin, hay vung La tinh. phn tch hai nhn t, th nghim c b tr theo kiu khi ngu nhin, kiu trc giao, kiu chia ln, nh. T ba nhn t tr ln th cn b tr th nghim sao cho mi nhn t c hai mc hay mi nhn t c ba mc.

1.3.1. Phn tch phng sai mt nhn t Phn tch phng sai mt nhn t c s dng phn tch s liu khi theo di nh

hng ca cc mc ca nhn t ti kt qu, nh nh hng ca cc cng thc cho n n nng sut tht ln, nh hng ca cc cng thc iu tr thuc n t l bnh...

phn tch phng sai mt nhn t cn thit k th nghim kiu hon ton ngu nhin, mi mc lp li mt s ln, s ln lp ca cc mc ca nhn t khng cn phi bng nhau. S liu c in theo ct hoc theo hng (nu vo theo hng th mi hng ng vi mt mc ca nhn t), u tin ghi tn mc, cc tip theo ghi s liu.

Gi s th nghim c b tr theo k mc tc ng khc nhau ca nhn t A, mi mc c lp li ni ln, i= k,1 v n1 + n2++ nk l tng s cc th nghim.

Gi Xij l s liu thu c ca th nghim mc i v ln lp th j. Ta c bng thc nghim sau:

Mc ca nhn t A S liu thc nghim 1 X11 X12 X1n1

2 X21 X22 X2n2

k Xk1 Xk2 Xknk

Nu k m ng c phn phi chun N(mi,2), i = k,1 th i lng2

21

2

SSF =

Trong S21 l phng sai gy ra do tc ng ca cc mc, S22 l phng sai do ngu nhin. F c phn phi Fisher vi k-1; n-k bc t do.

Bi ton phn tch phng sai a v vic kim nh gi thit: H0: m1= m2= = mk i gi thit H1: C t nht hai tr trung bnh khc nhau. Gi thit H0 b bc b mc nu: F > F(k-1,n-k) vi F(k-1,n-k) l s tm c

bng F, mc vi k-1, n-k bc t do.

41

a. Cc bc thc hin trong Excel Chn Tools> Data Analysis > Anova: Single Factor v khai bo: - Input range: Khai bo min d liu vo (mt ch nht bao trm ton b cc cha

tn mc v ton b cc s liu). - Grouped by: Column (s liu theo ct) hoc row (s liu theo hng) - Label in First column: nhn dng u. - Alpha: 0.05 mc ngha . - Output range: min ra. - Chn nt OK

b. Phn tch kt qu - Kt qu in ra gm cc thng k c bn cho tng mc (trung bnh, lch chun...) v

bng phn tch phng sai. - Nu gi tr xc sut P-value >= alpha (hoc F thc nghim F l thuyt) th bc b Ho

chp nhn H1 cc cng thc c tc ng khc nhau ti kt qu. - Khi kt lun cc cng thc c tc ng khc nhau ti kt qu th phi tin hnh bc

tip theo l so snh cc cng thc rt ra cng thc no tt nht.

1.3.2. So snh cc trung bnh dng ngng so snh LSD (Least sinificance diffrence) Phn mm Excel khng cho php so snh cc trung bnh ca cc nhm ng vi cc

mc ca nhn t (cc cng thc). Tuy nhin, nu cn so snh trung bnh mi (vi ri ln lp) vi trung bnh mj (rj ln lp) ngi dng c th t tnh thm LSD (Least Significance Difference) theo cng thc LSD = t,f SQRT(s2(1/ri + 1/rj)), trong s2 l phng sai chung c c lng bi trung bnh ca sai s bnh phng trong ni b nhm (MS within groups), = 1-p, v t,f l gi tr t ca bng Student ng vi mc ngha v f bc t do. t,f c th tm c bng cch tra bng s hay bng hm TINV trong Excel.

* Tnh tr tuyt i ca hiu cc trung bnh mi, mj: |mi- mj| * So snh nu |mi- mj| > LSD th hai trung bnh l khc nhau, ngc li 2 trung bnh

c coi l khng khc nhau. Thng thng ngi ta lp bng hiu cc trung bnh, sau lp bng ghi kt qu so snh.

V d 1.8: Theo di tng trng ca c (kg), th nghim vi 5 cng thc nui (A, B, C, D, E). . S liu thu c nh bng sau. Hy cho bit cng thc no tt nht

* Cc bc thc hin trong Excel

42

Chn Tools> Data Analysis > Anova: Single Factor v khai bo theo hp thoi sau:

* Kt qu thu c nh sau:

Anova: Single Factor

SUMMARY

Groups Count Sum Average Variance

A 4 3.55 0.8875 0.002292 B 4 1.7 0.425 0.000433 C 4 3.05 0.7625 0.008958 D 4 3.75 0.9375 0.002292 E 4 3.8 0.95 0.001667

ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.76325 4 0.190813 60.99494 4.24E-09 3.055568 Within Groups 0.046925 15 0.003128

Total 0.810175 19

* Kt lun: P- value < 0.05 (mc ngha ca kim nh) nn bc b Ho chp nhn H1

cc cng thc c tc ng khc nhau ti kt qu. * So snh cc trung bnh:

43

2.3.3. Phn tch phng sai hai nhn t Khi phn tch phng sai hai nhn t A v B th c th xy ra cc hai trng hp:

trng hp A v B khng tng tc (bin ng gy nn bi tc ng ng thi ca A v B gn st 0) v trng hp A v B tng tc (nu tri li). Phn tch phng sai mt nhn t b tr kiu khi hon ton ngu nhin c coi l trng hp ring ca phn tch phng sai hai nhn t khng tng tc (nhn t khi l nhn t th hai khng tng tc vi nhn t th nht). Khi phn tch phng sai hai nhn t khng tng tc, s liu cn c sp xp theo cch sau: hng l cc mc ca nhn t th nht, ct l cc mc ca nhn t th hai (trong trng hp cn phn tch phng sai mt nhn t b tr kiu khi ngu nhin th hng l cc mc ca nhn t, ct l cc khi ngu nhin).

a. Phn tch phng sai hai nhn t khng tng tc (khng lp) Xt trng hp th nghim lin quan ti 2 nhn t A v B, mi nhn t c mt s mu.

Xt trng hp khng c tng tc gia Av B. Nhn t A

Nhn t B

1 2 kA

1 X11 X12 X1kA

2 X21 X22 X2kA

kB XkB1 XkB2 XkBkA

44

Ta i kim nh gi thuyt H0A v H0B vi cc i thuyt H1A v H1B (Gi thit H0A: Cc mc ca nhn t A c tc ng nh nhau. Gi thit H0B: Cc mc ca nhn t B c tc ng nh nhau)

Cc i lng thng k: R

AA

s

sF 22

= v R

B

B s

sF 22

=

Trong S2A l phng sai do nhn t A, S2B l phng sai do nhn t B, S2R l phng sai do nhn t ngu nhin.

Nu: FA > F 0.05A kt lun cc mc ca nhn t theo ct (A) c nh hng khc nhau n s liu nghin cu.

FB > F 0.05B kt lun cc mc ca nhn t theo dng (B) c nh hng khc nhau n s liu nghin cu.

* Cc bc thc hin trong Excel Chn Tools >Data Analysis >Anova: Two Factor Without Replication sau khai bo

tip cc thng tin trong hnh sau:

Hnh 1.4. Hp thoi khai bo phn tch phng sai khng tng tc * Phn tch kt qu - Nu FA > F Crit A th cc mc ca nhn t A c nh hng khc nhau n kt qu. - Nu kt lun cc mc ca nhn t A c nh hng khc nhau n kt qu th ta tin

hnh so snh trung bnh ca cc mc trong nhn t A theo ch s LSD (tng t trong phn

phn tch phng sai mt nhn t). - Nu FB > F Crit B th cc mc ca nhn t B c nh hng khc nhau n kt qu. - Nu kt lun cc mc ca nhn t B c nh hng khc nhau n kt qu th ta tin

hnh so snh trung bnh ca cc cng thc trong nhn t B theo ch s LSD (tng t trong

phn phn tch phng sai mt nhn t). Ch : F l F thc nghim, F Crit l F l thuyt c th tm bng hm FINV(...) F Crit A = FINV(, kA -1, (kA-1)(kB-1)) , F Crit B = FINV(, kB -1, (kA-1)(kB-1)) V d 1.9: Mead v cng s nghin cu s lng t bo Lymph chut (1000 t

bo mm-3mu) , s dng 4 loi thuc, qua 5 la. S liu c cho trn bng sau. Thc hin trong Excel khai bo d liu theo hp thoi sau:

45

Kt qu x l cho trong bng sau: Anova: Two-Factor Without Replication

SUMMARY Count Sum Average Variance Thuc A 5 32.1 6.42 0.367 Thuc B 5 28.6 5.72 0.442 Thuc C 5 30.3 6.06 0.578 Thuc D 5 28.3 5.66 0.373

La 1 4 27.6 6.9 0.053333 La 2 4 22.4 5.6 0.193333 La 3 4 24.7 6.175 0.275833 La 4 4 20.9 5.225 0.069167 La 5 4 23.7 5.925 0.235833 ANOVA

Source of Variation SS df MS F P-value F crit Rows 1.8455 3 0.615167 11.5887 0.0007392 3.490295 Columns 6.403 4 1.60075 30.15542 3.544E-06 3.259167 Error 0.637 12 0.053083

Total 8.8855 19

Kt lun: + Vi nhn t thuc th khi s dng cc loi thuc khc nhau c nh hng ti s

lng t bo lymph trong mu (F > F crit). + Vi nhn t la th cc la khc nhau cng nh hng ti s lng t bo lymph

trong mu (F > F crit). b. Phn tch phng sai hai nhn t c tng tc

(c lp) Trong trng hp ny khi phn tch phng sai ta phi tnh n s tc ng ng thi

ca A v B. S liu sp xp nh sau: - Nhn t 1 nh theo hng vi cc mc khc nhau, nhn t 2 nh theo ct vi cc

mc khc nhau.

46

- Mi mc ca nhn t 1 (thng gi l nhn t A) c dnh m hng (cho m ln lp) cn mi mc ca nhn t 2 (thng gi l nhn t B) l 1 ct.

- Tn mi mc ca nhn t A ch vit mt ln trong u tin ca mc , cc tn mc ca nhn t B th ghi u mi ct. Cc t hng 2 ct 2 tr i ghi s liu.

S liu b tr theo bng sau: B

A 1 2 ... kB

X111 X121 ... X1kB1

X112 X122 ... X1kB2

... ... ... ...

1

X11m X12m ... X1kBm

X211 X221 ... X2KB1

X212 X222 ... X2kB2

... ... ... ...

2

X21m X22m ... X2kBm

... ... ... ... ...

XkA11 XkA21 ... XkAkB1

XkA12 XkA22 ... XkAkB2

... ... ... ...

kA

XkA1m XkA2m ... XkAkBm

Tng s lng quan st: n = m kA kB

Cc i lng thng k: R

ABAB

R

BB

R

AA S

SFSSF

SSF 2

2

2

2

2

2

,, ===

Trong S2A l phng sai do nhn t A, S2B l phng sai do nhn t B, SAB l phng sai do tng tc AB, S2R l phng sai do nhn t ngu nhin.

* Cc bc thc hin trong Excel Chn Tools >Data Analysis >Anova: Two Factor With Replication, sau khai bo

cc thng tin nh sau:

Trong Rows per sample l s ln lp.

47

* Phn tch kt qu - Nu FA > F Crit A th cc mc ca nhn t A c nh hng khc nhau n kt qu. - Nu FB > F Crit B th cc mc ca nhn t B c nh hng khc nhau n kt qu. - Nu FAB > F Crit AB th tng tc A B c nh hng n kt qu. V d 1.10: Mt nghin cu tin hnh xc nh nh hng ca vic b sung 2 loi

vitamin (A v B) vo thc n tng trng (kg/ngy) ca ln. Hai mc i vi vitamin A (0 v 4 mg) v 2 mc i vi vitamin B (0 v 5 mg). S liu thu c khi kt thc th nghim c trnh by nh sau:

Vitamin A 0 mg 4 mg Vitamin B 0 mg 5 mg 0 mg 5 mg

0.585 0.567 0.473 0.684 0.536 0.545 0.450 0.702 0.458 0.589 0.869 0.900 0.486 0.536 0.473 0.698 0.536 0.549 0.464 0.693

Khi x l trong Excel s liu c b tr li nh sau:

Chn Tools >Data Analysis >Anova: Two Factor With Replication, sau khai bo cc thng tin nh sau:

48

Ch : Min d liu vo (Input Range) A2: C12. Khng chn c nhn Vitamin B, m y ch nhp xem choo. S ln lp l 5.

Kt qu thu c nh bng sau: Anova: Two-Factor With Replication SUMMARY 0 mg 5 mg Total

0 mg Count 5 5 10 Sum 2.601 2.786 5.387 Average 0.5202 0.5572 0.5387 Variance 0.0024342 0.0004432 0.00165912

4 mg Count 5 5 10 Sum 2.729 3.677 6.406 Average 0.5458 0.7354 0.6406 Variance 0.0327317 0.0085118 0.02831604

Total Count 10 10 Sum 5.33 6.463 Average 0.533 0.6463 Variance 0.015811333 0.0128009

ANOVA Source of Variation SS df MS F P-value F crit Sample 0.05191805 1 0.05191805 4.706889479 0.045448 4.493998 Columns 0.06418445 1 0.06418445 5.818961082 0.028222 4.493998 Interaction 0.02910845 1 0.02910845 2.638971553 0.123804 4.493998 Within 0.1764836 16 0.01103023 Total 0.32169455 19

Theo kt qu x l, ta rt ra kt lun: - Vitamin A c nh hng n tng trng ca ln (F > F crit). - Vitamin B c nh hng n tng trng ca ln (F > F crit). - Tng tc ca Vitamin A v Vitamin B khng nh hng n tng trng ca ln (F < F crit).

2.4. Tng quan v Hi quy

2.4.1. H s tng quan H s tng quan dng o mc quan h gia 2 bin. H s tng quan c th

nhn gi tr t -1 n +1. Nu 1 bin theo chiu tng cn bin kia th gim th h s tng quan l m. Ngc li nu c 2 bin u theo chiu tng th h s tng quan dng. H s tng quan || 0,7 tng quan tuyn tnh. || = 1 th quan h hon ton tuyn tnh.

H s tng quan c k hiu l i vi tng th v k hiu l r i vi mu. * Tnh h s tng quan mu r

49

i vi 2 bin x v y, h s tng quan mu r c tnh theo cng thc sau:

r =

( ) ( )yx

ii

ss)1n(

n

1iYX yx

=

y x v sx l trung bnh v lch chun mu i vi mu th nht, y v sy l trung bnh v lch chun ca mu th 2.

* Tnh h s tng quan trong Excel: Excel cho php tnh h s tng quan n gia cc bin sp xp thnh mt bng gm

n hng, n ct (mi ct l 1 bin). a. Cc bc thc hin Chn Tools>Data Analysis>Correlation v khai bo cc mc: - Input range: min d liu k c nhn. - Grouped by: Column (s liu theo ct). - Labels in first row: nh du vo ny nu c nhn dng u. - Output range: min ra. - OK.

b. Phn tch kt qu - H s tng quan ca dng v ct ghi giao gia dng v ct. - H s tng quan m

(< 0) th hin mi tng quan nghch bin. - Cc h s tng quan c gi tr tuyt i xp x 0.7 tr ln th hin mi tng quan

tuyn tnh (tng quan mnh) gia hai bin. V d 1.11: Xc nh mi tng quan gia khi lng ca g mi (kg) v thu nhn

thc n trong mt nm (kg). Tin hnh quan st 10 g mi v thu c kt qu sau: Khi lng g mi 2.3 2.6 2.4 2.2 2.8 2.3 2.6 2.6 2.4 2.5 Khi lng thc n 43 46 45 46 50 46 48 49 46 47

- Chn Tools>Data analysis>Correlation. - Khai bo cc mc nh hnh sau:

50

- Kt qu thu c trn bng sau: Khi lng g mi Khi lng thc n

Khi lng g mi 1 Khi lng thc n 0.779445522 1

- Kt lun: H s tng quan gia khi lng g mi v khi lng thc n l 0.779445522 , th hin mi tng quan tuyn tnh.

2.4.2. Hi quy tuyn tnh trong excel Excel cho php tm phng trnh hi quy tuyn tnh n y= a+ bx v hi quy tuyn

tnh bi y= a0 + a1x1 + a2x2 + . . . + anxn. Cc bin c lp cha trong n ct, bin ph thuc y trong mt ct, cc gi tr tng ng gia bin c lp v bin ph thuc c xp trn cng mt hng.

a. Cc bc thc hin Chn Tools>Data Analysis>Regression v khai bo cc mc: - Input y range: min d liu bin y. - Input x range: min d liu cc bin x. - Label: nh du vo ny nu c nhn dng u. - Confidence level: 95% ( tin cy 95%). - Constant in zero: nh du nu h s t do a0 = 0 . - Output range: min xut kt qu. - Residuals: nh du vo ny hin phn d hay sai lch gia y thc nghim v

y theo hi quy. - Standardized residuals: nh du hin phn d chun ho. - Residuals plot: nh du hin th phn d. - Line fit plots: nh du hin th cc ng d bo. - Normal probability plot: nh du hin th phn d chun ho. - OK.

b. Phn tch kt qu - Nu h s tng quan bi xp x 0.7 hoc ln hn th m hnh hi quy tuyn tnh l

thch hp (ngc li nn tm m hnh khc). - H s tng quan R square trong cho bit bao nhin % s bin ng ca y l do cc

yu t x gy nn. - H s Adjusted R square nu khng st gn vi R square chng t khng phi tt c

cc bin a vo l thc s cn thit. - Trong bng phn tich hi quy nu mc ngha kim nh F (Significiance F) nh

hn mc ngha th phng trnh hi quy tuyn tnh c chp nhn. - Nhn vo cc h s ca cc bin ta vit c ng hi quy d bo - Nu sut cho ct P-value ca h s ca xi > th h s ca bin c th coi l

bng khng. Trong trng hp ny, cn tin hnh lc bt bin xi c ng hi quy vi cc h s u c ngha.

51

V d 1.12: Xc nh phng trnh hi quy gia khi lng ca g mi (kg) v thu nhn thc n trong mt nm (kg). Tin hnh quan st 10 g mi v thu c kt qu sau:

Khi lng g mi 2.3 2.6 2.4 2.2 2.8 2.3 2.6 2.6 2.4 2.5 Khi lng thc n 43 46 45 46 50 46 48 49 46 47

S liu nhp vo trong Excel theo ct. Chn Tools>Data Analysis>Regression v khai bo cc mc nh trn hnh sau:

Kt qu thu c theo bng sau: SUMMARY OUTPUT

Regression Statistics

Multiple R 0.779445522 R Square 0.607535322

Adjusted R Square 0.558477237 Standard Error 0.121517421

Observations 10

ANOVA

df SS MS F Significance F

Regression 1 0.182868 0.1828681 12.384 0.007856347

Residual 8 0.118132 0.0147665

Total 9 0.301

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Upper 95.0%

Intercept -0.832967033 0.939372 -0.886728 0.4010953 -2.999161935 1.333227869 1.333227869

Khi lng thc n 0.070879121 0.020141 3.5190908 0.0078563 0.024433162 0.11732508 0.11732508

52

BI TP CHNG I Bi 1: Mt th nghim c tin hnh nhm so snh nng Epinephrine (PEP) trong

huyt tng ch cc thuc gy m khc nhau. Trong nghin cu ny 10 cho c chn tham gia th nghim. Ba loi thuc gy m c la chn ngu nhin ln lt gy m cho mi ch. Kt qu thu c nh sau:

Ch s 1 2 3 4 5 6 7 8 9 10 Thuc A 1,07 1,35 0,69 0,28 1,24 1,53 0,49 0,56 1,02 0,30 Thuc B 0,30 0,39 0,63 0,68 0,38 0,21 0,88 0,39 0,51 0,32 Thuc C 0,28 0,51 1,00 0,39 0,29 0,36 0,32 0,69 0,17 0,33

So snh hm lng Epinephrine 3 loi thuc gy m khc nhau? Bi 2: Tin hnh mt nghin cu v cng thc thc n trn gia cm. C 2 cng thc

thc n (Cng thc 1 v Cng thc 2) v tin hnh th nghim trn c con trng v mi. Khi lng thc n thu nhn (gam) th nghim nu trn c trnh by nh sau:

Trng Mi Cng thc 1 Cng thc 2 Cng thc 1 Cng thc 2

70,9 59,2 65,7 50,8 67,9 53,8 59,4 50,5 69,9 47,6 67,7 50,5

So snh lng thc n thu nhn qua th nghim nu trn?