chuong_2.pdf
TRANSCRIPT
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9 Chng 4
B MN TON GVGD: Nguyn nh Huy
Chng 2
P DNG MS-EXCEL TRONG THNG K SUY L
So snh gi tr trung bnh
Phng sai bit trc
D liu tng ng tng cp
Phng sai bng nhau
Phng sai khc nhau
So snh t s
So snh phng sai
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10 Chng 4
B MN TON GVGD: Nguyn nh Huy
A- SO SNH GI TR TRUNG BNH VI PHNG SAI BIT TRC
4.1 Khi nim thng k
Nu mu ln (N > 30) th phng sai ca mu , 2iS , c th c xem l phng sai ca
dn s , 2i
, khi y bn c th p dng trc nghim z so snh gi tr trung bnh ca hai mu
vi phng sai bit trc.
Gi thuyt:
Trc nghim bn phi
211
210
:H
:H
Trc nghim bn tri
211
210
:H
:H
Trc nghim hai bn
211
210
:H
:H
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Chng 4 11
B MN TON GVGD: Nguyn nh Huy
Gi tr thng k:
2
2
2
1
2
1
21
2
2
2
1
2
1
2121
NN
)XX(
NN
)()XX(z
Phn phi chun
Bin lun
Nu z < z (hai bn) hay z/2 (mt bn) Chp nhn gi thuyt H0
4.2 p dng Ms-EXCEL
Th d 6: Ngi ta chn hai mu, mi mu c 10 my, t hai l (I v II c sn xut vi
phng sai bit trc tng ng l 1 v 0,98) kho st thi gian hon thnh cng vic (pht)
ca chng:
I 6 8 9 10 6 15 9 7 13 11
II 5 5 4 3 9 9 6 13 17 12
Hi kh nng hon thnh cng vic ca hai my c khc nhau?
Nhp d liu vo bng tnh
Book1
A B C D E F G H I J K
1 I 6 8 9 10 6 15 9 7 13 11
2 II 5 5 4 3 9 9 6 13 17 12
Hnh 4.1: Hp thoi z-Test: Two Sample for Means
p dng z-test: Two Sample for Means
a. Nhp ln lt n lnh Tools v lnh Data Analysis.
b. Chn chng trnh z-Test: Two Sample for Means trong hp thoi DataAnalysis ri
nhn nt OK.
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Chng 4 12
B MN TON GVGD: Nguyn nh Huy
c. Trong hp thoi z-Test: Two Sample for Means, n ln lt cc chi tit cng ging nh
hai mu c d liu tng ng, song c thm cc chi tit:
- Phng sai ca d liu 1 (Variance 1 Variance),
- Phng sai ca d liu 2 (Variance 2 Variance),
z-Test: Two Sample for Means
I II
Mean 9.4 8.3
Known Variance 1 0.98
Observations 10 10
Hypothesized Mean Difference 0
z 2.472066162
P(Z
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Chng 4 13
B MN TON GVGD: Nguyn nh Huy
N/S
D
N/S
Dt
DD
D
Phn phi Student vi = N 1
Bin lun
Nu t < t hay t/2 ( = N 1) Chp nhn gi thuyt H0
4.4 p dng MS-EXCEL
Th d 7: Hm lng (mg) ca mt ch phm c xc nh trc v sau khi c lo ho
cp tc nh sau:
Trc 7,5 6,8 7,1 7,5 7,2 6,8 6,9 6,7 6,8 6,8
Sau 6,1 6,3 6,5 6,4 6,8 6,3 6,1 6,4 6,5 6,3
Hy cho bit hm lng hot cht c gim sau th nghim?
Nhp d liu vo bng tnh
A B C D E F G H I J K
1 Trc 7.5 6.8 7.1 7.5 7.2 6.8 6.9 6.7 6.8 6.8
2 Sau 6.1 6.3 6.5 6.4 6.8 6.3 6.1 6.4 6.5 6.3
4.5 p dng t-Test: Paired Two Sample for Means
a. Nhp ln lt n lnh Tools v lnh Data Analysis.
b. Chn chng trnh t-Test: Paired Two Sample for Means trong hp thoi Data Analysis
ri nhp nt OK.
c. Trong hp thoi t-Test: Paired Two Sample for Means, ln lt n nh cc chi tit:
- Phm vi ca d liu 1 (Variable 1 Range),
- Phm vi ca d liu 2 (Variable 2 Range),
- Nhn d liu (Labels),
- Ngng tin cy (Alpha),
- Sai bit gia hai gi tr trung bnh c tnh (Hypothesized Mean Difference),
- Phm vi u ra (Output Range).
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Chng 4 14
B MN TON GVGD: Nguyn nh Huy
Hnh 4.2: Hp thoi t-Test: Paired Two Sample for Means
t-Test: Paired Two Sample for Means
Trc Sau
Mean 7.01 6.37
Variance 0.089888889 0.042333333
Observations 10 10
Pearson Correlation 0.023415671
Hypothesized Mean Difference 0
df 9
t Stat 5.627619665
P(T t0,05 = 1,833 Bc b gi thuyt H0.
Vy hm lng thuc gim sau th nghim.
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Chng 4 15
B MN TON GVGD: Nguyn nh Huy
C- SO SNH GI TR TRUNG BNH VI PHNG SAI BNG NHAU
4.6 Khi nim thng k
Trong trng hp hai mu nh (N < 30) c lp v c phng sai bng nhau*, bn c th
p dng trc nghim t ng phng sai (homoscedastic t-test) so snh gi tr trung bnh ca
hai mu y.
Gi thuyt
Nh trng hp hai mu c d liu tng ng tng cp
Gi tr thng k
21
2
2121
11
)()(
NNS
XX
p
21
2
p
21
N
1
N
1S
)XX(
Phn phi Student
2NN21
2NN
S)1N(S)1N(S
21
1
22
2
112
p
Bin lun
Nu t < t hay t/2 ( = N1 + N2 - 2) Chp nhn gi thuyt H0.
4.7 p dng MS-EXCEL
Th d 8: Ngi ta cho 10 bnh nhn ungthuc h cholesterol ng thi cho bnh nhn khc
ung gi c (placebo) ri xt nghim v nng cholesterol trong mu (g/L) ca c hai nhm:
Thuc 1,10 0,99 1,05 1,01 1,02 1,07 1,10 0,98 1,03 1,12
Gi c 1,25 1,31 1,28 1,20 1,18 1,22 1,22 1,17 1,19 1,21
Theo bng kt qu trn, thuc c tc dng h cholesterol trong mu?
Nhp d liu vo bng tnh
A B C D E F G H I J K
1 Thuc 1,10 0,99 1,05 1,01 1,02 1,07 1,10 0,98 1,03 1,12
2 Gi c 1,25 1,31 1,28 1,20 1,18 1,22 1,22 1,17 1,19 1,21
4.8 p dng t-Test: Two-Sample Assuming Equal Variances
a. Nhp ln lt n lnh Tools v lnh Data Analysis.
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Chng 4 16
B MN TON GVGD: Nguyn nh Huy
b. Chn chng trnh t-Test: Two-Sample Assuming Equa! Variances trong hp thoi Data
Analysis ri nhp nt OK.
c. Trong hp thoi t-Test: Two-Sample Assuming Equa! Variances, n nh ln lt cc
chi tit nh hai mu c d liu tng ng.
t-Test: Two-Sample Assuming Equal Variances
Thuc Gi c
Mean 1.047 1.223
Variance 0.002401111 0.002001111
Observations 10 10
Pooled Variance 0.002201111
Hypothesized Mean Difference 0
df 18
t Stat -8.388352782
P(T
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Chng 4 17
B MN TON GVGD: Nguyn nh Huy
D- SO SANH GI TR TRUNG BNH VI PHNG SAI KHC NHAU
4..9 Khi nim thng k
Vi hai mu nh (N < 30) c lp v c phng sai khc nhau (hai mu phn bit), bn c
th p dng trc nghim t d phng sai (betero scedastic test) so snh gi tr trung bnh
ca hai mu y.
Gi thuyt
Tng t nh trng hp hai mu vi phng sai bng nhau.
Gi tr thng k
2
2
2
1
2
1
2121
N
S
N
S
)()XX(t
2
2
2
1
2
1
21
N
S
N
S
)XX(t
Phn phi Student
1N
N/S
1N
N/S
N
S
N
S
2
2
2
2
2
1
2
1
2
1
2
2
2
2
1
2
1
(Smith - Satterthwaite)
Bin lun
Nu t < t hay t/2 ( c tnh) Chp nhn gi thuyt H0.
4.10 p dng MS-EXCEL
Th d 9: Thi gian tan r (pht) ca mt loi vin bao t hai x nghip dc phm
(XNDP) khc nhau c kim nghim nh sau:
XNDP I 61 71 68 73 71 70 69 74
XNDP II 62 69 65 65 70 71 68 73
Thi gian tan r ca vin bao thuc hai XNDP c ging nhau?
Nhp d liu vo bng tnh
A B C D E E G H I J
1 XNDP I 61 71 68 73 71 70 69 74
2 XNDP II 62 69 65 65 70 71 68 73
4.11 p dng t-Test: Two-Sample Assuming Unequal Variances
a. Nhp ln lt n lnh Tools v lnh Data Analysis.
b. Chn chng trnh t-Test: Two-Sample Assuming Unequal Variances trong hp thoi
Data Analysis ri nhp nt OK.
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Chng 4 18
B MN TON GVGD: Nguyn nh Huy
c. Trong hp thoi t-Test: Two-Sample Assuming Unequal Variances, n nh ln lt cc
chi tit nh hai mu c d liu tng ng.
t-Test: Two-Sample Assuming Unequal Variances
XNDP I XNDP II
Mean 69.625 67.875
Variance 15.98214286 13.26785714
Observations 8 8
Hypothesized Mean Difference 0
df 14
t Stat 0.915208631
P(T
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Chng 4 19
B MN TON GVGD: Nguyn nh Huy
E- SO SNH T S
4.12 Khi nim thng k
i vi mt th nghim c hai kt qu (binomial experiment) th d, i vi mt thuc
c k n: c hay khng - bn thng so snh hai t s vi nhau (thc nghim vi l thuyt hay
thc nghim vi thc nghim). Song i vi mt th nghim c nhiu kt qu (multinomial
experiment)-th d, bc s nh gi tnh trng ca cc bnh nhn c iu tr bi thuc trong
mt khong thi gian - bn cn so snh nhiu t s. Trc nghim khi bnh phng (X2) cho
php bn so snh khng nhng hai m cn nhiu t s (hay t l hoc xc sut) mt cch tin li.
X2 l phn phi v xc sut, khng c tnh i xng v ch c gi tr 0. Gi s bn c mt cng
trnh nghin cu vi N th nghim c lp, mi th nghim c k kt qu v mi kt qu mang
mt cc xc sut thc nghim l Pi(i = 1, 2, k). Nu gi Pi,0 l cc gi tr l thuyt tng ng
vi Pi th cc tn s l thuyt s l Ei = NPi,0. iu kin p dng trc nghim X2 mt cch
thnh cng l cc tn s l thuyt Ei phi 5.
Gi thuyt
H0 : P1 = P1,0, P2 = P2,0,..., Pk,0 Cc cp Pi v Pi,0 ging nhau.
H1: t nht c mt cp Pi v Pi,0 khc nhau.
Gi tr thng k
k
1i i
2
ii2
E
)EO(;
Oi: cc tn s thc nghim (observed frequency);Ei: cc tn s l thuyt (expected frequency)
Bin lun
Nu 2a
2 Bc b gi thuyt H0 (DF = k 1)
Trong chng trnh MS-EXCEL c hm s CHITEST c th tnh:
- Gi tr 2 theo biu thc:
r
1j
c
1j ij
2
ijij2
E
)EO(
Oij: tn s thc nghim ca thuc hng i v ct j;
Eij: tn s l thuyt ca thuc hng I vi ct j, r: s hng; v c: s ct.
- Xc sut P(X > 2 ) vi bc t do DF = (r 1)(c 1); trong , r l s hng v c l s ct
trong bng ngu nhin (contingency table).
Nu P(X > 2 ) > Chp nhn gi thuyt H0, v ngc li.
4.13 p dng MS-EXCEL
Th d 10: Kt qu iu tr trn hai nhm bnh nhn: rut nhm dng thuc v mt nhm
gi dc c tm tt nh sau:
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Chng 4 20
B MN TON GVGD: Nguyn nh Huy
Bin php iu tr S bnh nhn khi bnh S bnh nhn khng khi
Thuc 24 15
Gi dc 20 23
T l khi bnh do thuc (24/39 = 61%) v gi dc (20/43 = 46%) c khc nhau v mt
thng k?
Nhp d liu vo bng tnh
B9 =CHIEST (B3:C4,B7:C8)
A B C D
1 THC NGHIM Khi bnh Khng khi Tng hng
2 iu tr 24 15 39
3 Thuc 20 23 43
4 Gi dc 44 38 82
5 Tng ct
6 L THUYT
7 Thuc 20.92682927 18.07317073
8 Gi dc 23.07317073 19.92682927
9 GI TR P 0.172954847
Sp xp d liu theo bng trc nghim hai mu c lp.
Tnh cc tng s
Tng hng (Row totals): chn D3 v nhp biu thc = SUM(B3:C3).
Dng con tr ko nt t in t D3 n D4.
Tng ct (Column totals): chn B5 v nhp biu thc = SUM(B3:B4).
Dng con tr ko nt t in t B5 n C5.
Tng cng (Grand total): chn D5 v nhp biu thc = SUM(D3:D4)
Tnh cc tn s l thuyt
Tn s l thuyt = (tng hng tng ct)/tng cng
Khi bnh do thuc: chn B7 v nhp biu thc D3*B5/D5
Khng khi bnh do thuc: chn C7 v nhp biu thc = D3*C5/D5
Khi bnh do gi dc: chn B8 v nhp biu thc = D4*B5/D5
Khng khi bnh do gi dc: chn C8 v nhp biu thc = D4*C5/D5
Hnh
4.13 p dng hm s CHITEST
Tnh xc sut P(X> 2 ) bng cch chn B9 v nhp biu thc nh trn hay s dng hp
thoi ca CHITEST.
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Chng 4 21
B MN TON GVGD: Nguyn nh Huy
Kt qu: P(X> 2 ) = 0,17 > = 0,05 nhn gi thuyt H0.
Vy t l khi bnh do thuc v do gi dc khng khc nhau.
F- SO SNH PHNG SAI
4.14 Khi nim thng k
Trc nghim so snh hai phng sai thng c p dng so snh chnh xc ca hai
phng php nh lng khc nhau.
Gi thuyt: 2
2
2
11
2
2
2
10
:H
:H
Gi tr thng k: 2
2
2
1
2
2
2
1
2
2
2
1
2
1
2
2
S
S
S
S
S
SF
Phn phi Fischer: 2N;1N2211
Bin lun
Nu F < F(1, 2) Chp nhn gi thuyt H0 vi xc sut (1 - )100%
4.15 p dng MS-EXCEL
Th d 11: Mt mu c phn tch bi hai phng php A v B vi kt qu c tm tt
trong bng sau:
A 6,4 5,2 4,8 5,2 4,3 4,4 5,1 5,8
B 2,6 3,5 3,4 3,2 3,4 2,8 2,9 2,8
Cho bit phng php no chnh xc hn?
Nhp d liu vo bng tnh
A B C D E F G H I
1 6,4 5,2 4,8 5,2 4,3 4,4 5,1 5,8
2 2,6 3,5 3,4 3,2 3,4 2,8 2,9 2,8
p dng F-Test Two-Sample for Variances
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Chng 4 22
B MN TON GVGD: Nguyn nh Huy
a. Nhp ln lt n lnh Tools v lnh Data Analysis.
b. Chn chng trnh F-Test Two-Sample for Variances trong hp thoi Data Analysis ri
nhp nt OK.
c. Trong hp thoi F-Test Two-Sample for Variances, ln lt n nh cc chi tit:
- Ta ca d liu 1 (Variable 1 Range),
- Ta ca d liu 2 (Variable 2 Range),
- Nhn d liu (Labels),
- Ngng tin cy (Alpha),
- Ta u ra (Output Range)
Hnh 4.3: Hp thoi F-Test Two-Sample for Variaces
F-Test Two-Sample for Variances
6.4 2.6
Mean 4.971428571 3.142857143
Variance 0.269047619 0.092857143
Observations 7 7
df 6 6
F 2.897435897
P(F F0,05 = 3,787 Bc b gi thuyt H0.
Vy chnh xc ca phng php B cao hn phng php A.
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Chng 4 23
B MN TON GVGD: Nguyn nh Huy