H22 BioS t (i) treat1 treat2 data d1; input patno treat1 treat2; cards; ; run; 1 (i) treat = 1 treat =
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1 H BioS t (i) treat treat data d; input patno treat treat; cards; ; run; (i) treat treat
2 data d; input group patno period treat y; label group patno period ; cards; run; t (i) proc gplot data d; plot y * period patno; by group; run; symbol y
3 (ii) t proc ttest data d; paired treat * treat; run; 3
4 paired-t:proc ttest TTEST N treat - treat t t Pr > t treat - treat
5 (iii) : dif i i dif i dif i N(µ, σ ) H : µ H : µ t t (ii) µ ( ) σ { ( 3.333) + ( ) + ( 3.333) + ( 3.333) + ( ) + ( ) } (ii) σ σ (ii) 95 t [ ] [ ] σ σ µ + t(5,.5), µ + t(5,.975) , [.686, 7.353] σ V[ µ] H : µ (t ) t µ bσ
6 p SAS data p value; p * ( - cdf( t,.3, 5)); run; p.86 (i) proc glm proc glm data d; class treat patano; model y treat patno/ ss3 solution p; run; paierd-t : proc glm GLM : y F Pr > F Model Error Corrected Total Type III F Pr > F treat patno
7 t Pr > t Intercept B treat B treat. B... patno -6. B patno -.5 B patno 3. B patno 4.5 B patno 5-4. B patno 6. B... Note X X B paierd-t : proc glm GLM (ii) d i (i : i : ) p j (j,, 3, 4, 5, 6) y ij µ + d i + p j + ɛ ij (ɛ ij N(, σ )) () 7
8 y µ + d + p + ɛ y µ + d + p + ɛ y µ + d + p + ɛ y µ + d + p + ɛ y 3 µ + d + p 3 + ɛ 3 y 3 µ + d + p 3 + ɛ 3 y 4 µ + d + p 4 + ɛ 4 () y 4 µ + d + p 4 + ɛ 4 y 5 µ + d + p 5 + ɛ 5 y 5 µ + d + p 5 + ɛ 5 y 6 µ + d + p 6 + ɛ 6 y 6 µ + d + p 6 + ɛ 6 y y y y y 3 8 y 3 7 y, X y 4 8 y 4 8 y 5 5 y 5 y 6 3 y 6, β µ d d p p p 3 p 4 p 5 p 6, ɛ ɛ ɛ ɛ ɛ ɛ 3 ɛ 3 ɛ 4 ɛ 4 ɛ 5 ɛ 5 ɛ 6 ɛ 6 y X β + ɛ (ɛ N(, σ I )) (3) SAS d, p 6 () y µ + d +p +ɛ y µ +p +ɛ y µ + d +p +ɛ y µ +p +ɛ y 3 µ + d +p 3 +ɛ 3 y 3 µ +p 3 +ɛ 3 y 4 µ +p 4 +ɛ 4 (4) y 4 µ + d +p 4 +ɛ 4 y 5 µ +p 5 +ɛ 5 y 5 µ + d +p 5 +ɛ 5 y 6 µ +ɛ 6 y 6 µ + d +ɛ 6 8
9 X, β µ d p p p 3 p 4 p 5 (3) y + X β + ɛ (ɛ N(, σi )) (5) (iii) SAS SAS β β (X X ) X y (6) X X
10 6 6 6 (X X ) X y
11 (6) β (X X ) X y β µ d p 6, p.5, p 3, p 4.5, p 5 4 d, p 5 µ Intercept d treat d treat p 6 patno p.5 patno p 3 patno3 p 4.5 patno4 p 5 4 patno5 p 6 patno6 SAS β ŷ ŷ X β
12 µ d d p p p 3 p 4 p 5 p
13 e , e y ŷ (iv) H : d d p p p 3 p 4 p 5 p 6 H : () d i p j y ij µ + ɛ ij 3
14 y µ + ɛ y µ + ɛ y µ + ɛ y µ + ɛ y 3 µ + ɛ 3 y 3 µ + ɛ 33 y 4 µ + ɛ 4 y 4 µ + ɛ 4 y 5 µ + ɛ 5 y 5 µ + ɛ 5 y 6 µ + ɛ 6 y 6 µ + ɛ 6 y µ + ɛ (ɛ N(, σ I )) µ µ µ ( ) y (7) ( ) ( ) ( y )
15 (7) µ ( ) y ŷ, e ŷ µ (8) e y ŷ (9) * y ŷ }{{} Corrected Total y ŷ }{{} Error + ŷ ŷ }{{} Model y : ŷ : µ ŷ : µ, d, p,, p 5 7 * Corrected Total H Error H Model H H e e + by by 5
16 (CorrectedTotal) y ŷ : (Error) y ŷ : 7 5 (Model) ŷ ŷ : 7 6 (CorrectedTotal) y ŷ e ( 5.667) + ( 4.667) + ( 3.667) (.667) + ( 5.667) (.333) (Error) y ŷ e (.667) + (.3334) (.667) +(.6667) (.8334) (.8334) (Model) ŷ ŷ ( ) + ( 3) + (.8333) ( ) + ( 4.333) (.3333).999 (Error) 5 y ŷ (Model) 6 ŷ ŷ F F Model Error Error σ σ Error e () 6
17 * *3 p 6 5 data p value; p - cdf( F,.7936, 6, 5); run; p.397 (v) H d : d d H d : d d H d () d i y ij µ + p j + ɛ ij (ɛ ij N(, σ )) y µ + p + ɛ y µ + p + ɛ y µ + p + ɛ y µ + p + ɛ y 3 µ + p 3 + ɛ 3 y 3 µ + p 3 + ɛ 3 y 4 µ + p 4 + ɛ 4 y 4 µ + p 4 + ɛ 4 y 5 µ + p 5 + ɛ 5 y 5 µ + p 5 + ɛ 5 y 6 µ + p 6 + ɛ 6 y 6 µ + p 6 + ɛ 6 * bσ σ bσ *3 F 5 by by bσ 7
18 X d, β d µ p p p 3 p 4 p 5 p 6 y X d β d + ɛ (ɛ N(, σ I )) () SAS p 6 X d, β d () y X d β d + ɛ (ɛ N(, σ I )) µ p p p 3 p 4 p 5 β d β d (X dx d ) X dy () 8
19 X dx d (X dx d ) 9
20 X dy () β d (X dx d ) X dy
21 β d µ p p p 3 p 4 p 5 p 6 µ 6.5 p 6 p.5 p 3 p 4.5 p 5 4 p 6 β d ŷ d ŷ d X d βd
22 *4 TypeIII treat H d H d H ŷ ŷ d *4 SAS proc glm data d; class patno; model y patno / solution ss3 p; run;
23 ŷ ŷ d (.6666) + (.6667) + (.6666) + (.6667) + (.6666) + (.6667) +(.6666) + (.6667) + (.6666) + (.6667) + (.6666) + (.6667) ŷ : µ, d, p,, p 5 7 ŷ d : µ, p,, p 5 6 ŷ ŷ d : 7 6 ŷ ŷ d F σ Error F ŷ ŷ d σ p σ 5 data p value; p - cdf( F, 4.55,, 5); run; p.86 TypeIII Treat p (vi) (v) p p t p t t TypeIII treat F (t ) (F ) 3
24 t.5635 ( t ) () σ Error e t t j y j, y j σ dif j y j y j V [dif j ] V [y j ] + V [y j ] σ + σ σ t Treat Treat treat: treat: treat treat (i) proc glm data d; class treat patno period; model y treat patno period / run; solution p ss3; patno(fixed) + period GLM : y F Pr > F Model Error Corrected Total
25 Type III F Pr > F treat patno period t Pr > t Intercept B treat B treat. B... patno -6. B patno -.5 B patno 3. B patno 4.5 B patno 5-4. B patno 6. B... period B period. B... Note:X X B 5
26 patno(fixed) + period GLM (ii) d i (i : i : ) p j (j,, 3, 4, 5, 6) t k (k, ) y ijk µ + d i + p j + t k + ɛ ijk (ɛ ij N(, σ )) (3) y µ + d + p + t + ɛ y µ + d + p + t + ɛ y µ + d + p + t + ɛ y µ + d + p + t + ɛ y 3 µ + d + p 3 + t + ɛ 3 y 3 µ + d + p 3 + t + ɛ 3 y 4 µ + d + p 4 + t + ɛ 4 (4) y 4 µ + d + p 4 + t + ɛ 4 y 5 µ + d + p 5 + t + ɛ 5 y 5 µ + d + p 5 + t + ɛ 5 y 6 µ + d + p 6 + t + ɛ 6 y 6 µ + d + p 6 + t + ɛ 6 6
27 y y y y y y 3 y 3 y 4 y 4 y 5 y 5 y 6 y , X, β µ d d p p p 3 p 4 p 5 p 6 t t, ɛ ɛ ɛ ɛ ɛ ɛ 3 ɛ 3 ɛ 4 ɛ 4 ɛ 5 ɛ 5 ɛ 6 ɛ 6 y X β + ɛ (ɛ N(, σ I )) (5) SAS d, p 6, t y µ +d +p +t +ɛ y µ +p +ɛ y µ +d +p +t +ɛ y µ +p +ɛ y 3 µ +d +p 3 +t +ɛ 3 y 3 µ +p 3 +ɛ 3 y 4 µ +p 4 +t +ɛ 4 (6) y 4 µ +d +p 4 +ɛ 4 y 5 µ +p 5 +t +ɛ 5 y 5 µ +d +p 5 +ɛ 5 y 6 µ +t +ɛ 6 y 6 µ +d +ɛ 6 X, β µ d p p p 3 p 4 p 5 t 7
28 (5) y X β + ɛ (ɛ N(, σ I )) (iii) β β (X X ) X y (7) X X (X X )
29 X y β (7) β (X X ) X y 9
30 β µ d p p p 3 p 4 p 5 t µ , d , p 6, p.5, p 3, p 4.5, p 5 4, t
31 d, p 6, t β µ d d p p p 3 p 4 p 5 p 6 t t µ Intercept d treat d treat p 6 patno p.5 patno p 3 patno3 p 4.5 patno4 p 5 4 patno5 p 6 patno6 t.6667 period t period ŷ ŷ X β
32 e e y ŷ (iv) H : d d p p p 3 p 4 p 5 p 6 t t H : (3) d i, p j, t k y ijk µ + ɛ ijk 3
33 y µ + ɛ y µ + ɛ y µ + ɛ y µ + ɛ y 3 µ + ɛ 3 y 3 µ + ɛ 33 y 4 µ + ɛ 4 y 4 µ + ɛ 4 y 5 µ + ɛ 5 y 5 µ + ɛ 5 y 6 µ + ɛ 6 y 6 µ + ɛ 6 (8) (9) ŷ e ŷ, e y ŷ y ŷ + ŷ ŷ y : ŷ : µ ŷ : µ, d, p,, p 5, t 8 (CorrectedTotal) y ŷ : (Error) y ŷ : 8 4 (Model) ŷ ŷ : 8 7 (CorrectedTotal) y ŷ e ( 5.667) + ( 4.667) + ( 3.667) (.667) + ( 5.667) (.333) 33
34 59.53 (Error) y ŷ e (.8333) + (.6667) (.8333) +( ) (.5) (.5) (Model) ŷ ŷ ( 6) + ( ) + (.5) (.6667) + ( ) (.6667) 4.33 (Error) 4 y ŷ (Model) 7 ŷ ŷ F F Model Error Error σ σ Error e (8) F F 7 by by bσ p 7 4 data p value; p - cdf( F,.8, 7, 4); run; p.66 34
35 (v) H d : d d H d : d d H d H d (3) d i y ijk µ + p j + t k + ɛ ijk y µ + p + t + ɛ y µ + p + t + ɛ y µ + p + t + ɛ y µ + p + t + ɛ y 3 µ + p 3 + t + ɛ 3 y 3 µ + p 3 + t + ɛ 3 y 4 µ + p 4 + t + ɛ 4 y 4 µ + p 4 + t + ɛ 4 y 5 µ + p 5 + t + ɛ 5 y 5 µ + p 5 + t + ɛ 5 y 6 µ + p 6 + t + ɛ 6 y 6 µ + p 6 + t + ɛ 6 X d, β d µ p p p 3 p 4 p 5 p 6 t t y X d β d + ɛ (ɛ N(, σ I )) (9) 35
36 SAS p 6, t X d, β d (9) y X d β d + ɛ (ɛ N(, σ I )) µ p p p 3 p 4 p 5 t β d β d (X dx d ) X dy () X dx d
37 (X dx d ) X dy
38 () β d β d µ p p p 3 p 4 p 5 t p 6, t µ p 6 p.5 p 3 p 4.5 p 5 4 p 6 t.6667 t β d 38
39 ŷ d ŷ d X d βd
40 e d e d y ŷ d H d H d ŷ ŷ d (.6667) (.6667) (.6666) (.6667) (.6667) (.6667) TypeIII ŷ : µ, d, p,, p 5, t 8 ŷ d : µ, p,, p 5, t 7 ŷ ŷ d : 8 7 ŷ ŷ d (8) σ F F ŷ ŷ d σ
41 4 p data p value; p - cdf( F, ,, 4); run; p.4 4
H22 BioS (i) I treat1 II treat2 data d1; input group patno treat1 treat2; cards; ; run; I
H BioS (i) I treat II treat data d; input group patno treat treat; cards; 8 7 4 8 8 5 5 6 ; run; I II sum data d; set d; sum treat + treat; run; sum proc gplot data d; plot sum * group ; symbol c black
t sex N y y y Diff (1-2)
Armitage 1 1.1 2 t 1.2 SAS Proc GLM 2 2.1 1 1 2.1.1 50 1 1 t sex N y 50 116.45 119.6 122.75 11.071 1.5657 93.906 154.32 y 50 127.27 130.7 134.13 12.072 1.7073 102.68 163.37 y Diff (1-2) -15.7-11.1-6.504
5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )
5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y
(iii) x, x N(µ, ) z = x µ () N(0, ) () 0 (y,, y 0 ) (σ = 6) *3 0 y y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y ( ) *4 H 0 : µ
t 2 Armitage t t t χ 2 F χ 2 F 2 µ, N(µ, ) f(x µ, ) = ( ) exp (x µ)2 2πσ 2 2 0, N(0, ) (00 α) z(α) t * 2. t (i)x N(µ, ) x µ σ N(0, ) 2 (ii)x,, x N(µ, ) x = x + +x ( N µ, σ2 ) (iii) (i),(ii) x,, x N(µ,
α β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β *3 2.3 * *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P + 10) 15 (µ A = µ P +
Armitage 1 1.1 2 t *1 α β 1.2 µ x µ 2 2 2 α β 2.1 1 α β α ( ) β *1 t t 1 α β *2 α α β β α = α 1 β = 1 β 2.2 α 0 β 1 0 0 1 1 5 2.5 *3 2.3 *4 3 3.1 1 1 1 *2 *3 *4 (µ A ) (µ P ) (µ A > µ P ) 10 (µ A = µ P
i
14 i ii iii iv v vi 14 13 86 13 12 28 14 16 14 15 31 (1) 13 12 28 20 (2) (3) 2 (4) (5) 14 14 50 48 3 11 11 22 14 15 10 14 20 21 20 (1) 14 (2) 14 4 (3) (4) (5) 12 12 (6) 14 15 5 6 7 8 9 10 7
,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i
![,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i](/thumbs/87/95421301.jpg ",, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i")
Armitage.? SAS.2 µ, µ 2, µ 3 a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 µ, µ 2, µ 3 log a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 * 2 2. y t y y y Poisson y * ,, Poisson 3 3. t t y,, y n Nµ,
*1 * Wilcoxon 2 2 t t t t d t M t N t M t n t N t n t N t d t N t t at ri
Wilcoxon H23 BioS 1 Wilcoxon 2 2.1 1 2 1 0 1 1 5 0 1 2 7 0 1 3 8 1 1 4 12 0 2 5 2 0 2 6 3 1 2 7 4 1 2 8 10 0 Wilcoxon 2.2 S 1 t S 2 t Wilcoxon H 0 H 1 H 0 : S 1 t S 2 t H 1 : S 1 t S 2 t 1 *1 *2 2.3 2.3.1
i ii iii iv v vi vii ( ー ー ) ( ) ( ) ( ) ( ) ー ( ) ( ) ー ー ( ) ( ) ( ) ( ) ( ) 13 202 24122783 3622316 (1) (2) (3) (4) 2483 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 11 11 2483 13
2 H23 BioS (i) data d1; input group patno t sex censor; cards;
H BioS (i) data d1; input group patno t sex censor; cards; 0 1 0 0 0 0 1 0 1 1 0 4 4 0 1 0 5 5 1 1 0 6 5 1 1 0 7 10 1 0 0 8 15 0 1 0 9 15 0 1 0 10 4 1 0 0 11 4 1 0 1 1 5 1 0 1 1 7 0 1 1 14 8 1 0 1 15 8
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(1) I 44 II 45 III 47 IV 52 44 4 I (1) ( ) 1945 8 9 (10 15 ) ( 17 ) ( 3 1 ) (2) 45 II 1 (3) 511 ( 451 1 ) ( ) 365 1 2 512 1 2 365 1 2 363 2 ( ) 3 ( ) ( 451 2 ( 314 1 ) ( 339 1 4 ) 337 2 3 ) 363 (4) 46
i ii i iii iv 1 3 3 10 14 17 17 18 22 23 28 29 31 36 37 39 40 43 48 59 70 75 75 77 90 95 102 107 109 110 118 125 128 130 132 134 48 43 43 51 52 61 61 64 62 124 70 58 3 10 17 29 78 82 85 102 95 109 iii
178 5 I 1 ( ) ( ) 10 3 13 3 1 8891 8 3023 6317 ( 10 1914 7152 ) 16 5 1 ( ) 6 13 3 13 3 8575 3896 8 1715 779 6 (1) 2 7 4 ( 2 ) 13 11 26 12 21 14 11 21
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i Armitage Q. Bonferroni 1 SAS ver9.1.3 version up 2 *1 *2 FWE *3 2.1 vs vs vs 2.2 5µg 10µg 20µg 5µg 10µg 20µg vs 5µg vs 10µg vs 20µg *1 *2 *3 FWE 1
i Armitage Q Boferroi SAS ver93 versio up * * FWE *3 vs vs vs 5µg 0µg 0µg 5µg 0µg 0µg vs 5µg vs 0µg vs 0µg * * *3 FWE 3 A B C D E (i A B C D E (ii A B C D E (iii A B C D E (iv A B C D A < B C D A < B
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第１部 一般的コメント
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I? 3 1 3 1.1?................................. 3 1.2?............................... 3 1.3!................................... 3 2 4 2.1........................................ 4 2.2.......................................
20 15 14.6 15.3 14.9 15.7 16.0 15.7 13.4 14.5 13.7 14.2 10 10 13 16 19 22 1 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 2,500 59,862 56,384 2,000 42,662 44,211 40,639 37,323 1,500 33,408 34,472
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2 1980 8 4 4 4 4 4 3 4 2 4 4 2 4 6 0 0 6 4 2 4 1 2 2 1 4 4 4 2 3 3 3 4 3 4 4 4 4 2 5 5 2 4 4 4 0 3 3 0 9 10 10 9 1 1
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1 (1) (2)
1 2 (1) (2) (3) 3-78 - 1 (1) (2) - 79 - i) ii) iii) (3) (4) (5) (6) - 80 - (7) (8) (9) (10) 2 (1) (2) (3) (4) i) - 81 - ii) (a) (b) 3 (1) (2) - 82 - - 83 - - 84 - - 85 - - 86 - (1) (2) (3) (4) (5) (6)
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y = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f() + f() + f(3) + f(4) () *4
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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218 6 219 6.11: (EQS) /EQUATIONS V1 = 30*V999 + 1F1 + E1; V2 = 25*V999 +.54*F1 + E2; V3 = 16*V999 + 1.46*F1 + E3; V4 = 10*V999 + 1F2 + E4; V5 = 19*V999 + 1.29*F2 + E5; V6 = 17*V999 + 2.22*F2 + E6; CALIS.
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講義のーと : データ解析のための統計モデリング. 第３回
Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
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