H22 BioS (i) I treat1 II treat2 data d1; input group patno treat1 treat2; cards; ; run; I
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1 H BioS (i) I treat II treat data d; input group patno treat treat; cards; ; run; I II sum data d; set d; sum treat + treat; run; sum proc gplot data d; plot sum * group ; symbol c black v dot; run;
2 I II (ii) t proc ttest data d; class group; var sum; run;
3 TTEST group N sum sum sum Diff (-) t t Pr > t sum Pooled Equal sum Satterthwaite Unequal F Pr > F sum Folded F
4 (iii) I II I II (P) (A) (P) (A) 8(P) 7(A) 5 4 8(A) 8(P) 6 5 5(A) (P) 5 6 (A) (P) t µ, µ σ σ µ ( + + 5) 9., µ ( ). σ 4 {( 9.) + ( 9.) + (5 9.) σ +(6.) + (5.) + (.) } 4. σ (ii) proc ttest t µ µ t ( + ) σ proc ttest p data p; p value *( - cdf( t, abs(-.7), 4); * t 4; run; p.787 proc ttest 4
5 (i) data d; input group patno period treat y; label group patno period ; cards; ; run; proc glm data d; class group treat patno period ; model y group treat patno(group) period / solution p ss; test h group e patno(group); run; quit; 5
6 GLM : y F Pr > F Model Error Corrected Total R y Type III F Pr > F group treat patno(group) period Type III patno(group) Type III F Pr > F group
7 t Pr > t Intercept 7.8 B group. B group. B... treat -. B treat. B... patno(group) -7. B patno(group) -.5 B patno(group). B... patno(group) 4.5 B patno(group) 5-4. B patno(group) 6. B... period B period. B... Note:X X B patno(fixed) + period GLM TypeIII patno(group) p.787 t p 7
8 (ii) g i i (i, ) d j (j : j : ) p k k (k,, 6) t l (l : I l : II ) y ijkl µ + g i + d j + p k + t l + ɛ ijkl y µ + g + d + p + t + ɛ y µ + g + d + p + t + ɛ y µ + g + d + p + t + ɛ y µ + g + d + p + t + ɛ y µ + g + d + p + t + ɛ y µ + g + d + p + t + ɛ y 4 µ + g + d + p 4 + t + ɛ 4 y 4 µ + g + d + p 4 + t + ɛ 4 y 5 µ + g + d + p 5 + t + ɛ 5 y 5 µ + g + d + p 5 + t + ɛ 5 y 6 µ + g + d + p 6 + t + ɛ 6 y 6 µ + g + d + p 6 + t + ɛ 6 () X, β µ g g d d p p p p 4 p 5 p 6 t t () () y Xβ + ɛ () SAS g, d, p, p 6, t p,, 4, 5, 6 8
9 * X, β () y X β + ɛ µ g d p p p 4 p 5 t (iii) () β β β (X X ) X y (4) X X * X,, 4, 5, 6 9
10 (X X ) X y
11 (4) β (X X ) X y
12 β µ ĝ d p p p 4 p 5 t ĝ, d, p, p 6, t β µ 7.8 ĝ ĝ d. d p 7 β p.5 p p 4.5 p 5 4 p 6 t.6667 t Intercept group group treat treat patno(group) patno(group) patno(group) patno(group) 4 patno(group) 5 patno(group) 6 period period proc glm ŷ
13 ŷ X β
14 e e y ŷ proc glm (iv)..... F.. p + p + p, p 4 + p 5 + p 6 p, p 6 X g, β g () y X g β g + ɛ µ d p p p 4 p 5 t 4
15 β g β g (X gx g ) X gy (5) X gx g (X gx g ) X gy
16 β g (5) β g (X gx g ) X gy ( 4) ( ) ( 4) + 4 ( ) 4 ( 8) + 4 ( 8) ŷ g 6
17 ŷ g X g βg
18 ŷ ŷ g (.5) + (.5) + (.5) + (.5) + (.5) + (.5) proc glm group TypeIII. () X p, β p µ g g d d t t () y X p β p + ɛ 8
19 g, d, t * X p, β p β p µ g d t β p (X px p ) X py (6) X px p ( ) X p X p * 9
20 X py β p (6) β p ( X px p ) X p y
21 ĝ, d, t β p µ ĝ ĝ d d t t ŷ p ŷ p X p βp
22 ŷ ŷ p ( 4.666) + ( 4.667) (.667) + (.667) proc glm patno(group) TypeIII. ŷ ŷ g, ŷ ŷ p ŷ : µ, g, d, p, p, p 4, p 5, t 8 ŷ g : µ, d p, p, p 4, p 5, t 7 ŷ p : µ, g, d, t 4 ŷ ŷ p : ŷ ŷ g : 8 7 F F ŷ ŷ g 4 ŷ ŷ p
23 p data p value; p - cdf( F,.85,, 4) run; p.787 proc glm TypeIII patno(group)
H22 BioS t (i) treat1 treat2 data d1; input patno treat1 treat2; cards; ; run; 1 (i) treat = 1 treat =
H BioS t (i) treat treat data d; input patno treat treat; cards; 3 8 7 4 8 8 5 5 6 3 ; run; (i) treat treat data d; input group patno period treat y; label group patno period ; cards; 3 8 3 7 4 8 4 8 5
More informationt 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
More information5 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
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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
More information*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
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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,
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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,
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3180, 3599, 3280, 2980, 3500, 3099, 3200, 2980, 3380, 3780, 3199, 2979, 3680, 2780, 2950, 3180, 3200, 3100, 3780, 3200 DATA Sample1 /**/ INPUT Price @@ /* @@1 */ DATALINES 3180 3599 3280 2980 3500 3099
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