(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
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1 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, ) z = x µ N(0, ) N(0, ) ( N(0, 2), N(9, 4) N(0, 2) N(9, 4) N(0, ) *2 * 733 de Moivre 00 *2 (i) (iii) N(0, 2) z(0.95) N(9, 4) 9 + 4z(0.95)
2 (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 = 20 H : µ 20 (iii) y,, y 0 z = ȳ µ 0 (2) N(0, ) ȳ = y + +y 0 0 = 09.5, µ = 20 σ = 6 ( ) z = = 2.08 N(0, ) 5 z(0.975) =.96, z(0.025) =.96 ( 2.08 =) z < z(0.025) H 0 : µ = 20 3 t 3. t t t Studet( Gosset: ) 2 *3 *4 2
3 2 0 (y,, y 0 ) ( ) y y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y ( ) *5 H 0 : µ = 20 H : µ 20 ȳ = (ii) ( ) ȳ N 20, σ (iii) z = ȳ 20 0 z N(0, ) (3) (3) z z z(0.975) =.96, z(0.025) =.96 z = 0 z z z = ȳ µ 0 = ȳ 20 0 = 0 i= (y i ȳ) (4) z N(0, ) *6 z z *5 t *6 z z(0.975) =.96 z(0.025) =
4 *7 (4) z Gosset z t y,, y 0 z z z z t t z t t z t z t t t t ( ) *8 (0 ) = 9 t *9 t N(0, ) ((4) z t t ) t y,, y N(µ, ) t = ȳ µ ( ȳ = i= y i, = ) (y i ȳ) 2 i= ( ) t t( ) t( ) (00 α) t (α) () t t 9 t 5 t < t 9 (0.025) t 9 (0.975) < t *7 *8 χ 2 2 ( ) 2( ) *9 4
5 t 9 (0.025) = 2.26, t 9 (0.975) = 2.26 (4) z (= t) = 2.2 t 9 (0.025) t t 9 (0.975) H 0 : µ = 20 ( ) 3.2 t 2 N(5, 6) 0 ( ) t t t t t 2 t t y, y 2,, y N(µ, ) y 2, y 22,, y 22 N(µ 2, ) H 0 µ = µ 2 H µ µ µ = y j (= ȳ ), µ 2 = 2 y 2j (= ȳ 2 ) 2 j= µ, µ 2 ( µ N µ, d d = µ µ 2 N j= ) (, µ 2 N µ 2, ) 2 ( ( µ µ 2, + ) ) 2 5
6 * 0 H 0 : µ = µ 2 ( ( d N 0, + ) ) 2 d z = ( ) N(0, ) (5) + 2 t = j= (y j ȳ ) 2, 2 = 2 (y 2j ȳ 2 ) 2 (6) = (y j ȳ ) 2 + (y 2j ȳ 2 ) 2 (7) ( ) + ( 2 ) j= j= j= * *2 (7) (6), 2 { } = ( ) σ ( ) + ( 2 ) 2 + ( 2 ) 2 (8), 2 ( ) ( 2 ), 2 = j= (y j ȳ ) 2, 2 = 2 (y 2j ȳ 2 ) 2 2 t * 3 j= *0 V [ d] = V [ µ µ 2 ] = V [ µ ] V [ µ 2 ] = + ( = + ) 2 2 * ( ) + ( 2 ) = ( + 2 2) χ 2 µ, µ *2 H 0 : µ = µ 2 ȳ = + 2 = i (y ij ȳ) 2 i= j= 2 y ij i= j= t *3 Duett Tukey t F 6
7 3.3.4 (5) d t = ( ) + 2 H 0 : µ = µ 2 ( ) + ( 2 ) = ( + 2 2) t 5 t < t + 2 2(0.025) t + 2 2(0.975) < t ( = 6, 2 = 5) µ, µ 2 5 H 0 : µ = µ 2 H : µ µ 2 ( ) µ = ȳ = 6 ( ) =.0, µ 2 = ȳ 2 = ( ) = d = µ µ 2 = = 0.4 = [{ (8 ) 2 + (9 ) 2 + (6 ) 2 + (4 ) 2 + ( ) 2 + (8 ) 2} { (8 0.6) 2 + (9 0.6) 2 + (5 0.6) 2 + (7 0.6) 2 + (4 0.6) 2}] = 25.5 t d t = ( ) = + 2 ( ) ( ) ( ) 7
8 H 0 : µ = µ 2 t ( ) + ( 2 ) = (6 ) + (5 ) = 9 t t t 9 (0.025) = 2.26, t 9 (0.975) = 2.26 t 9 (0.025) t (= 0.3) t 9 (0.975) H 0 : µ = µ ( = 5, 2 = 4) * µ, µ 2 H 0 : µ = µ 2 H : µ µ 2 5 ( ) t µ = 5, µ 2 = 0, σ = 3, = 2 d d = µ µ 2 = 5 0 = 5 σ = 3, = 2 = 5 2 = 4 (8) = t { } ( ) σ ( ) + ( 2 ) 2 + ( 2 ) 2 = 7 ( ) 6.9 d t = ( ) = ( ) t t 7 (0.025) = 2.36, t 7 (0.975) = 2.36 H 0 : µ = µ 2 t 7 (0.975) < t (= 2.84) *4 y,, y σ x = x i i= σ = (x i x) 2 i= 8
9 3.4 2 t 2 t 3.4. t 2 t t µ µ 2 p,, p * 5 ( ) y N(µ + p, ) y 2 N(µ 2 + p, ) (2 ) y 2 N(µ + p 2, ) y 22 N(µ 2 + p 2, ) (3 ) y 3 N(µ + p 3, ) y 32 N(µ 2 + p 3, )... ( ) y N(µ + p, ) y 2 N(µ 2 + p, ) µ, µ 2 p + p 2 + p p = 0 * 6 H 0 µ = µ 2 H µ µ p,, p d i = y i2 y i (i =,, ) d i * 7 E[d i ] = E[y i2 y i ] = (µ 2 + p i ) (µ + p i ) = µ 2 µ V [d i ] = V [y i2 y i ] = V [y i2 y i ] = V [y i2 ] + V [y i ] = + = 2 *5 *6 ȳ = y i i= [ ] E[ȳ ] = E y i = E[y i ] = (µ + p i ) = µ + (p + p p ) = µ i= i= i= µ *7 9
10 d i N(µ 2 µ, 2 ) d i H 0 : µ = µ 2 d i N(0, 2 ) = 2 d,, d N(0, ) d,, d t * 8 d = i= = t = d i (d i d) 2 (9) i= d t 5 t < t (0.025) t (0.975) < t (mg/dl) t * 9 ( ) t ( ) ( ) *8 H 0 : µ 2 µ = 0 d,, d 0 *9 t 0
11 0 t d = ( ( 5) + ( 2) + 0) = = 5 {(0 5)2 + (5 5) 2 + (2 5) 2 + ( 5 5) 2 + ( 2 5) 2 + (0 5) 2 } 49.6 t = = t 5 t 2.5 t 5 (0.025) = 2.57, t 5 (0.975) = 2.57 t 5 (0.025) < (.739 =) t < t 5 (0.975) H 0 : µ = µ SAS t SAS data d; iput before cards; ; ru; proc ttest data=d; paired after*before; ru;
t χ 2 F Q t χ 2 F 1 2 µ, σ 2 N(µ, σ 2 ) f(x µ, σ 2 ) = 1 ( exp (x ) µ)2 2πσ 2 2σ 2 0, N(0, 1) (100 α) z(α) t χ 2 *1 2.1 t (i)x N(µ, σ 2 ) x µ σ N(0, 1
t χ F Q t χ F µ, σ N(µ, σ ) f(x µ, σ ) = ( exp (x ) µ) πσ σ 0, N(0, ) (00 α) z(α) t χ *. t (i)x N(µ, σ ) x µ σ N(0, ) (ii)x,, x N(µ, σ ) x = x+ +x N(µ, σ ) (iii) (i),(ii) z = x µ N(0, ) σ N(0, ) ( 9 97.
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
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
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
* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H
1 1 1.1 *1 1. 1.3.1 n x 11,, x 1n Nµ 1, σ x 1,, x n Nµ, σ H 0 µ 1 = µ = µ H 1 µ 1 µ H 0, H 1 * σ σ 0, σ 1 *1 * H 0 H 0, H 1 H 1 1 H 0 µ, σ 0 H 1 µ 1, µ, σ 1 L 0 µ, σ x L 1 µ 1, µ, σ x x H 0 L 0 µ, σ 0
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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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Armitage 1 2 11 10 3.32 *1 9 5 5.757 3.3667 7.5 1 9 6 5.757 7 7.5 7.5 9 7 7 9 7.5 10 9 8 7 9 9 10 9 9 9 10 9 11 9 10 10 10 9 11 9 11 11 10 9 11 9 12 13 11 10 11 9 13 13 11 10 12.5 9 14 14.243 13 12.5 12.5
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
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統計学のポイント整理
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パワポカバー入稿用.indd
i 1 1 2 2 3 3 4 4 4 5 7 8 8 9 9 10 11 13 14 15 16 17 19 ii CONTENTS 2 21 21 22 25 26 32 37 38 39 39 41 41 43 43 43 44 45 46 47 47 49 52 54 56 56 iii 57 59 62 64 64 66 67 68 71 72 72 73 74 74 77 79 81 84
これでわかるAccess2010
i 1 1 1 2 2 2 3 4 4 5 6 7 7 9 10 11 12 13 14 15 17 ii CONTENTS 2 19 19 20 23 24 25 25 26 29 29 31 31 33 35 36 36 39 39 41 44 45 46 48 iii 50 50 52 54 55 57 57 59 61 63 64 66 66 67 70 70 73 74 74 77 77
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（個別のテーマ） 薬剤に関連した医療事故
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（個別のテーマ） 放射線検査に関連した医療事故
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平成18年版 男女共同参画白書
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取扱説明書
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エクセルカバー入稿用.indd
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Microsoft Word - 表紙.docx
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LLG-R8.Nisus.pdf
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