統計的仮説検定とExcelによるt検定

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "統計的仮説検定とExcelによるt検定"

Transcription

1 I L14( Fri) : Time-stamp: Fri 14:03 JST hig 1,,,, p, Excel p, t. ( ) L14 Excel t I(015) 1 / 0

2 L13-Q1 Quiz : n = 9. σ 0.95, S n 1 (n 1) <σ < S χ α <σ < <σ < 64. χ 1 α n 1 (n 1) L13-Q Quiz : n = 9., X = 1 9 [ ] = 80g., S = [(78 80) + + (8 80) ] = 4g., µ 80g, σ 4g. ( ) L14 Excel t I(015) / 0

3 µ 0.95, S X t 0.05 (9 1) n <µ < X + t 0.05(9 1) <µ < <µ < σ 0.95, S n 1 (n 1) <σ < S χ α <σ < <σ < χ 1 α n 1 (n 1) S n ( ) L14 Excel t I(015) 3 / 0

4 3 4 Excel t Excel ( ) L14 Excel t I(015) 4 / 0

5 ( ) N(µ, σ ), σ 0!(σ 0 ) H 1 σ σ 0. ( ) H 0 σ = σ 0. n S,, Y = (n 1) S, n 1. σ0 y 0 = χ 1 α (n 1), y 1 = χ α (n 1) ( ) L14 Excel t I(015) 5 / 0

6 1 α = 0.95, ( ) P χ 1 α (n 1) < (n 1) S σ0 < χ α (n 1) = 1 α., S,, S S < σ 0 χ 1 α (n 1), σ0 n 1,. χ α (n 1) < S n 1 ( ) L14 Excel t I(015) 6 / 0

7 L14-Q1 TA Prob and Sol: S, σ 0 = 4g., S 9, ( g). 76, 76, 76, 76, 80, 84, 84, 84, 84. S σ, σ 0?, α = 0.05,. 1 α = 0.05,. ( ) L14 Excel t I(015) 7 / 0

8 3, σ, σ0 = 4 4 n S, χ = (n 1) s, n 1. σ0. 5 χ = (n 1) s = (9 1) 16 σ0 4 = 3. 6,, χ < χ 1 α (n 1) =.180, χ > χ α (n 1) = σ 0 = 4.,. σ0 ( σ0 )., p Excel p, p = < α,. ( ) L14 Excel t I(015) 8 / 0

9 3 4 Excel t Excel ( ) L14 Excel t I(015) 9 / 0

10 ,, q 0 = H 1 q q 0 H 0 q = q 0 : 100 X. X = 0, 5, 6,..., 100. ( ) L14 Excel t I(015) 10 / 0

11 L14-Q q 0 = 0.03,, α. α., α. ( ) L14 Excel t I(015) 11 / 0

12 L14-Q3 q( q 0 ),, β., 1 β β.. ( ) L14 Excel t I(015) 1 / 0

13 ,, H 0 H 0 H 0 ( β ) H 0 1 ( α ) α: 1 α: 1 β: or, β α., α, β. ( ) L14 Excel t I(015) 13 / 0

14 p (t ) p (p-value),. p < α. ( ) L14 Excel t I(015) 14 / 0

15 Excel 3 4 Excel t Excel ( ) L14 Excel t I(015) 15 / 0

16 Excel Excel 013 Excel average var stdev : average, varp, stdevp. ( ) L14 Excel t I(015) 16 / 0

17 Excel Excel 013 t n: t Excel p =t.dist.rt(t, n) t =t.inv( p, n) Excel Excel,. R II, II ( ) L14 Excel t I(015) 17 / 0

18 Excel Excel t T T p p < α t, t II ( ) L14 Excel t I(015) 18 / 0

19 Excel Excel 013 n: t Excel p =chisq.dist.rt(y 1, n) 1 p =chisq.dist.rt(y 0, n) y 1 =chisq.inv( p, n) y 0 =chisq.inv(1 p, n) ( ) L14 Excel t I(015) 19 / 0

20 Excel t Math., Quiz , Quiz 4 6(1-50) manaba / https://manaba. ryukoku.ac.jp ( ) L14 Excel t I(015) 0 / 0

データの分布と代表値

データの分布と代表値 I L01(2015-09-18 Fri) : Time-stamp: 2015-09-26 Sat 10:37 JST hig e, http://hig3.net ( ) L01 I(2015) 1 / 26 ? 1? 2? ( ) L01 I(2015) 2 / 26 ?,,.,., 1..,. (,, 1, 2 ),.,. ( ) L01 I(2015) 3 / 26 ? I. M (3 )

More information

データの分布

データの分布 I L01(2016-09-22 Thu) : Time-stamp: 2016-09-27 Tue 11:12 JST hig e LINE@, 4, http://hig3.net () L01 I(2016) 1 / 20 ? 1? 2? () L01 I(2016) 2 / 20 ?,,.,., 1..,. (,, 1, 2 ),.,. () L01 I(2016) 3 / 20 ? I.

More information

1 913 10301200 A B C D E F G H J K L M 1A1030 10 : 45 1A1045 11 : 00 1A1100 11 : 15 1A1115 11 : 30 1A1130 11 : 45 1A1145 12 : 00 1B1030 1B1045 1C1030

1 913 10301200 A B C D E F G H J K L M 1A1030 10 : 45 1A1045 11 : 00 1A1100 11 : 15 1A1115 11 : 30 1A1130 11 : 45 1A1145 12 : 00 1B1030 1B1045 1C1030 1 913 9001030 A B C D E F G H J K L M 9:00 1A0900 9:15 1A0915 9:30 1A0930 9:45 1A0945 10 : 00 1A1000 10 : 15 1B0900 1B0915 1B0930 1B0945 1B1000 1C0900 1C0915 1D0915 1C0930 1C0945 1C1000 1D0930 1D0945 1D1000

More information

untitled

untitled 11 10 267 6 129 48.3 6 63 2 1 2JIS ME JIS T 1005JIS 1994 1 11 A 10 1999 5 3 13 ME 4 2 11 B B 1999 4 10 267 6 B 7 9 6 10 12 3 11 Excel MODE Excel STANDARDIZE STANDARDIZE(X,)X AVERAGE STDEVP Excel VAR 0.5

More information

リスクとは何か?

リスクとは何か? http://www.craft.titech.ac.jp/~nakagawa/dir2/lecture.html#tit2005_1 Agenda Value at Risk 2 3 TOPIX 10 95% 4 TOPIX or Value at Risk 5 TOPIX = log TOPIX N 6 7 N TOPIX x, x, 1 2, L x N 8 x = N 1 EXCEL AVERAGE

More information

aisatu.pdf

aisatu.pdf 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71

More information

54_2-05-地方会.indd

54_2-05-地方会.indd 82 58 59 21 83 84 2 9 4 85 86 1. 87 6 88 89 β 1 90 2 3 p 4 t 5 6 EQ 91 7 8 9 1 10 2 92 11 3 12 13 IT p 14 93 15 16 ACTIVE 17 18 94 p p p 19 20 21 22 95 23 24 25 2 26 β β 96 27 1 28 29 30 97 31 32 33 1

More information

3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α

3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α 2 2.1. : : 2 : ( ): : ( ): : : : ( ) ( ) ( ) : ( pp.53 6 2.3 2.4 ) : 2.2. ( ). i X i (i = 1, 2,..., n) X 1, X 2,..., X n X i (X 1, X 2,..., X n ) ( ) n (x 1, x 2,..., x n ) (X 1, X 2,..., X n ) : X 1,

More information

3 3.1 *2 1 2 3 4 5 6 *2 2

3 3.1 *2 1 2 3 4 5 6 *2 2 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

More information

第85 回日本感染症学会総会学術集会後抄録(III)

第85 回日本感染症学会総会学術集会後抄録(III) β β α α α µ µ µ µ α α α α γ αβ α γ α α γ α γ µ µ β β β β β β β β β µ β α µ µ µ β β µ µ µ µ µ µ γ γ γ γ γ γ µ α β γ β β µ µ µ µ µ β β µ β β µ α β β µ µµ β µ µ µ µ µ µ λ µ µ β µ µ µ µ µ µ µ µ

More information

一般演題(ポスター)

一般演題(ポスター) 6 5 13 : 00 14 : 00 A μ 13 : 00 14 : 00 A β β β 13 : 00 14 : 00 A 13 : 00 14 : 00 A 13 : 00 14 : 00 A β 13 : 00 14 : 00 A β 13 : 00 14 : 00 A 13 : 00 14 : 00 A β 13 : 00 14 : 00 A 13 : 00 14 : 00 A

More information

P1-1 P1-2 P1-3 P1-4 P1-5 P1-6 P3-1 P3-2 P3-3 P3-4 P3-5 P3-6 P5-1 P5-2 P5-3 P5-4 P5-5 P5-6 P7-1 P7-2 P7-3 P7-4 P7-5 P7-6 P9-1 P9-2 P9-3 P9-4 P9-5 P9-6 P11-1 P11-2 P11-3 P11-4 P13-1 P13-2 P13-3 P13-4 P13-5

More information

P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22

P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22 1 14 28 16 00 17 30 P-1 P-2 P-3 P-4 P-5 2 24 29 17 00 18 30 P-6 P-7 P-8 P-9 P-10 P-11 P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22 5 24 28 16 00 17 30 P-23

More information

... 3... 3... 3... 3... 4... 7... 10... 10... 11... 12... 12... 13... 14... 15... 18... 19... 20... 22... 22... 23 2

... 3... 3... 3... 3... 4... 7... 10... 10... 11... 12... 12... 13... 14... 15... 18... 19... 20... 22... 22... 23 2 1 ... 3... 3... 3... 3... 4... 7... 10... 10... 11... 12... 12... 13... 14... 15... 18... 19... 20... 22... 22... 23 2 3 4 5 6 7 8 9 Excel2007 10 Excel2007 11 12 13 - 14 15 16 17 18 19 20 21 22 Excel2007

More information

日本糖尿病学会誌第58巻第1号

日本糖尿病学会誌第58巻第1号 α β β β β β β α α β α β α l l α l μ l β l α β β Wfs1 β β l l l l μ l l μ μ l μ l Δ l μ μ l μ l l ll l l l l l l l l μ l l l l μ μ l l l l μ l l l l l l l l l l μ l l l μ l μ l l l l l l l l l μ l l l l

More information

2 1 2 3 27 2 6 2 5 19 50 1 2

2 1 2 3 27 2 6 2 5 19 50 1 2 1 2 1 2 3 27 2 6 2 5 19 50 1 2 2 17 1 5 6 5 6 3 5 5 20 5 5 5 4 1 5 18 18 6 6 7 8 TA 1 2 9 36 36 19 36 1 2 3 4 9 5 10 10 11 2 27 12 17 13 6 30 16 15 14 15 16 17 18 19 28 34 20 50 50 5 6 3 21 40 1 22 23

More information

受賞講演要旨2012cs3

受賞講演要旨2012cs3 アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート α β α α α α α

More information

1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1

1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 1 21 10 5 1 E-mail: qliu@res.otaru-uc.ac.jp 1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 B 1.1.3 boy W ID 1 2 3 DI DII DIII OL OL 1.1.4 2 1.1.5 1.1.6 1.1.7 1.1.8 1.2 1.2.1 1. 2. 3 1.2.2

More information

診療ガイドライン外来編2014(A4)/FUJGG2014‐01(大扉)

診療ガイドライン外来編2014(A4)/FUJGG2014‐01(大扉) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

More information

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ( ) 24 25 26 27 28 29 30 ( ) ( ) ( ) 31 32 ( ) ( ) 33 34 35 36 37 38 39 40 41 42 43 44 ) i ii i ii 45 46 47 2 48 49 50 51 52 53 54 55 56 57 58

More information

23 15961615 1659 1657 14 1701 1711 1715 11 15 22 15 35 18 22 35 23 17 17 106 1.25 21 27 12 17 420,845 23 32 58.7 32 17 11.4 71.3 17.3 32 13.3 66.4 20.3 17 10,657 k 23 20 12 17 23 17 490,708 420,845 23

More information

untitled

untitled i ii (1) (1) (2) (1) (3) (1) (1) (2) (1) (3) (1) (1) (2) (1) (3) (2) (3) (1) (2) (3) (1) (1) (1) (1) (2) (1) (3) (1) (2) (1) (3) (1) (1) (1) (2) (1) (3) (1) (1) (2) (1) (3)

More information

橡Taro13-EXCEL統計学.PDF

橡Taro13-EXCEL統計学.PDF Excel 4.1 4.1.1 1 X n X,X, 1,Xn X=X X X /n 1 n Excel AVERAGE =AVERAGE Excel MEDIAN 3 =MEDIAN Excel MODE =MODE 4.1. 1 Excel MAX MIN =MAX MIN n X,X,,X X 4-1 1 n V X1-X + X-X + + Xn-X V= n 0 0 Excel VARP

More information

36

36 36 37 38 P r R P 39 (1+r ) P =R+P g P r g P = R r g r g == == 40 41 42 τ R P = r g+τ 43 τ (1+r ) P τ ( P P ) = R+P τ ( P P ) n P P r P P g P 44 R τ P P = (1 τ )(r g) (1 τ )P R τ 45 R R σ u R= R +u u~ (0,σ

More information

untitled

untitled 1 1 Excel3 2008.8.19 2 3 10 1 () 4 40596079 2 OK 1 5 341 1 1 6 3-1 A134A135 B135 COUNTIF OK 3-1 7 3 B6B132 1 B135 COUNTIF) OK B6B132 8 2 3-1 3 3-1 3 1 2A133 A134 A135 3B133 SUBTOTAL 9 2 B5B131 OK 4SUBTOTAL

More information

第86回日本感染症学会総会学術集会後抄録(II)

第86回日本感染症学会総会学術集会後抄録(II) χ μ μ μ μ β β μ μ μ μ β μ μ μ β β β α β β β λ Ι β μ μ β Δ Δ Δ Δ Δ μ μ α φ φ φ α γ φ φ γ φ φ γ γδ φ γδ γ φ φ φ φ φ φ φ φ φ φ φ φ φ α γ γ γ α α α α α γ γ γ γ γ γ γ α γ α γ γ μ μ κ κ α α α β α

More information

15 2004.03 194

15 2004.03 194 The Statistical Processing using EXCEL MIYOSHI Yoshihiko In this paper, I summarize the method of performing statistical processing using only the basic function of EXCEL without the VBA macro, add-in

More information

untitled

untitled 186 17 100160250 1 10.1 55 2 18.5 6.9 100 38 17 3.2 17 8.4 45 3.9 53 1.6 22 7.3 100 2.3 31 3.4 47 OR OR 3 1.20.76 63.4 2.16 4 38,937101,118 17 17 17 5 1,765 1,424 854 794 108 839 628 173 389 339 57 6 18613

More information

untitled

untitled 1. 3 14 2. 1 12 9 7.1 3. 5 10 17 8 5500 4. 6 11 5. 1 12 101977 1 21 45.31982.9.4 79.71996 / 1997 89.21983 41.01902 6. 7 5 10 2004 30 16.8 37.5 3.3 2004 10.0 7.5 37.0 2004 8. 2 7 9. 6 11 46 37 25 55 10.

More information

2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26 $ $E26 E$26 E$26 $G34 $ E26 F4

2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26 $ $E26 E$26 E$26 $G34 $ E26 F4 1234567 0.1234567 = 2 3 =2+3 =2-3 =2*3 =2/3 =2^3 1:^, 2:*/, 3:+- () =2+3*4 =(2+3)*4 =3*2^2 =(3*2)^2 =(3+6)^0.5 A12 =A12+B12 ( ) ( )0.4 ( 100)0.9 % 1 2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26

More information

データの分布

データの分布 I L01(2014-09-19 Fri) /Excel /Excel http://hig3.net () L01 I(2014) 1 / 24 1 2 Quiz=? () L01 I(2014) 2 / 24 ,,.,., 1..,. (,, 1, 2 ),.,. () L01 I(2014) 3 / 24 I. M (3 ) II, II,! CPU,,, (AI), (machine learning)!!

More information

(interval estimation) 3 (confidence coefficient) µ σ/sqrt(n) 4 P ( (X - µ) / (σ sqrt N < a) = α a α X α µ a σ sqrt N X µ a σ sqrt N 2

(interval estimation) 3 (confidence coefficient) µ σ/sqrt(n) 4 P ( (X - µ) / (σ sqrt N < a) = α a α X α µ a σ sqrt N X µ a σ sqrt N 2 7 2 1 (interval estimation) 3 (confidence coefficient) µ σ/sqrt(n) 4 P ( (X - µ) / (σ sqrt N < a) = α a α X α µ a σ sqrt N X µ a σ sqrt N 2 (confidence interval) 5 X a σ sqrt N µ X a σ sqrt N - 6 P ( X

More information

" " " " "!!

    !! ""!!!!! "! "! " " " " " " " "!! !!!!!!!!! ! !!!!! "β!"β"! " " "!! "! "!!! "!! !!! "! "!!!! "! !!!!! !!! " "!! "!!! " " "!!! ! "!! !!!!!!! " " " " "!! α!!!!! ! "! " " !!!!!!! "! ! ""!!!! !!!!!! " "! "!

More information

136 pp p µl µl µl

136 pp p µl µl µl 135 2006 PCB C 12 H 10-n Cl n n 1 10 CAS No. 42 PCB: 53469-21-9, 54 PCB: 11097-69-1 0.01 mg/m 3 PCB PCB 25 µg/l 136 pp p µl µl µl 137 1 γ 138 1 γ γ γ µl µl µl µl µl µl µl l µl µl µl µl µl l 139 µl µl µl

More information

日本分子第4巻2号_10ポスター発表.indd

日本分子第4巻2号_10ポスター発表.indd JSMI Report 62 63 JSMI Report γ JSMI Report 64 β α 65 JSMI Report JSMI Report 66 67 JSMI Report JSMI Report 68 69 JSMI Report JSMI Report 70 71 JSMI Report JSMI Report 72 73 JSMI Report JSMI Report 74

More information

(Nov/2009) 2 / = (,,, ) 1 4 3 3 2/8

(Nov/2009) 2 / = (,,, ) 1 4 3 3 2/8 (Nov/2009) 1 sun open-office calc 2 1 2 3 3 1 3 1 2 3 1 2 3 1/8 (Nov/2009) 2 / = (,,, ) 1 4 3 3 2/8 (Nov/2009) 1 (true) false 1 2 2 A1:A10 A 1 2 150 3 200 4 250 5 320 6 330 7 360 8 380 9 420 10 480 (1)

More information

<4D6963726F736F667420576F7264202D204850835483938376838B8379815B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

<4D6963726F736F667420576F7264202D204850835483938376838B8379815B83578B6594BB2D834A836F815B82D082C88C60202E646F63> 例 題 で 学 ぶ Excel 統 計 入 門 第 2 版 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. http://www.morikita.co.jp/books/mid/084302 このサンプルページの 内 容 は, 第 2 版 発 行 当 時 のものです. i 2 9 2 Web 2 Excel Excel Excel 11 Excel

More information

第89回日本感染症学会学術講演会後抄録(I)

第89回日本感染症学会学術講演会後抄録(I) ! ! ! β !!!!!!!!!!! !!! !!! μ! μ! !!! β! β !! β! β β μ! μ! μ! μ! β β β β β β μ! μ! μ!! β ! β ! ! β β ! !! ! !!! ! ! ! β! !!!!! !! !!!!!!!!! μ! β !!!! β β! !!!!!!!!! !! β β β β β β β β !!

More information