P 値と有意差／分散分析 / P-value and Analysis of Variance

早稲田大学大学院経営管理研究科「企業データ分析」2023 冬の第9-10回で使用したスライドです。

Transcript

1. generated by Stable Diffusion XL v1.0 2023 9-10 P (WBS) 2023 9-10 P — 2024-01-11 – p.1/26
2. https://speakerdeck.com/ks91/collections/corporate-data-analysis-2023-winter 2023 9-10 P — 2024-01-11 – p.2/26
3. ( ) 1 11 30 • 2 11 30 (B A ) • 3 12 7 • 4 12 7 • 5 12 14 • 6 12 14 t • 7 12 21 2 ( ) t • 8 12 21 2 ( ) t • 9 1 11 P • 10 1 11 • 11 1 18 12 1 18 13 1 25 14 1 25 W-IOI 2023 9-10 P — 2024-01-11 – p.3/26
4. ( 20 ) 1 • 2 R • 3 • 4 • 5 • 6 ( ) • 7 (1) • 8 (2) • 9 R ( ) (1) — Welch 10 R ( ) (2) — χ2 11 R ( ) (1) — 12 R ( ) (2) — 13 GPT-4 14 GPT-4 15 ( ) LaTeX Overleaf 8 (12/21 ) / (2 ) OK / 2023 9-10 P — 2024-01-11 – p.4/26
5. ( Student µ 95% ) 7 2 t ( t ) 2 ( ) 2 d ( ) ← [ 3] σd 2 t 8 2 t ( t ) 2 ( ) ( ) ← [ 4] σ 2 t 2023 9-10 P — 2024-01-11 – p.5/26
6. 2 2 t 1 9 P P 10 H0 HA k, N, ¯ ¯ x σ2 ( )MSwithin ( )MSbetween MStotal F F 2023 9-10 P — 2024-01-11 – p.6/26
7. 2023 9-10 P — 2024-01-11 – p.7/26
8. 4. t (1) 2 t (2) 2 t (3) 2024 1 7 ( ) 23:59 JST ( ) Waseda Moodle (Q & A ) (1)(2) Discord 2023 9-10 P — 2024-01-11 – p.8/26
9. . . . . . . 10 7 (1/9( ) ) ( ) → 7 ( ) ( ) → 1 ( ) → 1 0 ( 2 ) vs. 0 ( 2 ) ( 2 ) vs. ( 2 ) → 5 2023 9-10 P — 2024-01-11 – p.9/26
10. I (1/2) 2 t BMI 5 (A B C D E) 1 BMI ( ) 2 t 0 5 BMI A 34 ⇒ 21 B 35 ⇒ 24 C 38 ⇒ 26 D 40 ⇒ 32 E 33 ⇒ 35 ⇒ ↑ I 2023 9-10 P — 2024-01-11 – p.10/26
11. 2 t d : µd 0 ( 2 ) : (1) d d, sd , n, df (2) |d| sd n |t| (3) t0.05 (df) < |t| ( ) R > t.test(sample2, sample1, paired=T) 2023 9-10 P — 2024-01-11 – p.11/26
12. I (2/2) 2 t 2 5 5 2 t 0 10 A 5.6 4.9 5.3 6.0 5.1 B 8.2 7.6 6.8 7.5 8.3 ⇒ ↑ I 2023 9-10 P — 2024-01-11 – p.12/26
13. 2 t xA xB : µA − µB 0 ( 2 ) : (1) xA − xB , sp , nA nB , df (2) |xA − xB | sp nA nB |t| (3) t0.05 (df) < |t| ( ) R > t.test(sample2, sample1, var.equal=T) 2023 9-10 P — 2024-01-11 – p.13/26
14. I ⇒ 12 R “ .txt” “ .txt” 2023 9-10 P — 2024-01-11 – p.14/26
15. S 2 2 t ⇒ p.28 2023 9-10 P — 2024-01-11 – p.15/26
16. K ⇒ 2023 9-10 P — 2024-01-11 – p.16/26
17. 9 P P 2023 9-10 P — 2024-01-11 – p.17/26
18. α β P P H0 ( ) P 0.05 (P = 0.015) (P = 0.361) 2023 9-10 P — 2024-01-11 – p.18/26
19. 10 H0 HA k, N, ¯ ¯ x σ2 ( ) MSwithin ( )MSbetween MStotal ( SStotal dftotal ) F F 2023 9-10 P — 2024-01-11 – p.19/26
20. (1/3) k (1) : (2) : σ2 ( ) N(µ, σ2) µ1 = µ2 = · · · = µk N ( ) ¯ ¯ x ¯ ¯ x = k j=1 nj i=1 xji N (j i N ) 2023 9-10 P — 2024-01-11 – p.20/26
21. (2/3) ( )MSwithin σ2 MSwithin = SSwithin dfwithin = k j=1 nj i=1 (xji − ¯ xj )2 N − k ( N− ) ( )MSbetween σ2 MSbetween = SSbetween dfbetween = k j=1 nj (¯ xj − ¯ ¯ x)2 k − 1 ( −1 ) ( H0 σ2 ) 2023 9-10 P — 2024-01-11 – p.21/26
22. (3/3) MStotal MStotal = SStotal dftotal = k j=1 nj i=1 (xji − ¯ ¯ x)2 N − 1 ( N − 1 ) : SStotal = SSbetween + SSwithin, dftotal = dfbetween + dfwithin F F = MSbetween MSwithin F0.05 (dfbetween, dfwithin ) < F ( H0 ) 2023 9-10 P — 2024-01-11 – p.22/26
23. U ( p.227) 20 4 “ U.R” ( anova() ) pp.226–227 2023 9-10 P — 2024-01-11 – p.23/26
24. 2023 9-10 P — 2024-01-11 – p.24/26
25. 5. (1) ( ) (2) 2024 1 14 ( ) 23:59 JST ( ) Waseda Moodle (Q & A ) (1)(2) Discord 2023 9-10 P — 2024-01-11 – p.25/26
26. 2023 9-10 P — 2024-01-11 – p.26/26