P 値と有意差／分散分析 / P-value, Significant Difference 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」2024 冬の第9-10回で使用したスライドです。

Transcript

1. Corporate data analysis — generated by Stable Diffusion XL v1.0 2024 9-10 P (WBS) 2024 9-10 P — 2025-01-06 – p.1/33
2. https://speakerdeck.com/ks91/collections/corporate-data-analysis-2024-winter 2024 9-10 P — 2025-01-06 – p.2/33
3. ( ) 1 12 2 • 2 12 2 (B A ) • 3 12 9 • 4 12 9 • 5 12 16 • 6 12 16 t • 7 12 23 2 ( ) t • 8 12 23 2 ( ) t • 9 1 6 P • 10 1 6 • 11 1 20 12 1 20 13 1 27 14 1 27 W-IOI 2024 9-10 P — 2025-01-06 – p.3/33
4. ( 20 25 ) 1 (20 ) • 2 R ( 55 ) • 3 (32 ) • 4 (14 ) • 5 ( Git) (22 ) • 6 ( ) (24 ) • 7 (1) (25 ) • 8 (2) (25 ) • 9 R ( ) (1) — Welch (17 ) • 10 R ( ) (2) — (21 ) • 11 R ( ) (1) — (15 ) • 12 R ( ) (2) — (19 ) • 13 GPT-4 (19 ) • 14 GPT-4 (29 ) • 15 ( ) LaTeX Overleaf (40 ) • 8 (12/16 ) / (2 ) OK / 2024 9-10 P — 2025-01-06 – p.4/33
5. ( Student µ 95% ) 7 2 t ( t ) 2 ( ) 2 d ( ) ← [ 3] σd 2 t 8 2 t ( t ) 2 ( ) ( ) ← [ 4] σ 2 t 2024 9-10 P — 2025-01-06 – p.5/33
6. 2 2 t 1 9 P P 10 H0 HA k, N, ¯ ¯ x σ2 ( )MSwithin ( )MSbetween MStotal F F 2024 9-10 P — 2025-01-06 – p.6/33
7. 2024 9-10 P — 2025-01-06 – p.7/33
8. 4. t (1) 2 t (2) 2 t (3) 2025 1 2 ( ) 23:59 JST ( ) Waseda Moodle (Q & A ) (1)(2) Discord 2024 9-10 P — 2025-01-06 – p.8/33
9. . . . . . . 17 14 (1/3( ) ) ( ) → 14 ( ) ( ) → 6 → 3 ( ) → 5 ( ) ( OK) 2 t . . . . . . / . . . ( ) 2024 9-10 P — 2025-01-06 – p.9/33
10. t t ⇒ ( ) A A xA 2 B B xB 2 df . . . ⇒ t σ z0.05 . . . ⇒ ( ) t 2024 9-10 P — 2025-01-06 – p.10/33
11. N (1/2) 2 t 2 2 “ ” 1. 1 2 2. 3. - 2 (n − 1) 4. ÷ ÷ t 5. t (n − 1) t t ⇒ . . . 0 ( ) 2024 9-10 P — 2025-01-06 – p.11/33
12. N (2/2) 2 t 2 2 1 2 1 2 2 “ ” 1. 2 1 2 2. 3. ( -2) 4. t 1÷ 2 t 5. t (n1 + n2 − 2) t t ⇒ 2024 9-10 P — 2025-01-06 – p.12/33
13. M ( ) [ 2 t ] 1Day 1Day 1Day ⇒ 2024 9-10 P — 2025-01-06 – p.13/33
14. K ⇒ . . . 2024 9-10 P — 2025-01-06 – p.14/33
15. 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) 2024 9-10 P — 2025-01-06 – p.15/33
16. 2 t ( ) 10 ( ) ( ) ( ) ( ) ( ) d ( ) d, ( ) sd , ( ) n, ( ) df ( ) t ( ) t ( ) d ( ) sd ( ) n ( ) t df 5% ( ) ( ) ( ) ( ) ( ) 2024 9-10 P — 2025-01-06 – p.16/33
17. 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) 2024 9-10 P — 2025-01-06 – p.17/33
18. 2 t ( ) ( ) ( ) ( ) ( ) ( ) ( ( ) A B ( ) ) ( ) xA − xB , A B ( ) ( ) sp , ( ) nA nB , ( ) df = nA + nB − 2 ( ) t ( ) t ( ) xA − xB ( ) sp ( ) nA ,nB ( ) t df 5% ( ) ( ) ( ) ( ) ( ) ( ) 2024 9-10 P — 2025-01-06 – p.18/33
19. K 2 t ( ) ⇒ 2 2024 9-10 P — 2025-01-06 – p.19/33
20. N ⇒ (σ) ( σ √n ) ( ) p.121 (standard error) (p.121) (sampling distribution) (p.120) (p.120) ( : ) 2024 9-10 P — 2025-01-06 – p.20/33
21. K ⇒ . . . AI ( ) . . . ^^; ( ) 2024 9-10 P — 2025-01-06 – p.21/33
22. H t 2 Student t t 1 sin(α + β) = sinαcosβ + cosαsinβ . . . ⇒ 2024 9-10 P — 2025-01-06 – p.22/33
23. U R ChatGPT ⇒ AI ( ) 2024 9-10 P — 2025-01-06 – p.23/33
24. 9 P P 2024 9-10 P — 2025-01-06 – p.24/33
25. α β P P H0 ( ) P 0.05 (P = 0.015) (P = 0.361) 2024 9-10 P — 2025-01-06 – p.25/33
26. 10 H0 HA k, N, ¯ ¯ x σ2 ( ) MSwithin ( )MSbetween MStotal ( SStotal dftotal ) F F 2024 9-10 P — 2025-01-06 – p.26/33
27. (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 ) 2024 9-10 P — 2025-01-06 – p.27/33
28. (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 ) 2024 9-10 P — 2025-01-06 – p.28/33
29. (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 ) 2024 9-10 P — 2025-01-06 – p.29/33
30. U ( p.227) 20 4 “ U.R” ( anova() ) pp.226–227 2024 9-10 P — 2025-01-06 – p.30/33
31. 2024 9-10 P — 2025-01-06 – p.31/33
32. 5. (1) ( ) (2) 2025 1 16 ( ) 23:59 JST ( ) Waseda Moodle (Q & A ) (1)(2) Discord 2024 9-10 P — 2025-01-06 – p.32/33
33. 2024 9-10 P — 2025-01-06 – p.33/33