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組織とデータ分析/統計的仮説検定 / Organization and Data Analysis, and Statistical Hypothesis Testing
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Kenji Saito
PRO
November 30, 2023
Business
1
100
組織とデータ分析/統計的仮説検定 / Organization and Data Analysis, and Statistical Hypothesis Testing
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1-2回で使用したスライドです。
Kenji Saito
PRO
November 30, 2023
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Transcript
generated by Stable Diffusion XL v1.0 2023 1-2 (WBS) 2023
1-2 — 2023-11-30 – p.1/36
https://speakerdeck.com/ks91/collections/corporate-data-analysis-2023-winter Discord . . . Discord 2023 1-2 — 2023-11-30
– p.2/36
( ) ( ) ( ) SFC ( ) CSO
(Chief Science Officer) 1993 ( ) 2006 ( ) SFC 23 P2P (Peer-to-Peer) 2011 ( ) 2018 2019 VR 2021.9 & VR 2022.3 2023 AI VR&RPG 2023.5 “Don’t Be So Serious” VOXEL 2023.7 DAZE 2023 In Maker Faire Tokyo 2023 → ( ) 2023 1-2 — 2023-11-30 – p.3/36
Dropbox Dropbox ( ) 2023 1-2 — 2023-11-30 – p.4/36
(B A ) 1 ( ) 2 (Wilcoxon-Mann-Whitney ) 2023
1-2 — 2023-11-30 – p.5/36
R 2023 1-2 — 2023-11-30 – p.6/36
[ ] , (2022) R R ( ) R 2023
1-2 — 2023-11-30 – p.7/36
( ) 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 1-2 — 2023-11-30 – p.8/36
( 20 ) 1 • 2 R • 3 •
4 • 5 6 ( ) 7 (1) 8 (2) 9 R ( ) (1) 10 R ( ) (2) 11 R ( ) (1) 12 R ( ) (2) 13 GPT-4 14 GPT-4 15 ( ) LaTeX Overleaf 8 (12/14 ) / (2 ) OK / 2023 1-2 — 2023-11-30 – p.9/36
. . . . . . ( ) ( 20
×(14+1) ) 2023 1-2 — 2023-11-30 – p.10/36
(2 )(160 ) (10∼20 ) ( ) and/or 1 (80
) 1 Q & A & (30∼40 ) (30∼40 ) 2023 1-2 — 2023-11-30 – p.11/36
Moodle ( Q&A ) ( ) Discord ( ) ←
( ) 2023 1-2 — 2023-11-30 – p.12/36
( ) A4 2 2 (Overleaf ) L ATEX PDF
( ) 2023 1-2 — 2023-11-30 – p.13/36
+ + [ ] R , (2008) R 2023 1-2
— 2023-11-30 – p.14/36
2023 1-2 — 2023-11-30 – p.15/36
= ⇒ (1) (2) (3) = ⇒ ( ) (
(2)) = ⇒ ( ) ( ) AI 2023 1-2 — 2023-11-30 – p.16/36
(observation) (sample) (random variable) (probability distribution) (population) (simple random sampling)
( )( 2 t , , ) 2 ( , ) 2023 1-2 — 2023-11-30 – p.17/36
(B A ) 1 ( ) 2 (Wilcoxon-Mann-Whitney ) 2023
1-2 — 2023-11-30 – p.18/36
1 ( ) P(X = x) = n C x
· px · (1 − p)n−x E[X] = np (1) (null hypothesis) H0 (2) (test statistic) ( x ) (3) H0 (null distribution) (4) (rejection region) ( ; 5% 1%) · (significance level) (5) ( H0 ) 2023 1-2 — 2023-11-30 – p.19/36
B ( p.47) RStudio R n C x ‘choose(n,x)’ n
= 18, x = 0 . . . choose(18,0)×0.50 × 0.518 = choose(18,0)×0.518 ( ) ⇒ ( ) 3 : : : 2023 1-2 — 2023-11-30 – p.20/36
R ( B)(1/2) — R n <- 18 # p
<- 0.5 # <- c() # ( ) # x 0 for (x in 0:n) { # <- c( , choose(n,x)*p^x*(1-p)^(n-x)) } halfp <- 0 # ( 0 1) ( ) 2023 1-2 — 2023-11-30 – p.21/36
R ( B)(2/2) — R # x 0 ( )
for (x in 0:n) { # 0.025 if (halfp + [x+1] > 0.025) { break } halfp <- halfp + [x+1] # } # color <- rep(c("red"), x) # rep 2 color <- c(color, rep(c("black"), n + 1 - x*2), color) <- 0:n # x # plot (lwd ) plot( , , type="h", lwd=3, col=color) 2023 1-2 — 2023-11-30 – p.22/36
0 5 10 15 0.00 0.05 0.10 0.15 ேᩘ ☜⋡
2023 1-2 — 2023-11-30 – p.23/36
R > binom.test(14, n=18, p=0.5) p-value (P )( 9 )
0.05 ↑ 2023 1-2 — 2023-11-30 – p.24/36
2 (Wilcoxon-Mann-Whitney ) WMW ( ) A B A B
( ) (2) U (U ) · U = min(nAnB + 1 2 nA (nA + 1) − RA, nAnB + 1 2 nB (nB + 1) − RB ) (4) ((3) ) U0.05 (5) U U0.05 2023 1-2 — 2023-11-30 – p.25/36
D ( p.70) RStudio . . . 2023 1-2 —
2023-11-30 – p.26/36
R ( D)(1/2) — GPT ChatGPT (GPT-4) R ( )
1 ( ) ⇒ GPT-4 (1/2) # calculate_rank_sum <- function(sample1, sample2) { # combined_samples <- c(sample1, sample2) sample_group <- c(rep("sample1", length(sample1)), rep("sample2", length(sample2))) # ranks <- rank(combined_samples) 2023 1-2 — 2023-11-30 – p.27/36
R ( D)(2/2) — GPT ⇒ GPT-4 (2/2) # df
<- data.frame(value = combined_samples, group = sample_group, rank = ranks) # rank_sum_sample1 <- sum(df[df$group == "sample1", "rank"]) rank_sum_sample2 <- sum(df[df$group == "sample2", "rank"]) return(list(sample1_rank_sum = rank_sum_sample1, sample2_rank_sum = rank_sum_sample2)) } # sample1 <- c(3, 1, 4) sample2 <- c(2, 5, 6) # calculate_rank_sum(sample1, sample2) 2023 1-2 — 2023-11-30 – p.28/36
GPT . . . GPT-4 . . . ‘rank(. .
.)’ RStudio Help → Search R Help ⇒ GPT GPT 3 (1) (GPT ) (2) (GPT ) (3) 2023 1-2 — 2023-11-30 – p.29/36
R ( D)(1/2) — R <- c(4.6, 5.6, 3.2, 3.2,
3.7, 4.0, 5.0, 4.6) <- c(4.6, 4.9, 7.1, 6.0, 5.2, 3.9, 5.3, 5.8) # combined_samples <- c( , ) sample_group <- c(rep(" ", length( )), rep(" ", length( ))) # ranks <- rank(combined_samples) # df <- data.frame(value = combined_samples, group = sample_group, rank = ranks) # ra <- sum(df[df$group == " ", "rank"]) rb <- sum(df[df$group == " ", "rank"]) 2023 1-2 — 2023-11-30 – p.30/36
R ( D)(2/2) — R # U na <- length(
) nb <- length( ) U <- min(na*nb + na / 2 * (na + 1) - ra, na*nb + nb / 2 * (nb + 1) - rb) print(paste("U =", U)) # paste # sdf <- data.frame( , ) # boxplot(sdf, ylim=c(0, 8.0), ylab=" ( : )") U U0.05 2023 1-2 — 2023-11-30 – p.31/36
⫧‶ ⫧‶࡛ࡣ࡞࠸ 0 2 4 6 8 ᖺ (༢:ⓒ) 2023
1-2 — 2023-11-30 – p.32/36
R WMW > wilcox.test( , ) p-value (P )( 9
) 0.05 P ↑ 2023 1-2 — 2023-11-30 – p.33/36
2023 1-2 — 2023-11-30 – p.34/36
1. (1) (2) 2023 12 3 ( ) 23:59 JST
( ) Waseda Moodle (Q & A ) 2023 1-2 — 2023-11-30 – p.35/36
2023 1-2 — 2023-11-30 – p.36/36