Boxes and whiskers — generated by Stable Diffusion XL v1.0 2024 9 R ( ) (1) — Welch (WBS) 2024 9 R ( ) (1) — Welch — 2024-11 – p.1/10

https://speakerdeck.com/ks91/collections/corporate-data-analysis-2024-winter 2024 9 R ( ) (1) — Welch — 2024-11 – p.2/10

( 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 (12/16 ) / (2 ) OK / 2024 9 R ( ) (1) — Welch — 2024-11 – p.3/10

t Welch R t.test() Welch Welch 2024 9 R ( ) (1) — Welch — 2024-11 – p.4/10

2 t ( ) (1/2) 2 ( ) xA − xB (1) : (2) : σ ( ) σ sp sp = s2 A (nA − 1) + s2 B (nB − 1) nA + nB − 2 (R var() ) nA + nB − 2 t Welch A B (µA = µB ) A B (µA = µB ) 2024 9 R ( ) (1) — Welch — 2024-11 – p.5/10

2 t ( ) (2/2) xA − xB Student µA = µB t = (xA − xB ) − (µA − µB ) sp 1 nA + 1 nB = xA − xB sp 1 nA + 1 nB (t ) t dfp = nA + nB − 2 t ( ) t0.05 (dfp ) t0.05 (dfp ) < |t| (P < 0.05) 2024 9 R ( ) (1) — Welch — 2024-11 – p.6/10

Welch t t = xA − xB s2 A nA + s2 B nB ( ) v . . . v ≈ ( s2 A nA + s2 B nB )2 s4 A n2 A (nA−1) + s4 B n2 B (nB−1) R 2024 9 R ( ) (1) — Welch — 2024-11 – p.7/10

( ) - (Shapiro-Wilk test) - (Anderson-Darling test for normality) - (Kolmogorov-Smirnov test for normality) ( ) ( ) (Bartlett’s test for homogeneity of variances) 2024 9 R ( ) (1) — Welch — 2024-11 – p.8/10

.txt A /B g <- read.table(" .txt", header=T) colnames(g) <- c(" ", " ") sampleA <- g$ sampleB <- g$ # ( ) shapiro.test(x=sampleA) shapiro.test(x=sampleB) # ( ) samples <- c(sampleA, sampleB) group_factor <- factor(rep(c("A", "B"), c(length(sampleA), length(sampleB)))) bartlett.test(formula=samples~group_factor) # Welch (t.test() ) ( Welch ) t.test(sampleA, sampleB) 2024 9 R ( ) (1) — Welch — 2024-11 – p.9/10

2024 9 R ( ) (1) — Welch — 2024-11 – p.10/10