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--- c:ms:2025:w07.2_factorial_anova [2025/04/16 00:00] – created hkimscil
+++ c:ms:2025:w07.2_factorial_anova [2026/04/14 23:34] (current) – removed hkimscil
@@ Line 1: / Line 1: @@
-<code>
-#################################################
-# two-way anova
-# subject = factor(paste('sub', 1:30, sep=''))
-#################################################
-n.a.group <- 3 # a treatment 숫자
-n.b.group <- 2 # b 그룹 숫자
-n.sub <- 30 # 총 샘플 숫자
-n.sub/n.a.group
-# 데이터 생성
-set.seed(9)
-a <- gl(3, 10, n.sub, labels=c('a1', 'a2', 'a3'))
-b <- gl(2, 5, n.sub, labels=c('b1', 'b2'))
-a
-b
-y <- rnorm(30, mean=10) +
-.14 * (a=='a1' & b=='b2') +
-.43 * (a=='a3' & b=='b2')
-y
-dat <- data.frame(a, b, y)
-dat
-# aov.dat <- aov(y~a*b) # anova test
-# summary(aov.dat) # summary of the test output
-# hand calculation
-table(a,b)
-tapply(y, list(a,b), mean) # 각 셀에서의 평균
-n.within.each <- tapply(y, list(a,b), length)
-n.within.each
-df.within.each <- n.within.each - 1  # 각 셀에서의 샘플숫자
-df.within.each
-df.within <- sum(df.within.each) # df within
-df.within
-var.within <- tapply(y, list(a,b), var) # var.within
-var.within
-ss.within.each <- tapply(y, list(a,b), var) * df.within.each
-ss.within.each
-ss.within <- sum(ss.within.each) # ss.within
-ss.within
-ms.within <- ss.within / df.within
-ms.within
-# interaction.plot(a,b,y)
-mean.a <- tapply(y, list(a), mean)
-mean.b <- tapply(y, list(b), mean)
-mean.a
-mean.b
-var.a <- tapply(y, list(a), var)
-var.b <- tapply(y, list(b), var)
-var.a
-var.b
-mean.tot <- mean(dat$y)
-var.tot <- var(dat$y)
-df.tot <- n.sub - 1
-ss.tot <- var.tot * df.tot
-ms.tot <- ss.tot/df.tot
-## between
-mean.each <- tapply(y, list(a,b), mean)
-mean.each
-mean.tot <- mean(y)
-mean.tot
-n.each <- tapply(y, list(a,b), length)
-n.a.each <- tapply(y, list(a), length)
-n.b.each <- tapply(y, list(b), length)
-n.each
-n.a.each
-n.b.each
-ss.bet <- sum(n.each*(mean.each-mean.tot)^2)
-ss.bet
-ss.tot
-ss.within
-ss.bet
-ss.bet + ss.within
-ss.a <- sum(n.a.each * ((mean.tot - mean.a)^2))
-ss.b <- sum(n.b.each * ((mean.tot - mean.b)^2))
-ss.a
-ss.b
-ss.ab <- ss.bet - (ss.a + ss.b) # ss.ab = ss.interaction
-ss.ab
-ss.tot
-ss.bet
-ss.within
-ss.a
-ss.b
-ss.ab
-df.tot <- n.sub - 1
-df.bet <- (n.a.group * n.b.group) - 1
-df.a <- n.a.group - 1
-df.b <- n.b.group - 1
-df.ab <- df.bet - (df.a + df.b)
-df.within <- sum(df.within.each)
-df.tot
-df.bet
-df.a
-df.b
-df.ab
-df.within
-ms.tot <- ss.tot/df.tot # we did it above
-ms.bet <- ss.bet - df.bet
-ms.a <- ss.a / df.a
-ms.b <- ss.b / df.b
-ms.ab <- ss.ab / df.ab
-ms.within <- ss.within / df.within
-ms.tot
-ms.bet
-ms.within
-ms.a
-ms.b
-ms.ab
-f.a <- ms.a / ms.within
-f.b <- ms.b / ms.within
-f.ab <- ms.ab / ms.within
-alpha <- .05
-# confidence interval
-ci <- 1 - alpha
-f.a
-# 봐야할 F분포표에서의 F-value
-# qt 처럼 qf 사용
-# qf(alpha, df.between, df.within, lower.tail=F) 처럼 사용
-qf(ci, df.a, df.within) # or
-qf(alpha, df.a, df.within, lower.tail = F)
-# 혹은
-# qf(alpha, df.a, df.within, lower.tail = F)
-# 도 마찬가지
-pf(f.a, df.a, df.within, lower.tail = F)
-f.b
-qf(ci, df.b, df.within)
-pf(f.b, df.b, df.within, lower.tail = F)
-f.ab
-qf(ci, df.ab, df.within)
-pf(f.ab, df.ab, df.within, lower.tail = F)
-# aov result
-summary(aov.dat)
-</code>