本文是實驗設計與分析（第6版，Montgomery著，傅玨生譯) 第章隨機化區組，拉丁方， 及有關設計4.5節思考題4.26~4.27?R語言解題。主要涉及方差分析，正交拉丁方。

batch <- c(rep("batch1",5), rep("batch2",5), rep("batch3",5), rep("batch4",5), rep("batch5",5))

? acid <- rep(c("oper1", "oper2", "oper3", "oper4", "oper5"),5)

? time <- c("A", "B", "C", "D", "E", "B", "C", "D", "E", "A", "C", "D", "E", "A", "B", "D", "E",

???????????? "A", "B", "C", "E", "A", "B", "C", "D")

catalyst <- c("a", "b", "y", "d", "e", "y", "d", "e", "a", "b", "e", "a", "b", "y", "d", "b", "y",

???????????? "d", "e", "a", "d", "e", "a", "b", "y")

? y1 <- c(26,16,19,16,13)

? y2 <- c(18,21,18,11,21)

? y3 <- c(20,12,16,25,13)

? y4 <- c(15,15,22,14,17)

? y5 <- c(10,24,17,17,14)

? y <- c(y1,y2,y3,y4,y5)

? rocket.data <- data.frame(batch, acid,time,catalyst, y)

fit <- lm(y~ acid +batch+ time + catalyst, data=rocket.data)

? anova(fit)

>?? anova(fit)

Analysis of Variance Table

Response: y

????????? Df Sum Sq Mean Sq F value?? Pr(>F)???

acid?????? 4?? 24.4??? 6.10? 1.0427 0.442543???

batch????? 4?? 10.0??? 2.50? 0.4274 0.785447???

time?????? 4? 342.8?? 85.70 14.6496 0.000941 ***

catalyst?? 4?? 12.0??? 3.00? 0.5128 0.728900???

Residuals? 8?? 46.8??? 5.85????????????????????

---

Signif. codes:? 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

order <- c(rep("order 1",4), rep("order 2",4), rep("order 3",4), rep("order 4",4))

? oper <- rep(c("oper1", "oper2", "oper3", "oper4"),4)

? method <- c("C", "B", "D", "A", "B", "C", "A", "D", "A", "D", "B", "C", "D", "A", "C", "B")

place <- c("b", "y", "d", "a", "a", "d", "y", "b", "d", "a", "b", "y", "y", "b", "a", "d")

? y1 <- c(11,10,14,8)

? y2 <- c(8,12,10,12)

? y3 <- c(9,11,7,15)

? y4 <- c(9,8,18,6)

? y <- c(y1,y2,y3,y4)

? rocket.data <- data.frame(order, oper, method, place, y)

fit <- lm(y~ method + order +oper+ place, data=rocket.data)

? anova(fit)

>?? anova(fit)

Analysis of Variance Table

Response: y

????????? Df Sum Sq Mean Sq F value Pr(>F)

method???? 3?? 95.5? 31.833? 3.4727 0.1669

order????? 3??? 0.5?? 0.167? 0.0182 0.9960

oper?????? 3?? 19.0?? 6.333? 0.6909 0.6157

place????? 3??? 7.5?? 2.500? 0.2727 0.8429

Residuals? 3?? 27.5?? 9.167??????????????