Lecture 6 系群演習問題

問1

y1 <- c(12,38)
y2 <- c(20,30)
y <- y1+y2

p1 <- y1/sum(y1)
p2 <- y2/sum(y2)
p <- y/sum(y)

tmp1 <- dmultinom(y1,sum(y1),p)*dmultinom(y2,sum(y2),p)
tmp2 <- dmultinom(y1,sum(y1),p1)*dmultinom(y2,sum(y2),p2)
T <- -2*log(tmp1/tmp2)
T

## [1] 2.964732

d <- 2-1
cc <- qchisq(0.95,d)
cc

## [1] 3.841459

if(T <= cc) print("H0 is accepted") else print("H0 is rejected")

## [1] "H0 is accepted"

問2

y1 <- c(7,7,0)
y2 <- c(0,4,52)
y <- y1+y2

p1 <- y1/sum(y1)
p2 <- y2/sum(y2)
p <- y/sum(y)

tmp1 <- dmultinom(y1,sum(y1),p)*dmultinom(y2,sum(y2),p)
tmp2 <- dmultinom(y1,sum(y1),p1)*dmultinom(y2,sum(y2),p2)
T <- -2*log(tmp1/tmp2)
T

## [1] 55.63574

d <- 4-2
cc <- qchisq(0.95,d)
cc

## [1] 5.991465

if(T <= cc) print("H0 is accepted") else print("H0 is rejected")

## [1] "H0 is rejected"