> #### Computing power for the specific sample sizes in Section 16.10 > > > r <- 4 > mu <- c(12.5,13,18,21) > n <- c(5,5,4,5) > nT <- sum(n) > > (mu_all <- sum(mu*n)/nT) [1] 16.02632 > > sigma <- 3.5 > > (lambda <- (1/sigma^2)*sum(n*(mu-mu_all)^2)) [1] 20.1826 > > (power <- 1-pf(qf(1-0.05,r-1,nT-r),r-1,nT-r,lambda)) [1] 0.9249169 > > > #### Computing power for increasing (balanced) sample sizes in Section 16.10 > > r <- 4 > mu <- c(12.5,13,18,21) > sigma <- 3.5 > mu_all <- sum(mu)/r > > n_vec <- 2:50 > power_vec <- rep(0,49) > > for (n in 2:50) { + nT <- r*n + + lambda <- (1/sigma^2)*sum(n*(mu-mu_all)^2) + + power_vec[n-1] <- 1-pf(qf(1-0.05,r-1,nT-r),r-1,nT-r,lambda) + + } > > print(cbind(n_vec,power_vec)) n_vec power_vec [1,] 2 0.3048842 [2,] 3 0.6269013 [3,] 4 0.8321413 [4,] 5 0.9330586 [5,] 6 0.9756041 [6,] 7 0.9917176 [7,] 8 0.9973459 [8,] 9 0.9991896 [9,] 10 0.9997625 [10,] 11 0.9999328 [11,] 12 0.9999816 [12,] 13 0.9999951 [13,] 14 0.9999987 [14,] 15 0.9999997 [15,] 16 0.9999999 [16,] 17 1.0000000 [17,] 18 1.0000000 [18,] 19 1.0000000 [19,] 20 1.0000000 [20,] 21 1.0000000 [21,] 22 1.0000000 [22,] 23 1.0000000 [23,] 24 1.0000000 [24,] 25 1.0000000 [25,] 26 1.0000000 [26,] 27 1.0000000 [27,] 28 1.0000000 [28,] 29 1.0000000 [29,] 30 1.0000000 [30,] 31 1.0000000 [31,] 32 1.0000000 [32,] 33 1.0000000 [33,] 34 1.0000000 [34,] 35 1.0000000 [35,] 36 1.0000000 [36,] 37 1.0000000 [37,] 38 1.0000000 [38,] 39 1.0000000 [39,] 40 1.0000000 [40,] 41 1.0000000 [41,] 42 1.0000000 [42,] 43 1.0000000 [43,] 44 1.0000000 [44,] 45 1.0000000 [45,] 46 1.0000000 [46,] 47 1.0000000 [47,] 48 1.0000000 [48,] 49 1.0000000 [49,] 50 1.0000000