## PowerTOST: CV in different designs [🇷 for BE/BA]

Hi roman_max,

❝ within this code in PowerTOST

100*CVfromCI(alpha=0.05, lower=0.8450985339, upper=1.104975299, n=c(5,5), design="2x2x4")

❝ if design is "parallel" it is a CVtotal? Am I right?

Yes, you are.

For the record:
1. Any replicate design: $$\small{CV_\text{intra}}$$, assuming homoscedasticity ($$\small{s_\text{wT}^2\equiv s_\text{wR}^2}$$).
2. Any crossover and a paired design: $$\small{CV_\text{intra}}$$.
3. Parallel design: $$\small{CV_\text{total}}$$, assuming homoscedasticity ($$\small{s_\text{T}^2\equiv s_\text{R}^2}$$).
Note that the $$\small{s^2}$$ components in #1 and #3 cannot be calculated from the confidence interval. You need the raw data.

library(PowerTOST) CI      <- c(0.85, 1 / 0.85) n       <- 24 designs <- known.designs()[c(1, 13, 3:6, 8:9, 12, 7, 10:11), c(2:3, 9)] res     <- data.frame(design = designs$design, name = designs$name,                       n = rep(n, nrow(designs)), df = designs$df, lower = CI[1], upper = CI[2], CV = NA, type = c("total", rep("intra", nrow(designs) - 1))) for (j in 1:nrow(designs)) { res$CV[j] <- sprintf("%.2f%%", 100 * CI2CV(lower = res$lower[j], upper = res$upper[j], n = n,                                              design = res\$design[j])) } print(res, row.names = FALSE, right = FALSE)  design   name                        n  df    lower upper    CV     type  parallel 2 parallel groups           24 n-2   0.85  1.176471 23.50% total  paired   paired means                24 n-1   0.85  1.176471 33.75% intra  2x2x2    2x2x2 crossover             24 n-2   0.85  1.176471 33.69% intra  3x3      3x3 crossover               24 2*n-4 0.85  1.176471 34.47% intra  3x6x3    3x6x3 crossover             24 2*n-4 0.85  1.176471 34.47% intra  4x4      4x4 crossover               24 3*n-6 0.85  1.176471 34.73% intra  2x2x4    2x2x4 replicate crossover   24 3*n-4 0.85  1.176471 50.60% intra  2x4x4    2x4x4 replicate crossover   24 3*n-4 0.85  1.176471 50.60% intra  2x2x2r   Liu's 2x2x2 repeated x-over 24 3*n-2 0.85  1.176471 50.62% intra  2x2x3    2x2x3 replicate crossover   24 2*n-3 0.85  1.176471 40.20% intra  2x3x3    partial replicate (2x3x3)   24 2*n-3 0.85  1.176471 40.20% intra  2x4x2    Balaam's (2x4x2)            24 n-2   0.85  1.176471 16.50% intra

You can calculate $$\small{CV_\text{wR}}$$ from the upper expanded limit (irrespective of the design and sample size):

U <- 1.4319 cat(sprintf("%.2f%%", 100 * U2CVwR(U)), "\n") 50.00%

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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