## Wrong formula for CV [Regulatives / Guidelines]

Hi Shatha,
$$\small{CV_\textrm{intra}=100\sqrt{MSE}}\tag{1}$$$$\small{CV_\textrm{intra}=100\sqrt{\exp(MSE)-1}}\tag{2}$$
$$\small{(1)}$$ was given in Health Canadas’ guidances of 1992 and 1996. $$\small{(1)}$$ is only approximate for relatively small variances. The bias is always negative and hence, when used in sample size estimations misleading (studies will be underpowered).

library(PowerTOST) CV        <- seq(0.05, 0.5, 0.05) mse       <- CV2mse(CV) CV.appr   <- sqrt(CV2mse(CV)) bias      <- sprintf("%+.2f%%", 100 * (CV.appr - CV) / CV) # sample size for T/R-ratio 0.95, at least 80% power res       <- data.frame(CV = CV, CV.appr = CV.appr, bias = bias,                         n = NA_integer_, power = NA_real_,                         n.appr = NA_integer_, power.appr = NA_real_) for (j in seq_along(CV)) {   res$n[j] <- sampleN.TOST(CV = CV[j], print = FALSE)[["Sample size"]] res$n.appr[j] <- sampleN.TOST(CV = CV.appr[j], print = FALSE)[["Sample size"]]   # minimum acc. to GLs   if (res$n[j] < 12) res$n[j]      <- 12   if (res$n.appr[j] < 12) res$n.appr[j] <- 12   res$power[j] <- round(power.TOST(CV = CV[j], n = res$n[j]), 5)   res$power.appr[j] <- round(power.TOST(CV = CV[j], n = res$n.appr[j]), 5) } CV.appr   <- round(CV.appr, 5) print(res, row.names = FALSE)    CV    CV.appr   bias  n   power n.appr power.appr  0.05 0.04996879 -0.06% 12 1.00000     12    1.00000  0.10 0.09975135 -0.25% 12 0.98835     12    0.98835  0.15 0.14916638 -0.56% 12 0.83052     12    0.83052  0.20 0.19804220 -0.98% 20 0.83468     20    0.83468  0.25 0.24622068 -1.51% 28 0.80744     28    0.80744  0.30 0.29356038 -2.15% 40 0.81585     38    0.79533  0.35 0.33993873 -2.87% 52 0.80747     50    0.79168  0.40 0.38525317 -3.69% 66 0.80525     62    0.77978  0.45 0.42942138 -4.57% 82 0.80691     76    0.77602  0.50 0.47238073 -5.52% 98 0.80322     88    0.75845

It took Health Canada until 2018 to give the correct $$\small{(2)}$$. Never trust in guidances. Dif-tor heh smusma 🖖🏼 Довге життя Україна! Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes  Ing. Helmut Schütz 