CV ≈ s for low variances [General Sta­tis­tics]

posted by Helmut Homepage – Vienna, Austria, 2023-02-28 11:24 (364 d 03:14 ago) – Posting: # 23479
Views: 1,484

Hi mittyri,

❝ some history porn


Hey, that’s a nice one!

❝ Historical interest only (but still popular in NONMEM wild forests)


The Canadian guidances (from 1992 to the draft of 2009) contained these goodies:$$\eqalign{
\text{Intrasubject CV}&=100\times\text{(MSResidual)}^{0.5}\\
\text{Intersubject CV}&=100\times\text{(MSSubj}\,\text{(Seq))}^{0.5}}$$ When using the wrong formula, estimated sample sizes will be too small. Example for 2×2×2, T/R 0.95, target power 0.8:

library(PowerTOST)
CV  <- seq(0.14, 0.4, 0.02)
mse <- CV2mse(CV)
x   <- data.frame(mse = mse, CV.right = CV, n.right = NA_integer_,
                  CV.wrong = sqrt(mse), n.wrong = NA_integer_)
for (j in seq_along(CV)) {
  x[j, c(3, 5)] <- c(sampleN.TOST(CV = CV[j], print = FALSE)[["Sample size"]],
                     sampleN.TOST(CV = x$CV.wrong[j], print = FALSE)[["Sample size"]])
}
names(x) <- c("MSE", "CV", "n", "CV ~ sqrt(MSE)", "~ n")
print(signif(x, 4), row.names = FALSE)

     MSE   CV  n CV ~ sqrt(MSE) ~ n
 0.01941 0.14 12         0.1393  10
 0.02528 0.16 14         0.1590  14
 0.03189 0.18 16         0.1786  16
 0.03922 0.20 20         0.1980  20
 0.04727 0.22 22         0.2174  22
 0.05600 0.24 26         0.2366  26
 0.06541 0.26 30         0.2558  30
 0.07548 0.28 34         0.2747  34
 0.08618 0.30 40         0.2936  38
 0.09749 0.32 44         0.3122  42
 0.10940 0.34 50         0.3307  46
 0.12190 0.36 54         0.3491  52
 0.13490 0.38 60         0.3673  56
 0.14840 0.40 66         0.3853  62


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