Danish ultra-conservatism [Power / Sample Size]
❝ Side effect 2:
❝ The Danish are ultra-conservative!
Confirmed. Try this one:
library(PowerTOST)
dk <- function(CV, n, lower, upper, theta0) { # Danish power
p0 <- power.TOST(CV=CV, n=n, theta0=theta0,
theta1=lower, theta2=upper)
p1 <- power.TOST(CV=CV, n=n, theta0=theta0,
theta1=lower, theta2=1)
p2 <- power.TOST(CV=CV, n=n, theta0=theta0,
theta1=1, theta2=upper)
p0-p1-p2
}
of <- function(x) { # objective function
(dk(CV=CV, n=n, lower=lower, upper=upper, theta0=x)-target)^2
}
lower <- 0.9 # NTID-range
upper <- 1/lower
CV <- 0.1
target <- 0.8
theta0 <- 0.9
n <- 22 # fixed
theta0.dk <- optimize(of, interval=c(lower, 1), tol=1e-12)$minimum
power <- dk(CV=CV, n=n, lower=lower, upper=upper, theta0=theta0.dk)
pwr.1 <- dk(CV=CV, n=n, lower=lower, upper=upper, theta0=theta0)
GMR <- seq(lower, upper, length.out=101)
pwr <- vector()
for (j in seq_along(GMR)) {
pwr[j] <- dk(CV=CV, n=n, lower=lower, upper=upper, theta0=GMR[j])
}
plot(GMR, pwr, log="x", ylim=c(0, 1), type="l", lwd=2, col="blue",
las=1, ylab="power with a Danish twist", cex.main=1,
main=paste0("theta0 = ", theta0, " (n = ", n, ")"))
grid()
abline(h=target)
abline(v=c(theta0, 1/theta0), lty=3, col="red")
abline(v=c(theta0.dk, 1/theta0.dk), lty=2, col="blue")
arrows(theta0, 0, theta0.dk, 0, length=0.1, angle=25,
code=2, lwd=2, col="red")
arrows(1/theta0, 0, 1/theta0.dk, 0, length=0.1, angle=25,
code=2, lwd=2, col="red")
BE <- sprintf("%s %.4f%s%.4f", "BE-limits:", lower, "\u2026", upper)
pwr <- sprintf("%s %.4g", "Power (theta0):", pwr.1)
op <- par(no.readonly=TRUE)
par(family="mono")
if (round(power, 6) >= target) {
legend("topright", bg="white", cex=0.9, x.intersp=0,
legend=c(BE, sprintf("%s %.4f%s%.4f",
"GMR-range:", theta0.dk, "\u2026", 1/theta0.dk),
pwr))
} else {
legend("topright", bg="white", cex=0.9, x.intersp=0,
legend=c(BE, sprintf("%s %.4f", "Achievable power:", power), pwr))
}
par(op)
It is courageous to assume theta0 0.9 for a NTID (
sampleN.TOST()
would tell you to get lost). If you believe in 0.95, n would be 44. To get 80% power the GMR-range is 0.9834…1.0169. Power for 0.95 is only 0.2333. Would it be ethical to perform the study?❝
Something wrong with the forum? It kicks me out nearly all the time.
You are not alone.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
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Helmut Schütz
![[image]](https://static.bebac.at/img/CC by.png)
The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Complete thread:
- Denmark Curiosa (1 in 90% CI in 0.8-1.25) zizou 2017-02-05 02:03 [Power / Sample Size]
- Kudos! Helmut 2017-02-05 19:16
- Kudos! ElMaestro 2017-02-05 21:15
- Joking! Helmut 2017-02-06 13:27
- Thanks, and DKMA ElMaestro 2017-02-06 13:46
- Power with a Danish twist Helmut 2017-02-07 15:23
- Danish ultra-conservatism d_labes 2017-02-08 10:57
- Danish ultra-conservatismHelmut 2017-02-08 11:47
- Danish ultra-conservatism d_labes 2017-02-08 10:57
- Power with a Danish twist Helmut 2017-02-07 15:23
- Thanks, and DKMA ElMaestro 2017-02-06 13:46
- Kudos to ElMaestro! d_labes 2017-02-06 15:06
- Plausible Helmut 2017-02-06 17:16
- Plausible to me too d_labes 2017-02-06 20:25
- Plausible to me too ElMaestro 2017-02-06 22:30
- Plausible to me too zizou 2017-02-06 22:42
- THX d_labes 2017-02-07 10:01
- Plausible to me too d_labes 2017-02-06 20:25
- Plausible Helmut 2017-02-06 17:16
- Joking! Helmut 2017-02-06 13:27
- Kudos! ElMaestro 2017-02-05 21:15
- 3D Helmut 2017-02-06 13:47
- Denmark Curiosa (1 in 90% CI in 0.8-1.25) d_labes 2017-02-06 14:54
- Denmark Curiosa (1 in 90% CI in 0.8-1.25) zizou 2017-02-08 21:03
- Alternative CI for BE decision d_labes 2017-02-09 11:18
- Alternative CI for BE decision ElMaestro 2017-02-09 11:36
- Alternative CI for BE decision d_labes 2017-02-09 11:48
- How decidedly odd ElMaestro 2017-02-09 13:28
- How decidedly odd zizou 2017-02-09 14:42
- How decidedly odd ElMaestro 2017-02-09 13:28
- Alternative CI for BE decision Helmut 2017-02-09 13:41
- No alternative d_labes 2017-02-09 20:37
- No alternative ElMaestro 2017-02-10 13:51
- No alternative? mittyri 2017-02-10 15:28
- Dinamarka? d_labes 2017-02-10 20:10
- OT: Czech beer d_labes 2017-02-10 19:57
- No alternative? mittyri 2017-02-10 15:28
- No alternative ElMaestro 2017-02-10 13:51
- No alternative d_labes 2017-02-09 20:37
- Alternative CI for BE decision d_labes 2017-02-09 11:48
- Alternative CI for BE decision ElMaestro 2017-02-09 11:36
- Alternative CI for BE decision d_labes 2017-02-09 11:18
- Denmark Curiosa (1 in 90% CI in 0.8-1.25) zizou 2017-02-08 21:03
- Denmark Curiosa (1 in 90% CI in 0.8-1.25): Gone Helmut 2019-11-08 12:47
- Kudos! Helmut 2017-02-05 19:16