Dear R-User,
I'm trying to visualize the results of the power calculation with the function
power.t.test(). Therefore I want to plot the related t-distributions and shade
the surfaces indicatingt the type I error, the type II error and the power. For
sample sizes greater 30 I got results which are very satisfying. For small
sample sizes I got stuck and did'nt find a mistake.
To show you the problem I wrote some lines in R:
par(mfrow = c(4,2))
for(n in c(2,6,10,14,18,22,26,30))
{
temp = power.t.test(n = n, sd = 1, power = 0.5, sig.level =
0.05, # power calculation --> power
is specified with 50%
type = "one.sample", alternative = "one.sided")
s =
temp$sd
# get standard deviation out of test distribution
n =
temp$n
# get sample size out of test distribution
delta =
temp$delta
# get delta (distance between centrality points) out of test ditribution
plot(1:10, xlim = c(-5,10), ylim = c(0, 0.5), type =
"n") # create
plot window
x = seq(-5, 10, length =
400)
# x-values
y1 = dt(x, df =
n-1)
# y-values calculated with related t-distribution (df=n-1)
lines(x, y1, col =
2)
# plot related t-distribution
lines(x + delta/(s/sqrt(n)),
y1)
# plot related t-distribution shifted with normalized delta
abline(v = qt(0.95, df =
n-1))
# draws a vertical line at the
abline(v=delta/(s/sqrt(n)),lty=2)
legend("topright",legend=c(paste("n=",n),
paste("bias=",round(qt(0.95, df =
n-1)-delta/(s/sqrt(n)),2)))) # creates
legend
}
This code creates some plots with different sample size n. I would expect the
solid vertical line and the dotted vertical line one above the other. But
indeed the space between both of them is increasing with a decreasing sample
size.
Whe re is my mistake? Is it a error in reasoning or is it "just" not possible
to visualize this problem for small sample sizes?
I look foward to any suggestions and hints. So much thanks in advance.
Étienne
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