[R] Problem with visualization of power of t test

[Etienne Stockhausen]

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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