R help - May 2011 - Problem with visualization of power of t test

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.

?tienne
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Etienne,

For this type of graph, I would use the functions in the HH package

## install.packages("HH")  ## if necessary
library(HH)

 normal.and.t.dist(std.dev=2, Use.alpha.left=FALSE, deg.free=6,
                   mu.H1=2, Use.mu.H1=TRUE,
                   obs.mean=2.5, Use.obs.mean=TRUE, xmin=-7)

Rich


On Tue, May 24, 2011 at 9:08 AM, Etienne Stockhausen
<einohr2002@web.de>wrote:
> 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.
>
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Dear Richard M. Heiberger,

I've some problems understanding your function. Where is the power
visualized? May you give me an example including the following parameter given
by?

power.t.test(n = 2, sd = 1, power = 0.5,? sig.level = 0.05, type =
"one.sample", alternative = "one.sided")
?
Thanks in advance

?tienne
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