Re: [R] power.t.test visualization problem

From: David Winsemius <dwinsemius_at_comcast.net>
Date: Tue, 24 May 2011 10:51:22 -0400

On May 24, 2011, at 8:44 AM, stocdarf_at_mail.tu-berlin.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.
> 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?

You do realize that you should be using the non-central t distribution when considering the alternate hypothesis, right? By the time you get down to sample sizes of 6 there should be a visible skew to the distribution of "observed" differences.

>
> I look foward to any suggestions and hints. So much thanks in advance.
>
> Étienne

-- 
David Winsemius, MD
West Hartford, CT

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Received on Tue 24 May 2011 - 15:17:12 GMT

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