t-test behavior given that the null hypothesis is true

Hi Ted,
thanks for the reply. I use a similar code which you can see below:

k <- 10000
c <- 6
rv <- array(NA, dim=c(k, c) )
for(i in 1:k){
   rv[i,] <- rnorm(c, mean=0, sd=1)
}

rv.t.pvalues <- array(NA, k)

for(i in 1:k){
   rv.t.pvalues[i] <- t.test(rv[i, 1:(c/2)], rv[i, (c/2+1):c],
equal.var=TRUE, alternative="two.sided")$p.value
}

hist(rv.t.pvalues)

The histogram is this one:
*http://tinyurl.com/histogram-rt-pvalues-pdf

*
*all the best
idaios
*


On Wed, Jan 9, 2013 at 12:29 PM, Ted Harding <Ted.Harding at wlandres.net>wrote:

On 09-Jan-2013 08:50:46 Pavlos Pavlidis wrote:

Dear all,
I observer a strange behavior of the pvalues of the t-test under
the null hypothesis. Specifically, I obtain 2 samples of 3
individuals each from a normal distribution of mean 0 and variance 1.
Then, I calculate the pvalue using the t-test (var.equal=TRUE,
samples are independent). When I make a histogram of pvalues
I see that consistently the bin of the smallest pvalues has a
lower frequency. Is this a known behavior of the t-test or it's
a kind of bug/random number generation problem?

kind regards,
idaios

Using the following code, I did not observe the behavious you describe.
The histograms are consistent with a uniform distribution of the
P-values, and the lowest bin for the P-values (when the code is
run repeatedly) is not consistently lower (or higher, or anything
else) than the other bins.

## My code:
N <- 10000
Ps <- numeric(N)
for(i in (1:N)){
   X1 <- rnorm(3,0,1) ; X2 <- rnorm(3,0,1)
   Ps[i] <- t.test(X1,X2,var.equal=TRUE)$p.value
}
hist(Ps)
################################################

If you would post the code you used, the reason why you are observing
this may become more evident!

Hoping this helps,
Ted.

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E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 09-Jan-2013  Time: 10:29:21
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