R help - Aug 2011 - How would you calculate this type of p-value using R?

Let's say you want to compare "one observation" with a sample, how
would you
use R to get a p-value for that single observation itself?


To clarify what I'm asking: We know you use a one-sample t test to compare
an actual sample to a hypothetical value, and a Wilcoxon test if it's not
normally distributed, in R either "t.test( )" or "wilcox.test(
)". However,
what do you use if you don't want a p-value for a sample itself, but instead
want to get a *p-value for the likelihood that just "one observation"
could
have its distance from a sample just by chance*?



Context for my question: Many of us know about the Casey Anthony case, and
how the medical examiner said they looked at the records and 100% of all
drownings were reported within one hour. It wasn't until a month after when
it was finally reported to the police the girl was missing by the
grandmother and even longer after that when Casey finally claimed it was
really a drowning rather than a "Zanny the Nanny" kidnapping the
little
girl.

So, I want to write the medical examiner to see if I can get a list of how
long it took for each of the drownings to be reported (she mentioned in
court), then calculate a standard deviation and based on the sample size
come up with a p-value for when Cindy Anthony finally reported the grand
daughter missing 31 days later. Then another p-value for when Casey Anthony
finally claimed it was a drowning years later.

How would you calculate a p-value for something like this? I'm guessing the
sample will probably not be normally distributed, so what would I use from R
if that's case?  I'm still quite new to R, so if at all possible
don't make
your answer too technical.

Thanks so much!

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On 08/17/2011 12:32 AM, RQuestion wrote:
> Let's say you want to compare "one observation" with a
sample, how would you
> use R to get a p-value for that single observation itself?
This is a rather vague question, but you seem to be describing the 
calculation of tail probabilities.  If, for example, you expected the 
distribution to be normal with mean 10 and SD 5, and then observed 23, 
the (one-sided) 'p-value' would be

 > 1-pnorm(23,mean=10,sd=5)
[1] 0.004661188

If you did not wish to assume a distribution (i.e., use the empirical 
distribution), the 'p-value' would simply be the fraction of cases in 
your sample as large or larger than the observation in question.

-- 
Patrick Breheny
Assistant Professor
Department of Biostatistics
Department of Statistics
University of Kentucky