[R] nonparametric significance test for one sample

[Greg Snow]

If you data is truly limited to be non-negative and you are testing a
null hypothesis that the true distribution mean is 0, then the test is
fairly straight forward.  There exists only one distribution with mean 0
and all values required to be >= 0 and that is a point mass of 1 at 0.
So if all of your data values are 0 then that means a p-value of 1 and
if any data values are greater than 0 (even if it is only 1 value and it
is only slightly greater than 0) then the p-value is 0.

If you want to then estimate what the true mean is for an unknown
distribution, then you may want to look at using a bootstrap estimate.

Hope this helps, 


-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at intermountainmail.org
(801) 408-8111
 

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of HelponR
Sent: Tuesday, December 19, 2006 8:29 AM
To: r-help
Subject: [R] nonparametric significance test for one sample

Hello, Gurus:

I tried to test if the sample mean of a dataset is zero.

The data has 1500 numbers with a lot of zeros and some small positive
numbers. The data range on [0,1] but the distribution is unknown.
It is zero inflated anyway.

I tried to use the  Wilcoxon Signed Ranks test. But I read from this
website that it does assume the population pdf is symmetric.

http://www.cas.lancs.ac.uk/glossary_v1.1/nonparam.html#wsrt
"The Wilcoxon Signed Ranks test does not require the assumption that the
population is normally distributed. In many applications, this test is
used in place of the one sample
t-test<http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#1sampt>when
the normality assumption is questionable. It is a more powerful
alternative to the sign test, but does assume that the population
probability distribution is symmetric."

I wonder if wilcox.test( ) in R also assumes the symmetric pdf?

I checked the sign test too. But "the sign *test* is not *testing
equality*of population "

If wilcox.test() cannot work for my data, I wonder if you could suggest
a kind of test? I already tried t-test (assume normality) but I want to
find something else.

Many thanks!

S

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