From: Joris Meys <jorismeys_at_gmail.com>

Date: Thu, 24 Jun 2010 13:13:19 +0200

Date: Thu, 24 Jun 2010 13:13:19 +0200

One way of looking at it is doing a sign test after substraction of the mean. For symmetrical data sets, E[X-mean(X)] = 0, so you expect to have about as many values above as below zero. There is a sign test somewhere in one of the packages, but it's easily done using the binom.test as well :

*> set.seed(12345)
*

> x1 <- rnorm(100)

*> x2 <- rpois(100,2)
*

*> binom.test((sum(x1-mean(x1)>0)),length(x1))
*

Exact binomial test

data: (sum(x1 - mean(x1) > 0)) and length(x1)
number of successes = 56, number of trials = 100, p-value = 0.2713
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:

0.4571875 0.6591640

sample estimates:

probability of success

0.56

*> binom.test((sum(x2-mean(x2)>0)),length(x2))
*

Exact binomial test

data: (sum(x2 - mean(x2) > 0)) and length(x2)
number of successes = 37, number of trials = 100, p-value = 0.01203
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:

0.2755666 0.4723516

sample estimates:

probability of success

0.37

Cheers

Joris

On Thu, Jun 24, 2010 at 4:16 AM, Atte Tenkanen <attenka_at_utu.fi> wrote:

*> PS.
**>
*

> Mayby I can somehow try to transform data and check it, for example, using the skewness-function of timeDate-package?

*>
**>> Thanks. What I have had to ask is that
**>>
**>> how do you test that the data is symmetric enough?
**>> If it is not, is it ok to use some data transformation?
**>>
**>> when it is said:
**>>
**>> "The Wilcoxon signed rank test does not assume that the data are
**>> sampled from a Gaussian distribution. However it does assume that the
**>> data are distributed symmetrically around the median. If the
**>> distribution is asymmetrical, the P value will not tell you much about
**>> whether the median is different than the hypothetical value."
**>>
**>> > On Wed, Jun 23, 2010 at 10:27 PM, Atte Tenkanen <attenka_at_utu.fi> wrote:
**>> > > Hi all,
**>> > >
**>> > > I have a distribution, and take a sample of it. Then I compare
**>> that
**>> > sample with the mean of the population like here in "Wilcoxon signed
**>>
**>> > rank test with continuity correction":
**>> > >
**>> > >> wilcox.test(Sample,mu=mean(All), alt="two.sided")
**>> > >
**>> > > Wilcoxon signed rank test with continuity correction
**>> > >
**>> > > data: AlphaNoteOnsetDists
**>> > > V = 63855, p-value = 0.0002093
**>> > > alternative hypothesis: true location is not equal to 0.4115136
**>> > >
**>> > >> wilcox.test(Sample,mu=mean(All), alt = "greater")
**>> > >
**>> > > Wilcoxon signed rank test with continuity correction
**>> > >
**>> > > data: AlphaNoteOnsetDists
**>> > > V = 63855, p-value = 0.0001047
**>> > > alternative hypothesis: true location is greater than 0.4115136
**>> > >
**>> > > What assumptions are needed for the population?
**>> >
**>> > wikipedia says:
**>> > "The Wilcoxon signed-rank test is a _non-parametric_ statistical
**>> > hypothesis test for... "
**>> > it also talks about the assumptions.
**>> >
**>> > > What can we say according these results?
**>> > > p-value for the "less" is 0.999.
**>> >
**>> > That the p-value for less and greater seem to sum up to one, and that
**>> > the p-value of greater is half of that for two-sided. You shouldn't
**>> > ask what we can say. You should ask yourself "What was the question
**>> > and is this test giving me an answer on that question?"
**>> >
**>> > Cheers
**>> > Joris
**>> >
**>> > --
**>> > Joris Meys
**>> > Statistical consultant
**>> >
**>> > Ghent University
**>> > Faculty of Bioscience Engineering
**>> > Department of Applied mathematics, biometrics and process control
**>> >
**>> > tel : +32 9 264 59 87
**>> > Joris.Meys_at_Ugent.be
**>> > -------------------------------
**>> > Disclaimer : **http://helpdesk.ugent.be/e-maildisclaimer.php
**>
*

-- Joris Meys Statistical consultant Ghent University Faculty of Bioscience Engineering Department of Applied mathematics, biometrics and process control tel : +32 9 264 59 87 Joris.Meys_at_Ugent.be ------------------------------- Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php ______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Thu 24 Jun 2010 - 11:15:13 GMT

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