Re: [R] Wilcoxon signed rank test and its requirements

From: Greg Snow <Greg.Snow_at_imail.org>
Date: Sat, 26 Jun 2010 14:30:00 -0600

No I mean something like this, assuming that the iris dataset contains the full population and we want to see if Setaso have a different mean than the population (the null would be that there is no difference in sepal width between species, or that species tells nothing about sepal width):

out1 <- replicate( 100000, mean(sample(iris$Sepal.Width, 50)) ) obs1 <- mean( iris$Sepal.Width[1:50] )

hist(out1, xlim=range(out1,obs1))
abline(v=obs1)

mean( out1 > obs1 )

I don't have a reference (other than a text book that defines sampling distributions).

--

Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow_at_imail.org
801.408.8111

From: Atte Tenkanen [mailto:attenka_at_utu.fi] Sent: Friday, June 25, 2010 10:08 PM
To: Atte Tenkanen
Cc: Greg Snow; David Winsemius; R mailing list Subject: Re: [R] Wilcoxon signed rank test and its requirements

Atte Tenkanen kirjoitti 26.6.2010 kello 5.15:

Greg Snow kirjoitti 25.6.2010 kello 21.55:

Let me see if I understand. You actually have the data for the whole population (the entire piece) but you have some pre-defined sections that you want to see if they differ from the population, or more meaningfully they are different from a randomly selected set of measures. Is that correct?

If so, since you have the entire population of interest you can create the actual sampling distribution (or a good approximation of it). Just take random samples from the population of the given size (matching the subset you are interested in) and calculate the means (or other value of interest), probably 10,000 to 1,000,000 samples. Now compare the value from your predefined subset to the set of random values you generated to see if it is in the tail or not.

I check, so you mean doing it this way:

t.test(sample(POPUL, length(SAMPLE), replace = FALSE), mu=mean(SAMPLE), alt = "less")

NO, this way:

t.test(POPUL[sample(1:length(POPUL), length(SAMPLE), replace = FALSE)], mu=mean(SAMPLE), alt = "less")

Atte

Atte

--

Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow_at_imail.org<mailto:greg.snow_at_imail.org> 801.408.8111

-----Original Message-----

From: r-help-bounces_at_r-project.org<mailto:r-help-bounces_at_r-project.org> [mailto:r-help-bounces_at_r- project.org] On Behalf Of Atte Tenkanen
Sent: Thursday, June 24, 2010 11:04 PM
To: David Winsemius
Cc: R mailing list
Subject: Re: [R] Wilcoxon signed rank test and its requirements

The values come from this kind of process: The musical composition is segmented into so-called 'pitch-class segments' and these segments are compared with one reference set with a distance function. Only some distance values are possible. These distance values can be averaged over music bars which produces smoother distribution and the 'comparison curve' that illustrates the distances according to the reference set through a musical piece result in more readable curve (see e.g. http://users.utu.fi/attenka/with6.jpg ), but I would prefer to use original values.

then, I want to pick only some regions from the piece and compare those values of those regions, whether they are higher than the mean of all values.

Atte

On Jun 24, 2010, at 6:58 PM, Atte Tenkanen wrote:

Is there anything for me?

There is a lot of data, n=2418, but there are also a lot of ties. My sample nó250-300

I do not understand why there should be so many ties. You have not described the measurement process or units. ( ... although you offer a

glipmse without much background later.)

i would like to test, whether the mean of the sample differ significantly from the population mean.

Why? What is the purpose of this investigation? Why should the mean of

a sample be that important?

The histogram of the population looks like in attached histogram, what test should I use? No choices?

This distribution comes from a musical piece and the values are 'tonal distances'.

http://users.utu.fi/attenka/Hist.png

That picture does not offer much insidght into the features of that measurement. It appears to have much more structure than I would expect for a sample from a smooth unimodal underlying population.

--

David.

Atte

On 06/24/2010 12:40 PM, David Winsemius wrote:

On Jun 23, 2010, at 9:58 PM, Atte Tenkanen wrote:

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."

You are being misled. Simply finding a statement on a statistics software website, even one as reputable as Graphpad (???), does not
mean
that it is necessarily true. My understanding (confirmed reviewing
"Nonparametric statistical methods for complete and censored data"
by M.
M. Desu, Damaraju Raghavarao, is that the Wilcoxon signed-rank test
does
not require that the underlying distributions be symmetric. The above
quotation is highly inaccurate.

To add to what David and others have said, look at the kernel that

the

U-statistic associated with the WSR test uses: the indicator (0/1) of
xi
+ xj > 0. So WSR tests H0:p=0.5 where p = the probability that the
average of a randomly chosen pair of values is positive. [If there
are
ties this probably needs to be worded as P[xi + xj > 0] = P[xi + xj
<

0], i neq j.

Frank

--

Frank E Harrell Jr Professor and Chairman School of Medicine

                     Department of Biostatistics   Vanderbilt
University

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