On Fri, May 7, 2010 at 9:45 PM, cheba meier <cheba.meier@googlemail.com>wrote:

> Hi all,
>
> Thank you for your reply.
>
> if done properly! What does this mean? The R-code I have is using the
> R-function sample without replacement. Am I doing this properly?
>
> median of the differences is zero!

This is only valid if the experiment consists of paired data.


> Does this mean if I run 1000 permutation and for each permutation I compute
> the median difference and as a result I have 1000 differences. Is the the
> H0: median(1000 differences) =0? If yes, which conclusion one would have
> from this H0?
>
Nope. the H0 is : median difference = 0
permutation tests run with replacement=F, bootstrapping (which is arguably
the better choice if you can't calculate all permutations)  is done with
replacement = T
# make some data
a <- 1:10
b <- 3:12
x <- c(a,b)
y <- rep(c("a","b"),each=10)

# define function difference of the medians. This can be any function, this
is just for demonstration purposes
med.diff <-function(x,y){
     tmp <- by(x,y,median)
     return(diff(tmp))
}
# bootstrap
med.diff.observed <- med.diff(x,y)  # observed test statistic

n <- 100 # number of bootstraps

boot.samples <- replicate(n,sample(x,replace=T)) # bootstrap samples
med.diff.boot <- apply(boot.samples,2,med.diff,y) # test statistic for
bootstrap samples
med.diff.boot <- scale(med.diff.boot) # centralization for 2-sided testing
pvalue <- mean(abs(med.diff.boot)>=abs(med.diff.observed)) # calculate
proportion of test statistic that is more extreme than the observed
pvalue

I use the central limit theorem in a way, assuming the distribution of the
statistic for the bootstrap sample is symmetric.


> Best wishes,
> Cheba
>
>
>
> 2010/5/7 Joris Meys <jorismeys@gmail.com>
>
> depends on how you interprete "absolute median difference". Is that the
>> absolute difference of the medians, or the median of the absolute
>> differences. Probably the latter one, so you would be right. If it's the
>> former one, then it is testing whether the difference of the medians is
>> zero.
>>
>> Cheers
>> Joris
>>
>>
>> On Fri, May 7, 2010 at 6:52 PM, Thomas Lumley <tlumley@u.washington.edu>wrote:
>>
>>> On Fri, 7 May 2010, cheba meier wrote:
>>>
>>>  Dear Thomas,
>>>>
>>>> I have been running simulations in order me to understand this problem!
>>>> I
>>>> have found something online where the absolute median difference is
>>>> computed
>>>> and permutations are ran to compute a p-value. Is such a test (if I can
>>>> call
>>>> it a test) tests the null hypothesis that median group 1 = median group
>>>> 2?
>>>>
>>>
>>> No, that is testing whether the median of the differences is zero.  This
>>> is not the same as testing whether the difference of the medians is zero.
>>>
>>>    -thomas
>>>
>>>
>>>
>>>  Thank you in advance for your help.
>>>>
>>>> Regards,
>>>> Cheba
>>>>
>>>> 2010/4/6 Thomas Lumley <tlumley@u.washington.edu>
>>>>
>>>>
>>>>>
>>>>> None of them.
>>>>>
>>>>>  - mood.test() looks promising until you read the help page and see
>>>>> that it
>>>>> does not do Mood's test for equality of quantiles, it does Mood's test
>>>>> for
>>>>> equality of scale parameters.
>>>>>  - wilcox.test() is not a test for equal medians
>>>>>  - ks.test() is not a test for equal medians.
>>>>>
>>>>>
>>>>> Mood's test for the median involves dichotomizing the data at the
>>>>> pooled
>>>>> median and then doing Fisher's exact test to see if the binary variable
>>>>> has
>>>>> the same mean in the two samples.
>>>>>
>>>>> median.test<-function(x,y){
>>>>>  z<-c(x,y)
>>>>>  g <- rep(1:2, c(length(x),length(y)))
>>>>>  m<-median(z)
>>>>>  fisher.test(z<m,g)$p.value
>>>>> }
>>>>>
>>>>> Like most exact tests, it is quite conservative at small sample sizes.
>>>>>
>>>>>    -thomas
>>>>>
>>>>>
>>>>> On Tue, 6 Apr 2010, cheba meier wrote:
>>>>>
>>>>>  Dear all,
>>>>>
>>>>>>
>>>>>> What is the right test to test whether the median of two groups are
>>>>>> statistically significant? Is it the wilcox.test, mood.test or the
>>>>>> ks.test?
>>>>>> In the text book I have got there is explanation for the Wilcoxon
>>>>>> (Mann
>>>>>> Whitney) test which tests ob the two variable are from the same
>>>>>> population
>>>>>> and also ks.test!
>>>>>>
>>>>>> Regards,
>>>>>> Cheba
>>>>>>
>>>>>>       [[alternative HTML version deleted]]
>>>>>>
>>>>>> ______________________________________________
>>>>>> R-help@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.
>>>>>>
>>>>>>
>>>>>>  Thomas Lumley                   Assoc. Professor, Biostatistics
>>>>> tlumley@u.washington.edu        University of Washington, Seattle
>>>>>
>>>>>
>>>>>
>>>>        [[alternative HTML version deleted]]
>>>>
>>>> ______________________________________________
>>>> R-help@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.
>>>>
>>>>
>>> Thomas Lumley                   Assoc. Professor, Biostatistics
>>> tlumley@u.washington.edu        University of Washington, Seattle
>>>
>>> ______________________________________________
>>> R-help@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.
>>>
>>
>>
>>
>> --
>> Joris Meys
>> Statistical Consultant
>>
>> Ghent University
>> Faculty of Bioscience Engineering
>> Department of Applied mathematics, biometrics and process control
>>
>> Coupure Links 653
>> B-9000 Gent
>>
>> tel : +32 9 264 59 87
>> Joris.Meys@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

Coupure Links 653
B-9000 Gent

tel : +32 9 264 59 87
Joris.Meys@Ugent.be
-------------------------------
Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php

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