[BioC] Testing for no difference

[Gustavo Fernández Bayón]

Hi Jack.  

I am not an expert in statistics, either, but I found this little paper to give me a simple hint on the drawbacks of ANOVA for equivalence testing.  

http://pareonline.net/pdf/v16n7.pdf

Regards,
Gus



---------------------------
Enviado con Sparrow (http://www.sparrowmailapp.com/?sig)


El lunes 23 de julio de 2012 a las 20:02, Yao Chen escribió:

> I am not an expert of statistic. Why not use ANOVA?
>  
> Jack
>  
> 2012/7/23 Wolfgang Huber <whuber at embl.de (mailto:whuber at embl.de)>
>  
> >  
> > Btw, a less complex way to approach such an analysis is highlighted here:
> >  
> > http://nsaunders.wordpress.**com/2012/07/23/we-really-dont-**
> > care-what-statistical-method-**you-used/<http://nsaunders.wordpress.com/2012/07/23/we-really-dont-care-what-statistical-method-you-used/>
> >  
> > Best wishes
> > Wolfgang
> >  
> > Jul/23/12 5:09 PM, Wolfgang Huber scripsit::
> >  
> > Gustavo,
> > >  
> > > it seems that your question can be rephrased as 'there is no evidence
> > > for these 5 samples forming any (nontrivial, i.e. different from size 1
> > > or 5) clusters'. If so, have a look at the package 'clue':
> > > http://cran.r-project.org/web/**packages/clue/vignettes/clue.**pdf<http://cran.r-project.org/web/packages/clue/vignettes/clue.pdf>
> > >  
> > > Of course, proving the absence of something (e.g., a systematic
> > > difference) is very difficult, and in your case as in most it's probably
> > > better to aim for saying that any difference that may exist is smaller
> > > than some (more or less arbitrary) measure.
> > >  
> > > Best wishes
> > > Wolfgang
> > >  
> > > Jul/23/12 9:52 AM, Gustavo Fernández Bayón scripsit::
> > >  
> > > > Hi everybody.
> > > >  
> > > > I have a set of only 5 samples of Illumina27k methylation data. We
> > > > have extracted some info from the probes, but now the researcher in
> > > > charge of the project wants something that could support his idea of
> > > > the five samples to be practically equivalent wrt to their methylation
> > > > levels.
> > > >  
> > > > I know that the sample is quite small. Intuitively, if you plot
> > > > densities from the 5 samples, they are almost equal. Problem is, I do
> > > > not know a way in which I could give a statistical significance about
> > > > this fact (yes, as always, there is the "I need a p-value" problem).
> > > >  
> > > > 1) I did PCA on both beta values and m-values, and found that the
> > > > first principal component accounts for between 90 and 91% of the total
> > > > variance. In the biplot, the five samples appear to be very close.
> > > >  
> > > > 2) I asked for advice to a statistician friend, and we tried to do the
> > > > following: probe by probe, we tried a Leave-One-Out approach, by
> > > > calculating a confidence interval for 4 of the samples and seeing if
> > > > the remaining probe falls within the interval. Then, for each probe, I
> > > > summed the number of times a methylation value fell out of the
> > > > confInt, only to find out that nearly 53% of the probes contain -in
> > > > this sense- 'outliers'.
> > > >  
> > > > At first it surprised me, but then I noticed -by plotting the outliers
> > > > against the samples- that these 'outliers' were uniformly distributed
> > > > among samples, which I think is again intuitive, i.e., there are
> > > > indeed differences (statistical differences, maybe not biological)
> > > > among samples, but there is no global difference of one of the samples
> > > > w.r.t. the others.
> > > >  
> > > > These differences might be related to technical noise, so I was
> > > > thinking of imposing a minimum difference in order to test again for
> > > > outliers. Would this be ok?
> > > >  
> > > > Is there any method I can use to try to show there is no difference
> > > > among the samples? Or should I stay with the graphs and the intuitive
> > > > description on the text?
> > > >  
> > > > Thanks. Any help or hint would be much appreciated.
> > > >  
> > > > Regards,
> > > > Gustavo
> > > >  
> > > > ---------------------------
> > > > Enviado con Sparrow (http://www.sparrowmailapp.**com/?sig<http://www.sparrowmailapp.com/?sig>
> > > > )
> > > >  
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> >  
> >  
> >  
> > --
> > Best wishes
> > Wolfgang
> >  
> > Wolfgang Huber
> > EMBL
> > http://www.embl.de/research/**units/genome_biology/huber<http://www.embl.de/research/units/genome_biology/huber>
> >  
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