[BioC] Testing for no difference

[Gustavo Fernández Bayón]

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

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