[BioC] Testing for no difference

[jones]

You might look into "tests of equivalence", one common procedure
involves defining an interval (-a,a) and doing two one sided
tests ("TOST") for H_0: delta > a and delta < -a, which is equivalent
to checking that the CI for the difference is contained in
the specified interval.

albyn

On 7/23/12 12:52 AM, Gustavo Fernández Bayón wrote:
> 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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