# Methylation data: beta values are normally distributed

I am trying to incorporate Methylation data (Illumina 450K) into my pipeline. I was provided with two versions of the same data: one (dataset $$a$$) normalized with ComBat and the other (dataset $$b$$) normalized using the residuals method (i.e., taking the residuals of the models fitted on the covariates). Looking at the distribution of the beta values, I noticed that:

• The values for dataset $$a$$ have a typical bimodal distribution with peaks at around $$0$$ and $$1$$
• The values for dataset $$b$$ are roughly normally distributed with the mean at around $$0.5$$.

I am not that familiar with Methylation data, so maybe this is expected. Is it? I did not find any paper showing similar results.

$$\beta$$ values are the ratio of methylated to unmethylated probe intensities. This means that $$\beta \in [0, 1]$$, so it can't be normally distributed, by definition. Its distribution may have sections that look like bell curves, but it isn't normally distributed. You can take a look at this paper by Du et al. [1] for details about the statistics of $$\beta$$ values.
That said, the distribution of all $$\beta$$ values from an array or bisulfite sequencing (or some other DNA methylation assay) should be bimodal with modes at 0 and 1. Nearly all CpGs in the human genome are methylated or unmethylated. There may be some hemi-methylated sites, but for the 450K array you mentioned, there should be few of these.
It sounds like you might be looking at some residual value, or some other value from the analysis in the paper for dataset $$b$$ other than $$\beta$$. Could you be looking at $$M$$ values, or something else?