Answers.Body: <p><span class="math-container">$\beta$</span> values are the ratio of methylated to unmethylated probe intensities.
  This means that <span class="math-container">$\beta \in [0, 1]$</span>, 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 <em>et al.</em> [1] for details about the statistics of <span class="math-container">$\beta$</span> values.</p>
  <p>That said, the distribution of all <span class="math-container">$\beta$</span> 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.</p>
  <p>It sounds like you might be looking at some residual value, or some other value from the analysis in the paper for dataset <span class="math-container">$b$</span> other than <span class="math-container">$\beta$</span>.
  Could you be looking at <span class="math-container">$M$</span> values, or something else?</p>
  <p>[1]: <a href="https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-11-587" rel="nofollow noreferrer">Du <em>et al.</em>, BMC Bioinformatics, 2010</a></p>
  
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Answers.UserDisplayName: James Hawley
Answers.Body: <p>It's not clear from your question what the statistical design of the experiment is, so I can't judge whether or not a distribution around 0.5 would be expected from the residuals after fitting.</p>
  <p>Given that dataset <em>a</em> looks like what you expect, I'd be inclined to use that (and perhaps ask the person who gave you this data why dataset <em>b</em> looks so different, and why it ended up with a 0.5 mean).</p>
  
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Answers.UserDisplayName: gringer
Body: <p>I am trying to incorporate Methylation data (Illumina 450K) into my pipeline. I was provided with two versions of the same data: one (dataset <span class="math-container">$a$</span>) normalized with ComBat and the other (dataset <span class="math-container">$b$</span>) 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:</p>
  <ul>
  <li>The values for dataset <span class="math-container">$a$</span> have a typical bimodal distribution with peaks at around <span class="math-container">$0$</span> and <span class="math-container">$1$</span></li>
  <li>The values for dataset <span class="math-container">$b$</span> are roughly normally distributed with the mean at around <span class="math-container">$0.5$</span>.</li>
  </ul>
  <p>I am not that familiar with Methylation data, so maybe this is expected. Is it? I did not find any paper showing similar results.</p>
  
Tags: <methylation><multi-omics><combat>
Title: Methylation data: beta values are normally distributed
ThreadText: # Methylation data: beta values are normally distributed
  
  (Asked by: username_0 on 2021-12-10)
  
  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.
  
  **Tags:** methylation, multi-omics, combat
  
  
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  ## 2 answers
  
  ### Answer by username_1 on 2022-09-09. Score: 2
  
  $\beta$ 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?
  
  [1]: [Du *et al.*, BMC Bioinformatics, 2010](https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-11-587)
  
  
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  ### Answer by username_2 on 2021-12-12. Score: 0
  
  It's not clear from your question what the statistical design of the experiment is, so I can't judge whether or not a distribution around 0.5 would be expected from the residuals after fitting.
  
  Given that dataset *a* looks like what you expect, I'd be inclined to use that (and perhaps ask the person who gave you this data why dataset *b* looks so different, and why it ended up with a 0.5 mean).
  
  
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