dispersion of a gene, what does it mean?

Question

[tonja.r]

In all RNA-seq analysis applications they talk about the dispersion of a gene. As far as I understood, it is not a variance of the normalized counts for a given gene. It is somehow much more complicated.

DESeq defines the dispersion as follows:


But what would a dispersion of 0.19 or a dispersion of 0.80 tell me? Can I still interpret it as a variance of a gene?

[sunhanice]

In my understanding, you can. From the definition of dispersion,

In statistics, dispersion (also called variability, scatter, or spread) denotes how stretched or squeezed a distribution (theoretical or that underlying a statistical sample) is. Common examples of measures of statistical dispersion are the variance, standard deviation and interquartile range.

[tonja.r]

That is a definition from wikipedia, however I am not sure that the authors really mean raw variance as we understand it when they talk about the dispersion

Answer 1

[Gordon Smyth]

https://support.bioconductor.org/p/75260/

Answer 2

[David Westergaard]

The dispersion is sometimes a synonym for the variance, but not in this case. DESeq assumaes a negative binomial distribution, which has two parameters: mean and dispersion. The dispersion is a parameter describing how much the variance deviates from the mean. The Poission distribution is sometimes said to be a special case of the NB distribution, when dispersion=1 and thereby mean = variance.

So to answer your question: no, the dispersion is not the variance of your gene. It's correlated but it cannot be translated exactly.

You can read more about this on https://en.wikipedia.org/wiki/Negative_binomial_distribution

[ED]

Wouldn't the dispersion be 0 for the mean = variance in that special case of the NB distibution that is the poisson distribution?