# Is binomial dispersion the same as binomial distribution?

I have been asked by a client to write a program in R which calculates the "binomial dispersion test." I have not found anything for this, but I have found that you can calculate the binomial distribution.

Are they the same thing? I suspect they are.

The binomial distribution is a probability distribution describing the results of a series Bernoulli trials with a specified size and probability of success. The classic example is describing the probability that a dice roll will return 6 if I roll the dice some number of times (say, 10). Knowing $Pr(6)$ allows one to describe the range of outcomes and the probability of each.
Here, dispersion is the concept underlying the term-of-art variance. This is important because the binomial distribution specifies a particular variance given the parameters (specifically, $np(1-p)$ for size $n$ and probability of success $p$). A sample with dispersion sufficiently far from its theoretical value under the assumption that it is drawn from a binomial distribution may be evidence that the distributional assumption is not met.