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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.

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Based on the discussion in this link, it would appear that the binomial dispersion test assesses whether the dispersion of the data is substantially divergent from what we would expect of a binomial distribution. The binomial distribution and binomial dispersion test are not the same, but are clearly related, since the former assesses a feature of data which may have been drawn from the latter.

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.

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  • $\begingroup$ +1. In addition to correctly noting that they "are not the same", it might be helpful for the OP (or future readers) if you explain what they are. $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 17, 2013 at 15:34
  • $\begingroup$ @gung That's a good point. Elaboration added. $\endgroup$
    – Sycorax ♦
    Commented Sep 17, 2013 at 15:47
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    $\begingroup$ Thanks, @DJE. You might also note that dispersion here is essentially a synonym for variance & that this issue is important because the binomial distribution necessitates a specific value for the variance as a function of the mean. Thus a value of sample dispersion that is sufficiently far from the theoretically appropriate value indicates that the distributional assumptions made by your inferential tests may not be met & hence their validity is in question. $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 17, 2013 at 16:04
  • $\begingroup$ That seems like a complete & very informative answer for the OP. $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 18, 2013 at 14:35

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