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When testing for over or underdispersion in a count variable there is a test (available for example in the glm.nb() function in the MASS package in R) that yields an $\alpha$ statistic, which is the inverse of a $\theta$ statistic, and with $\alpha$ < 1 indicating underdispersion and $\alpha$ > indicating overdispersion. I would like to report this statistic when justifying my decision to use either poisson or negative binomial regression. Does this test or the $\alpha$ statistic itself have a name?

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