A standard error is any standard deviation of any statistical parameter, thus while we have looked at the standard error of the mean, there exists standard errors of the variance and of coefficients of skew, kurtosis and dispersion. These standard errors are used to place confidence in these particular values. Of these standard errors, one deserves particular mention- the standard error of the Coefficient of Dispersion.
The coefficient of dispersion can be used as a rapid check to see if data are distributed in a Poisson or Binomial fashion. We have seen that Poisson data tend to have a coefficient equal to unity while those data that are binomilally distributed have a coefficient less than one. Thus by attaching a standard error to this coefficient we may examine the significance of any divergence from unity. the standard error of the coefficient of dispersion depends entirely on the sample size (n):