A shot noiseX(t) is a superposition of impulses occurring at timestj, where theTjfollow a Poisson point process. For the case of a rectangular impulse function (height a, length b) the cumulant generating function of the sample meanM(T), (2), is obtained, also the mean and variance of the sample varianceV(T), (3). This, together with the covariance ofVandM, is used to calculate the standard error of the coefficient of dispersionV/M. An approximate distribution is conjectured forI(T) =V(T)/aM(T) and based on it, percentage points of this statistic are given. They could be used to test the hypothesis that a given noise is shot noise. An application to a textile problem is described.