An important characterization of neural spiking is the ratio of the variance to the mean of the spike counts in a set of intervals--the Fano factor. For a Poisson process, the theoretical Fano factor is exactly one. For simulated or experimental neural data, the sample Fano factor is never exactly one, but often appears close to one. In this short communication, we characterize the distribution of the Fano factor for a Poisson process, allowing us to compute probability bounds and perform hypothesis tests on the distribution of recorded neural spike counts. We show that for a Poisson process the Fano factor asymptotically follows a gamma distribution with dependence on the number of observations of spike counts, and that convergence to this asymptotic distribution is fast. The analysis provides a simple method to determine how close to 1 the computed Fano factor should be and to formally test whether the observed variability in the spiking is likely to arise in data generated by a Poisson process.
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