Experiments are conducted to examine neutron emissions associated with electrolysis of 3 M LiOD in heavy water with a palladium electrode. The data show evidence of an increase in the number of neutrons detected during heavy water electrolysis relative to light water background experiments. No anomalous heat, tritium, or helium is detected. A rigorous statistical analysis is used to describe the distribution of both the neutron burst size and burst rate, each of which is characterized by a single parameter. The background neutron emission can be characterized by a burst size of 2 and a burst rate of 0.123 s−1, although some variability is observed. Analysis establishes the statistical significance of increased neutron emission during foreground (heavy water) runs, even when background variability is taken into account. In one case, the neutron emission is characterized by large but infrequent bursts. In the other case, only the burst rate increases to 0.203 s−1. Although the data are limited, the need for careful statistical analysis and the importance of experimental design are shown.