Detector effects on the statistics of neutron fluctuations are studied in this paper. The problem is formulated in a general way, thereby making it applicable in principle to a large variety of systems. As an illustration of these effects, however, expressions are obtained for the power spectral density and the cross power spectral density assuming gas-filled BF3 ionization chambers as detectors. The results show the anticipated break frequencies at the inverse of the average ion and electron collection times. Furthermore, the dependence of these detector break frequencies on chamber parameters such as density, temperature, and bias voltage is qualitatively revealed.