During searches for periodicity in very high energy (VHE) gamma ray data, the freedom usually exists to place a trial period anywhere within the spacing between independent periods normally associated with a Fourier transform of data of finite duration. The problem has been previously addressed by Monte Carlo techniques, which are limited by the demands of computing time to small data sets and signal strengths. This letter provides an analytical technique for calculating the oversampling factor for any data set size and any statistical test. The method is illustrated using the Rayleigh statistic, which is widely used in testing for periodicity