Statistical limits for detecting change in the cumulative sum derivative of the peristimulus time histogram

The peristimulus time histogram (psth) provides a means of correlating the discharges of neurones with other events. The cumulative sum (cusum) derived from the psth facilitates the detection of small changes in the psth that may be obscured by random fluctuations in counts. The cusum integrates differences from the mean control level of counts in the psth. Any signal in the data that is related to the stimulus appears as a slope in the cusum. Psth's constructed from the rhythmic discharges of single neurones are shown to contain periodical fluctuations in counts that arise from refractoriness. This periodicity results in a cusum which deviates less from the horizontal line than predicted from a Poisson distribution of points. The more regular the spike train, i.e., the lower the coefficient of variation of the distribution of interspike intervals, the flatter is the cusum. The theory of stochastic point processes is used to derive an algorithm for calculating the best approximation of variance of the cusum. Significance limits set at 3 standard deviations of the cusum are shown to provide a good fit to cusums for unit discharges over a wide range of coefficients of variation (0.09-0.60).