We provide both theoretical and computational improvements to the analysis of synaptic transmission data. Theoretically, we demonstrate the correlation structure of observations within evoked postsynaptic potentials (EPSP) are consistent with multiple random draws from a common autoregressive moving-average (ARMA) process of order (2, 2). We use this observation and standard time series results to construct a statistical hypothesis testing procedure for determining whether a given trace is an EPSP. Computationally, we implement this method in R, a freeware statistical language, which reduces the amount of time required for the investigator to classify traces into EPSPs or non-EPSPs and eliminates investigator subjectivity from this classification. In addition, we provide a computational method for calculating common functionals of EPSPs (peak amplitude, decay rate, etc.). The methodology is freely available over the internet. The automated procedure to index the quantal characteristics greatly facilitates determining if any one or multiple parameters are changing due to experimental conditions. In our experience, the software reduces the time required to perform these analyses from hours to minutes.