Testing for effects of different stimuli on neuronal firing relative to background activity

Objective. Statistical testing for effects of stimuli on the responses of large populations of recorded neurons is a key technique for analyzing data generated using multi-channel recording systems. Combining statistical tests for differences of the responses to different stimuli and tests for changes from background firing, while appealing as apparently focusing analysis on neurons which react to the stimuli, can lead to significant overestimates of the magnitudes of the effects of stimulation or even erroneous identification of responses as being statistically significant. Approach. As this type of combination is common in the neurophysiological literature, we derive a non-parametric hypothesis test for changes of responses to different types of stimuli relative to background firing. Main results. This test can be used to avoid improperly combining two statistical tests. We also model the overestimation of effects of stimulus type that can be observed in typical single-unit recordings when applying two statistical tests sequentially. Significance. Over-estimation of the fraction of neurons with a response can range up to 1800% in plausible recording scenarios. The method of testing derived here avoids this type of error.