Weakly modulated spike trains: significance, precision, and correction for sample size

Many single-unit electrophysiological studies of visual cortex have investigated strong evoked responses to simple stimuli such as oriented gratings. Experiments involving other types of stimuli, such as natural scenes, higher-order features, and surface brightness, produce single-unit responses that are more difficult to interpret. Experiments with brightness, in particular, evoke single-unit responses that are typically weakly modulated. When the brightness is generated by a visual illusion such as the Cornsweet illusion, statistical tests are often necessary to distinguish true responses from baseline fluctuations. Here, using data collected from cat Areas 17 and 18 in response to real and illusory brightness stimuli, we provide a method for detecting and quantifying weak but significant periodic responses. By randomizing spike trains (via bootstrap methods), we provide confidence levels for response significance, permitting the evaluation of both weak and strong responses. We show that because of a strong dependence on total spike number, response significance can only be appropriately determined with randomized spike trains of similar spike number. Such randomizations can be performed for both stimulus-elicited and spontaneously occurring spike trains. By developing a method for generating randomized modulated spike trains (phase-restricted randomization) from actual recordings, we calculate upper and lower confidence limits of modulated spike trains and describe how measurement precision varies as a function of total spike count. Finally, using this randomization method, we describe how a correction function can be determined to correct for measurement bias introduced at low spike counts. These methods may also be useful in the study of small but potentially significant responses in other systems.