Many statistical methods commonly used in neuroscience are invalid, and can lead to incorrect conclusions inferred with high levels of statistical significance. This is because traditional methods assume independence of samples, which is not the case for neurophysiological signals with slow continuous trends over time. I will discuss how to spot this problem of “nonsense correlations”, and describe a suite of statistical tests that can be validly used with slowly-drifting neurophysiological data. I will also discuss how to design behavioral paradigms that allow a wider range of valid tests for analysis of brain recordings.