Spectral change or Jensen gap? Log-ratio baseline correction for time-frequency M/EEG is negatively biased

We recommend against the "log-ratio" baseline correction method for time-frequency M/EEG analysis in which trial spectral is divided by baseline spectral power and then log-transformed. Though this approach has several desirable properties and is ubiquitously available in popular software tools, the concavity of the logarithm function means that, per Jensen's inequality, it negatively biases estimates of spectral change. We demonstrate this bias mathematically and using both simulated and real data. Because of this bias, the log-ratio correction can incorrectly yield opposite findings from other baseline corrections. We show that an alternative method, based on mean-subtraction baseline correction of log-transformed data, preserves the advantages of the log-ratio correction without introducing bias. We describe how this unbiased method can be implemented in a range of software tools.