Sources of bias in single-trial normalization procedures

Abstract

Baseline normalization procedures are essential for the analysis of brain activity. These use statistics of a reference (baseline) period to normalize data along the entire trial (baseline and stimulus periods). A very popular procedure is pseudo z-scoring, traditionally applied to time-frequency spectral power estimates, where it was recently shown to generate positive bias. Bias was thought to arise because of outliers stemming from the skewed distribution of spectral power values. Here we challenge this view and causally show that bias originates from a more general problem that affects a wide array of normalization techniques, including some that are routinely used. We show that bias is caused by the division of correlated terms and that it depends directly on the sign and magnitude of correlation between the numerator and denominator. Correlation emerges either from the properties of the data being normalized or from the properties of the normalization method. z-scoring produces bias when source data have a skewed distribution but it is bias-free when the distribution is symmetric, while methods such as dF/F for fluorescence data lead to bias because the numerator and denominator are inherently correlated. We provide a simple, fast and general solution to reduce and even eliminate bias by welding (fusing) baseline periods of multiple trials into a single, large baseline. This method is generic, can be used to normalize individual trials and provides bias-free estimates given a long enough extended baseline. We show that baseline fusing is superior to more complex techniques that have been proposed before.

Keywords: coherence; dF/F; percentage technique; time-frequency spectra; z-scoring.