Using GAMMs to model trial-by-trial fluctuations in experimental data: More risks but hardly any benefit

•We compared two modeling approaches applied to data with by-trial fluctuations.•Linear Mixed-Effects Models (LMEMs) did not show excess false positive rates.•Generalized Additive Mixed Models (GAMMs) impaired between-subject power.•Randomization is sufficient defense against by-trial noise in experimental datasets.