The application of Fourier deconvolution to reaction time data: a cautionary note

Area of Science:

• Cognitive Psychology
• Psychometrics
• Mathematical Psychology

Background:

• The Fourier transform method, combined with frequency domain smoothing, is a proposed technique for analyzing serial, additive reaction time models.
• Evaluating the robustness and sensitivity of this method to violations of serial model assumptions is crucial for its reliable application.

Purpose of the Study:

• To assess the robustness of the Fourier transform method when assumptions of the serial reaction time model are violated.
• To determine if the method can detect the use of an incorrect distribution in recovering unobserved components.

Main Methods:

• The study employed the Fourier transform method with frequency domain smoothing.
• Simulations involved recovering unobserved components using both correct and incorrect distributional assumptions.

Main Results:

• When an incorrect distribution was used, the method provided no indication of the error.
• Results obtained with incorrect distributions were as interpretable as those with correct distributions.
• The deconvolution results did not reveal violations of underlying assumptions or confirm component origins.

Conclusions:

• The Fourier transform method's deconvolution results cannot be used to assess the validity of its underlying assumptions.
• The method is incapable of verifying whether a recovered component truly originates from a serial combination.
• Researchers must be cautious about the interpretability and limitations of this method in reaction time modeling.