Abstract
Many experimental paradigms in neuroscience involve driving the nervous system with periodic sensory stimuli. Neural signals recorded using a variety of techniques will then include phase-locked oscillations at the stimulation frequency. The analysis of such data often involves standard univariate statistics such as T-tests, conducted on the Fourier amplitude components (ignoring phase), either to test for the presence of a signal, or to compare signals across different conditions. However, the assumptions of these tests will sometimes be violated because amplitudes are not normally distributed, and furthermore weak signals might be missed if the phase information is discarded. An alternative approach is to conduct multivariate statistical tests using the real and imaginary Fourier components. Here the performance of two multivariate extensions of the T-test are compared: Hotelling’s T2 and a variant called Tcirc2. A novel test of the assumptions of Tcirc2 is developed, based on the condition index of the data (the square root of the ratio of eigenvalues of a bounding ellipse), and a heuristic for excluding outliers using the Mahalanobis distance is proposed. The Tcirc2 statistic is then extended to multi-level designs, resulting in a new statistical test termed ANOVAcirc2. This has identical assumptions to Tcirc2, and is shown to be more sensitive than MANOVA when these assumptions are met. The use of these tests is demonstrated for two publicly available empirical data sets, and practical guidance is suggested for choosing which test to run. Implementations of these novel tools are provided as an R package and a Matlab toolbox, in the hope that their wider adoption will improve the sensitivity of statistical inferences involving periodic data.
Highlights
Baker, D.H.A widely used approach in many branches of neuroscience is to drive the nervous system using periodic stimuli
The Tc2i r c statistic makes the strong assumption that the dependent variables are uncorrelated and have equal variance
One possible remedy to control the Type I error rate would be to adjust either the α level or the degrees of freedom. This will reduce the statistical power of the Tc2i r c test, and its advantage over T 2 is relatively marginal in most situations to begin with
Summary
Many experimental paradigms in neuroscience involve driving the nervous system with periodic sensory stimuli. Neural signals recorded using a variety of techniques will include phase-locked oscillations at the stimulation frequency The analysis of such data often involves standard univariate statistics such as T-tests, conducted on the Fourier amplitude components (ignoring phase), either to test for the presence of a signal, or to compare signals across different conditions. This has identical assumptions to Tc2i r c , and is shown to be more sensitive than MANOVA when these assumptions are met The use of these tests is demonstrated for two publicly available empirical data sets, and practical guidance is suggested for choosing which test to run. Implementations of these novel tools are provided as an R package and a Matlab toolbox, in the hope that their wider adoption will improve the sensitivity of statistical inferences involving periodic data. Behavior, Data Analysis and Theory 2021; 5(3): 1-18 https://nbdt.scholasticahq.com/
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