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 $T^2$ and a variant called $T^2_{circ}$. A novel test of the assumptions of $T^2_{circ}$ 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 $T^2_{circ}$ statistic is then extended to multi-level designs, resulting in a new statistical test termed $ANOVA^2_{circ}$. This has identical assumptions to $T^2_{circ}$, 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.
翻译:神经科学的许多实验模式涉及以定期感官刺激的方式驱动神经系统。 使用各种技术记录的神经信号随后将包含刺激频率的振动。 对这些数据的分析通常包含标准的单向统计, 如T- 测试, 在 Freier 振幅部件上进行( 示光阶段), 测试信号的存在, 或者比较不同条件的信号。 然而, 这些测试的假设有时会被违反, 因为振幅通常不会分布, 如果放弃阶段信息, 可能会丢失更多的微弱信号 。 另一种办法是使用真实和想象的 Fourier 元件进行多变统计测试 。 在这里, T- 测试的两个多变化扩展的功能性统计 : Hotalling $T+2 $2 ⁇ circ} 和一个名为 $T2 的变异变体 。 根据数据的状况指数, 正在开发一个假设 $T+2 rc} 的假设, 新的振动性测试的平方根值比值的平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平方平。