神经科学周期性数据的统计分析

D. Baker
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引用次数: 5

摘要

神经科学中的许多实验范例都涉及到用周期性的感觉刺激来驱动神经系统。使用各种技术记录的神经信号将包括刺激频率下的锁相振荡。对这些数据的分析通常涉及标准的单变量统计,如t检验,对傅里叶振幅分量(忽略相位)进行检验,要么检验信号的存在,要么比较不同条件下的信号。然而,这些测试的假设有时会被违反,因为振幅不是正态分布,而且如果丢弃相位信息,可能会错过弱信号。另一种方法是使用实和虚傅立叶分量进行多元统计检验。这里比较了T检验的两种多元扩展的性能:Hotelling的$T^2$和一个称为$T^2_{circ}$的变体。基于数据的条件指数(边界椭圆特征值之比的平方根),提出了一种新的T^2_{circ}$假设检验方法,并提出了一种利用马氏距离排除异常值的启发式方法。然后将$T^2_{circ}$统计量扩展到多级设计,从而产生一个新的统计检验,称为$ANOVA^2_{circ}$。它具有与$T^2_{circ}$相同的假设,并且在满足这些假设时被证明比方差分析更敏感。对两个公开可用的经验数据集演示了这些测试的使用,并建议了选择运行哪个测试的实用指导。这些新工具的实现以R包和Matlab工具箱的形式提供,希望它们的广泛采用将提高涉及周期性数据的统计推断的灵敏度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Statistical analysis of periodic data in neuroscience
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.
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