### Abstract

A question subject to intense debate is whether scalp-recorded event-related brain potentials are due to phase resetting of the ongoing electroencephalogram (EEG) or rather to the superimposition of time-locked components on background activity. The two hypotheses are usually assessed by means of statistics in the time-frequency domain, for example, through wavelet transformation of multiple EEG trials that yield for each time and frequency a scatter plot of complex values coefficients. Currently, intertrial phase correlation (phase locking or phase coherence) is taken as evidence for phase resetting at a given frequency and latency. Here we present a formal analysis using a complex t-statistic to illustrate that such measures are, in effect, tests for the mean vector of the repeated trials, and as such on their own are inappropriate measures of phase resetting. We also propose simple t-like statistics for testing changes in (i) the mean (presence of an event-related potential), (ii) the amplitude variance (presence of (de)synchronization) and (iii) the concentration of phases (phase locking). The first two statistics are found to be proper measures of the presence of a non-zero mean activity and induced activity, respectively. In the third case, two different tests are introduced: one based on measuring the alignment of coefficients in the complex plane and another derived from the argument that phase locking persists when the mean of the coefficients is removed. Both statistics gave unambiguous evidence of the presence of phase locking suggesting that they constitute promising tools in the analysis of event-related brain dynamics.

Language | English |
---|---|

Pages | 2922-2947 |

Number of pages | 26 |

Journal | Statistics in Medicine |

Volume | 27 |

Issue number | 15 |

DOIs | |

Publication status | Published - 10 Jul 2008 |

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### Keywords

- Complex statistics
- EEG
- Event related brain dynamics
- Intertrial coherence
- Local FDR
- Phase locking

### Cite this

*Statistics in Medicine*,

*27*(15), 2922-2947. https://doi.org/10.1002/sim.3132

}

*Statistics in Medicine*, vol. 27, no. 15, pp. 2922-2947. https://doi.org/10.1002/sim.3132

**Exploring event-related brain dynamics with tests on complex valued time-frequency representations.** / Martínez-Montes, Eduardo; Cuspineda-Bravo, Elena R.; El-Deredy, Wael; Sánchez-Bornot, José M.; Lage-Castellanos, Agustín; Valdés-Sosa, Pedro A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Exploring event-related brain dynamics with tests on complex valued time-frequency representations

AU - Martínez-Montes, Eduardo

AU - Cuspineda-Bravo, Elena R.

AU - El-Deredy, Wael

AU - Sánchez-Bornot, José M.

AU - Lage-Castellanos, Agustín

AU - Valdés-Sosa, Pedro A.

PY - 2008/7/10

Y1 - 2008/7/10

N2 - A question subject to intense debate is whether scalp-recorded event-related brain potentials are due to phase resetting of the ongoing electroencephalogram (EEG) or rather to the superimposition of time-locked components on background activity. The two hypotheses are usually assessed by means of statistics in the time-frequency domain, for example, through wavelet transformation of multiple EEG trials that yield for each time and frequency a scatter plot of complex values coefficients. Currently, intertrial phase correlation (phase locking or phase coherence) is taken as evidence for phase resetting at a given frequency and latency. Here we present a formal analysis using a complex t-statistic to illustrate that such measures are, in effect, tests for the mean vector of the repeated trials, and as such on their own are inappropriate measures of phase resetting. We also propose simple t-like statistics for testing changes in (i) the mean (presence of an event-related potential), (ii) the amplitude variance (presence of (de)synchronization) and (iii) the concentration of phases (phase locking). The first two statistics are found to be proper measures of the presence of a non-zero mean activity and induced activity, respectively. In the third case, two different tests are introduced: one based on measuring the alignment of coefficients in the complex plane and another derived from the argument that phase locking persists when the mean of the coefficients is removed. Both statistics gave unambiguous evidence of the presence of phase locking suggesting that they constitute promising tools in the analysis of event-related brain dynamics.

AB - A question subject to intense debate is whether scalp-recorded event-related brain potentials are due to phase resetting of the ongoing electroencephalogram (EEG) or rather to the superimposition of time-locked components on background activity. The two hypotheses are usually assessed by means of statistics in the time-frequency domain, for example, through wavelet transformation of multiple EEG trials that yield for each time and frequency a scatter plot of complex values coefficients. Currently, intertrial phase correlation (phase locking or phase coherence) is taken as evidence for phase resetting at a given frequency and latency. Here we present a formal analysis using a complex t-statistic to illustrate that such measures are, in effect, tests for the mean vector of the repeated trials, and as such on their own are inappropriate measures of phase resetting. We also propose simple t-like statistics for testing changes in (i) the mean (presence of an event-related potential), (ii) the amplitude variance (presence of (de)synchronization) and (iii) the concentration of phases (phase locking). The first two statistics are found to be proper measures of the presence of a non-zero mean activity and induced activity, respectively. In the third case, two different tests are introduced: one based on measuring the alignment of coefficients in the complex plane and another derived from the argument that phase locking persists when the mean of the coefficients is removed. Both statistics gave unambiguous evidence of the presence of phase locking suggesting that they constitute promising tools in the analysis of event-related brain dynamics.

KW - Complex statistics

KW - EEG

KW - Event related brain dynamics

KW - Intertrial coherence

KW - Local FDR

KW - Phase locking

UR - http://www.scopus.com/inward/record.url?scp=47249106107&partnerID=8YFLogxK

U2 - 10.1002/sim.3132

DO - 10.1002/sim.3132

M3 - Article

VL - 27

SP - 2922

EP - 2947

JO - Statistics in Medicine

T2 - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 15

ER -